Studies on radiobiological parameters relevant to ... - CiteSeerX

I

Aus der Abteilung für Strahlentherapie und Radioonkologie (Direktor: Prof. Dr. Winfried Alberti) der Radiologischen Klinik des Universitätskrankenhauses Hamburg-Eppendorf

Studies on radiobiological parameters relevant to quantitative radiation oncology

Habilitationsschrift zur Erlangung der venia legendi für das Fach Biophysik und Strahlenbiologie vorgelegt dem Fachbereich Medizin der Universität Hamburg von Hans-Hermann Dubben

Hamburg, 1999

II

One cannot build another level of useful information without having a solid ground to build on. Gilbert H. Fletcher, 1988.

III

1.

Introduction

1 7

1.1.

The Ellis formula

1.2. 1.2.1 1.2.2.

The linear-quadratic model Fractionation Tumor control probability

13 14 18

1.3. 1.3.1. 1.3.2. 1.3.3. 1.3.4.

Extensions of the linear-quadratic model Linear-quadratic model with time-factor The time interval and incomplete repair Consequential late damage Hypersensitivity

19 19 21 21 22

1.4. 1.4.1. 1.4.2. 1.4.3. 1.4.4.

Predictions of the linear-quadratic model Total dose Number of clonogenic tumor cells Dose per fraction Duration of treatment

23 23 24 25 29

1.5. 1.5.1. 1.5.2.

Check of the linear-quadratic model Quality assurance and Evidence Based Medicine Aim of this study

30 30 33

2.

Materials and Methods

35

2.1.

Identification of trials

35

2.2.

Assessment criteria of clinical studies

35

2.3.

Metaanalysis and odds ratios

36

3.

Results

39

3.1. 3.1.1. 3.1.2. 3.1.3. 3.1.4. 3.1.5.

Tumour volume Theoretical background Experimental data Clinical data Discussion Conclusion

39 40 41 42 45 46

3.2. 3.2.1.

The dose per fraction in hyperfractionated radiotherapy Experimental evidence for sparing of late reactions by hyperfractionation Response of experimental tumors to hyperfractionation

47 47

3.2.2.

48

IV

3.2.3. 3.2.3.1. 3.2.3.2. 3.2.3.2.a 3.2.3.2.b 3.2.3.2.c 3.2.3.3. 3.2.3.4. 3.2.3.5. 3.2.3.6. 3.2.4.

Clinical studies Historical results Head and neck cancer Non-randomized studies Controlled randomized trials Randomized trials without control arm Non-small-cell lung cancer Malignant gliomas Bladder cancer The role of time interval between daily fractions Conclusion

52 52 52 52 55 64 66 70 74 74 75

3.3. 3.3.1. 3.3.2. 3.3.3. 3.3.4. 3.3.4.1. 3.3.4.2. 3.3.4.3. 3.3.4.4. 3.3.4.5. 3.3.5. 3.3.6. 3.3.7.

Treatment duration I: Split course radiotherapy Introduction Arguments for and against split-course treatment Identification of trials Clinical results from randomized split-course trials Tumors of the head and neck Tumors of lung and bronchus Tumors of the pelvis Tumors of the esophagus Synopsis Clinical results from non-randomized split-course studies Time dependence of clinical results Conclusion

77 77 78 79 79 79 83 86 90 90 91 96 97

3.4.

99

3.4.1. 3.4.2. 3.4.3. 3.4.4.

Treatment duration II: Tumor control dose TCD50 and dose-time prescription Introduction Carcinoma of the head and neck Carcinoma of the urinary bladder Conclusion

99 101 107 109

3.5. 3.5.1. 3.5.2. 3.5.3. 3.5.4. 3.5.5. 3.5.6.

Hyperfractionated accelerated radiotherapy CHART trial: Tumors of the head and neck CHART trial: Non-small-cell lung cancer EORTC 22851 trial: Tumors of the head and neck EORTC 22811 trial: Tumors of the head and neck Pure acceleration: Tumors of the head and neck Discussion and Conclusion

111 111 114 115 117 118 118

V

4.

Discussion

121

4.1.

Statistical power and isoeffects

121

4.2. 4.2.1. 4.2.1.1. 4.2.1.2. 4.2.2. 4.2.2.1. 4.2.2.2. 4.2.2.3.

Derivation of radiobiologic parameters from clinical data Fractionation The α/β-ratio Fractionation exponents of the Ellis formula Duration of treatment The time factor (γ/α-ratio) The time factor and tumor control dose TCD50 The time factor as a possible consequence of the Ellis formula

125 125 126 129 132 132 134 137

4.3. 4.3.1. 4.3.2. 4.3.3. 4.3.3.1. 4.3.3.2.

Tumor volume in study design Statistical power and heterogeneity Tumor volume and study power Tumor volume and prediction of tumor control rate Tumor volume and prediction using the surviving fraction SF2 Volume and prediction using potential doubling time Tpot

139 139 140 142 144 146

4.4.

General discussion

149

5.

Summary

157

6.

References

161

Acknowledgments

185

1

1.

Introduction

Cancer is the second-frequent cause of death in industrial nations. Currently about one of five of their citizens will be treated for cancer with ionizing radiation during lifetime. Within the European Union approximately 1.2 million new cases of cancer are diagnosed each year and about 45% of the patients will be cured from their cancer (Overgaard & Bartelink 1995, Thwaites et al. 1995). Cancer therapy is based on surgery, radiotherapy and chemotherapy (cf. DeVita 1997, Hellman 1997, Rosenberg 1997). Out of 100 cancer patients, presently 22 are cured by surgery. Eighteen are cured by radiotherapy, alone or in combination with other interventions but with radiotherapy as the main treatment, and 5 by chemotherapy, alone or, more frequently, combined with other modalities (Thwaites et al. 1995). This indicates that most cancer patients are cured by locoregional rather than systemic interventions. With increasing efforts towards screening and early diagnosis it is expected that an increasing number of patients will have cancers that are suitable for locoregional treatment. Therefore it is anticipated that the number of radiotherapy patients will further increase in the future. In Germany, the total number of deaths was 883,000 in 1996. Of these, 212,200 people (24%) died from malignant neoplasms (Statistisches Bundesamt 1998). The incidence of new diseases is, although varying between entities, estimated to be higher than mortality by a factor of about 1.5 to 2 (Brady et al. 1990). About half of all patients with malignant tumors are being irradiated during the course of their disease, either with curative or palliative intention (Thwaites et al. 1995, Perez & Brady 1997). Thus in Germany about 185,000 patients annually are treated with radiotherapy. Radiotherapy has a history of more than 100 years. Only a few months after Röntgen's discovery of the X-rays in 1895, attempts were made to use this new radiation for medical therapy. One of the first documented uses was by the dermatologist Freund in 1896 who irradiated a hairy naevus for epilation. First cures of skin cancer were reported by Stenbeck (1900) and Sjögren (1901; cf. Thames & Hendry 1988). In 1914, Schwarz suggested that single doses would be less effective because there would be a better chance for multiple exposures to hit cells in more radiosensitive phases. Krönig and Friedrich (1918) showed that the dose necessary to produce the same skin reaction had to be increased when multiple fractions were used instead of one. Regaud and Ferroux (1927) demonstrated experimentally that a ram can be sterilized by irradiation without skin damage to the scrotum when the dose is fractionated. Skin damage cannot be avoided when single doses are given. They concluded that cells in different physiological states differed in mitotic activity and response to fractionated irradiation. Assuming that cell multiplication in the

2

1. INTRODUCTION

testis could serve as a model for tumors, a therapeutic benefit was proposed for fractionated treatment. By 1934, Coutard had developed a protracted, fractionated scheme on head and neck cancers. This was established by varying the total dose in such a way that a certain skin reaction, an intense moist desquamation, was not exceeded. He established the first treatment technique with external Röntgen irradiation capable of lasting cures of deepseated tumors using one or two low-dose-rate fractions per day, extended over at least two weeks, and longer for larger tumors. Currently one daily fraction of 1.8 to 2 Gy, 5 times per week, over 6 to 7 weeks is regarded as standard or conventional fractionation schedule (cf. surveys: Dische 1993, Fletcher 1988, Thames & Hendry 1987, Thames 1992, Willers 1994). The first dose response data were reported for skin cancer by Miescher in 1934. Using this data and data on the formation of teleangiectasia, Holthusen (1936) constructed the first radiation dose response curves (Fig.1.1). For both tumor and normal tissue a characteristic sigmoid relationship was observed. Holthusen interpreted the shape as expression of an underlying distribution of radiosensitivities and concluded that for statistical reasons only observations of large samples of patients but not case-reports will contribute to radiotherapeutic progress: "... dann kann aber die Frage nach den Aussichten der Strahlentherapie ... nur durch eine statistische Betrachtung gefördert werden, nicht aber durch die kasuistische Betrachtung von Einzelfällen." Meanwhile it is axiomatic in radiation therapy that higher doses of irradiation produce better tumor control and higher rates of normal tissue reactions. The central objective of

100 Teleangiektasienbildung (%)

Heilung nach 1 Bestrahlung (%)

100

80

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40

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0

80

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0 0

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Dosis in Sabouraud-Volldosen

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1000 2000 3000 4000 5000 6000 7000 Dosis (r)

Fig.1.1: Tumor control rate after single dose exposure (left). Formation of teleangiectasia (right) after fractionated radiotherapy with 280 to 300 r per fraction. Redrawn from Holthusen 1934.

H.-H. DUBBEN: STUDIES ON RADIOBIOLOGICAL PARAMETERS RELEVANT TO QUANTITATIVE RADIATION ONCOLOGY

3

optimizing radiotherapy is therefore to obtain a differential effect of radiation on tumor and normal tissue. Numerous dose response curves for a variety of tumors and normal tissues have been published (cf. Bentzen 1994), though with a large variability in steepness from one study to another. Inspired by the clinical dose response relationship (Fig.1.1), Holthusen (1936) was the first to formulate the idea of optimizing the tumor dose applied (Fig.1.2). At low doses virtually no tumor is controlled. Above a threshold dose tumor control probability Pcontrol increases with dose. Theoretically, at sufficiently high doses, 100% tumor control rate may be achieved. Yet with increasing dose the probability to induce intolerable normal tissue complications increases as well. Assuming independent processes, the probability to achieve tumor control without complications can be calculated:

(

Puncomplicated control = Pcontrol × 1 − Pcomplication

)

This relationship is depicted in Fig.1.2. After a threshold dose, the probability for uncomplicated control increases with dose, reaches a maximum and declines again with further dose escalation. For a given radiotherapy schedule a therapeutic benefit in terms of uncomplicated control rate can be obtained by exploring the optimum dose, though in the clinical setting the ac-

1.0

1.0

tumor control

0.8

0.8

complications

Probability

Probability

tumor control normal tissue complications uncomplicated tumor control

0.6

0.4

0.2

0.6

0.4

0.2

0.0

uncomplicated tumor control

0.0 0

0 Tumor dose

Tumor dose

Fig.1.2: Probability for tumor control and normal tissue complications as a function of irradiation dose (redrawn from Holthusen 1936). The abscissa shows the dose given to the tumor. Physical irradiation planning allows to apply a higher dose to the tumor than to adjacent normal tissues. This is in general the reason why the curve for complications is located to the right from the tumor curve. It must not be concluded from the figure that tumor cells are more radiosensitive to irradiation than normal cells. Right panel: By exploiting radiobiological differences in the response of tumor and normal tissue the rate of uncomplicated tumor control may, in principle, be enhanced.

4

1. INTRODUCTION

cepted optimum also depends on ethical and forensic considerations. The schematic drawings in Fig.1.2 might suggest that tumors are more sensitive than normal tissue because at a given dose the tumor effect appears to be higher. This, however, is mainly due to physical treatment planning that allows to apply a higher dose to the tumor while adjacent normal tissues receive lower doses. The objective of optimizing radiotherapy is not limited to defining the optimum; much more important is to enhance the optimum further. Therefore, a major field of research in radiooncology is the exploration of irradiation schedules that are supposed to exploit radiobiological differences between tumor and normal tissue. This would yield further separation of the curves of tumor control and normal tissue complication and, thus, lead to a higher maximum for the uncomplicated control rate (right panel of Fig.1.2). In the past 30 years great efforts have been made to apply radiobiological concepts to design safer and more effective therapeutic strategies. Withers (1975a) suggested four basic mechanisms that contribute to the diverse reactions of different tissues to irradiation: redistribution of cells in the cell cycle, reoxygenation of hypoxic cells in the tumor, repair of cellular radiation damage, and repopulation of surviving cells during radiotherapy treatment. These are nowadays known as the "4 R's of Radiotherapy". Redistribution The radiosensitivity of cells varies considerably when they transit through the cell cycle (cf. Hall, 1994; Thames and Hendry, 1987). Radiation-induced partial synchrony is a consequence from selective killing of cells in a sensitive phase of the cell cycle as well as by progression delay in late G2-phase. Cells surviving irradiation are preferentially those which were in relatively resistant phases. During fractionated radiotherapy, redistribution of surviving cells within the mitotic cycle results in self-sensitization of proliferating cell populations. This process, however, only affects cells that divide frequently during the 4 to 8 weeks commonly taken to administer a course of curative radiotherapy, but there is little or no such an effect in slowly or non-proliferating tissues. Assuming a proliferating tumor surrounded by non-proliferating normal tissue, small doses per fraction and time intervals sufficient for redistribution, should result in an improved therapeutic differential (Elkind & Sinclair 1965). Reoxygenation In 1909, Schwarz observed different radiation effects depending on whether a radium applicator was loosely attached or tightly pressed onto the skin during irradiation. In the latter case the reaction was less and Schwarz hypothesized that reduced metabolism, due to reduced blood flow under the applicator, rendered cells more radioresistant. In 1953, Gray et al. (1953) reported that the presence of oxygen during irradiation considerably modifies


5

radiation effects. Hypoxic cells are about 2.5 to 3.0 times more resistant to X-irradiation than euoxic cells. In tumors, hypoxic cells arise because of imbalances between the rate of production of new cells and the vascularization of the tumor. The distance to which oxygen can diffuse from a blood vessel into the tumor is limited by the rate at which it is metabolized by respiring tumor cells. Cells are well oxygenated to a distance of about 100 µm from a capillary (cf. Brammer et al. 1979, Hall 1993). This will of course vary from the arterial to the venous end of a capillary. At greater distances partial oxygen pressure is so low that cells die and later become necrotic. At intermediate distances, the oxygen concentration is high enough to keep cells viable but at the same time low enough to increase their resistance to X-rays. These chronically hypoxic cells might limit radiocurability of the tumor. Irradiation preferentially sterilizes cells that are adequately oxygenated. This becomes obvious when a mixed population is irradiated. A biphasic dose response curve results (Powers and Tolmach 1964) which is steep at low doses but shallower at higher doses due to preferential survival of the more resistant hypoxic cells. Between fractions hypoxic cells may be reoxygenated (Kallman & Bleehen 1968; Kitakabu et al. 1991), which increases radiocurability of the tumor. There had been many attempts to overcome hypoxia by specific radiosensitizers, by improving oxygenation pharmacologically or by irradiation under hyperbaric oxygen pressure or by breathing carbogen ( cf. Dische 1991; Overgaard & Horsman 1993). In addition to chronic hypoxia it has been suggested that tumor blood vessels may open and close periodically, leading to transient or acute hypoxia. Repair The influence of repair of molecular injury on cell survival and the response of tissue to irradiation can be inferred from in vitro survival curves and from changes in the total dose required to produce a certain level of injury as a function of changes in dose per fraction, i.e. from isoeffect curves. Fractionation responses can be modeled in terms of two types of radiation-induced cellular injury, one resulting in a logarithmic decline in target cell survival that is linear with dose and another in which the decline increases proportionally to the square of the dose d (linear-quadratic model or LQ-model): ln( fraction of surviving cells)= −α × d − β × d 2 where α and β are tissue specific coefficients for the two types of injury. The linear component is assumed to reflect cell kill from a single molecular event, while the quadratic component might be due to two independent so-called sublethal events that have to interact to become lethal for the cell. Sublethal events may be repaired with half-times in the order of 20 minutes to some hours (Joiner 1993a). If a dose is split into two fractions with a time interval of several hours then a substantial portion of sublethal damage induced by the first fraction is already repaired when the second fraction is given. Thus the likelihood for interaction of two sublethal damages is diminished, resulting in less cell kill due to the

6

1. INTRODUCTION

quadratic component as compared to the same dose given in a single session (Elkind & Sutton 1960). Thus not only total dose but also the number of fractions or the dose per fraction, respectively, determine the magnitude of the radiation effect. Details of the linearquadratic model will be described later in detail. Repopulation Early reacting tissues like skin and mucosa counteract cell depletion by repopulation, usually after a delay that depends on the degree of denudation (Denekamp 1973; Dörr & Kummermehr 1990). Cells in late reacting tissues proliferate very slowly if at all. It has been concluded therefore that prolongation of treatment time might spare acute normal tissue damage but not late reactions (Thames et al. 1982; Fowler 1984). Proliferation of surviving tumor cells during treatment is frequently considered to be one of the main factors that determine the outcome of fractionated radiotherapy (Ang 1997b; Bentzen 1994; Horiot 1997; textbooks: Hall 1994; Perez & Brady 1997; Scherer & Sack 1996, Steel 1993). An increase in the number of viable tumor cells between fractions or during treatment interruptions is assumed to result in a failure to control the tumor. In an unperturbed tumor, cell number increases approximately exponentially with time. It was therefore concluded that irradiation treatment should be performed in as short a time as possible (Withers et al. 1988; Fowler & Lindstrom 1992). All investigations on repopulation during a continuous fractionated irradiation treatment share the problem that direct measurement of repopulation after irradiation is still impossible. Only functional endpoints can be used to indirectly quantify the effect. If reduced local tumor control rates are observed after a prolongation of overall treatment time without introduction of gaps, this observation is arbitrarily attributed to repopulation. However, repopulation is only one possible explanation among many others. Other mechanisms may also have contributed to the observed effects, e.g. hypoxia, heterogeneity, prescription habits, etc. If other mechanisms are neglected the contribution of repopulation might be overestimated (Beck-Bornholdt & Dubben 1992). To assess the clinical impact and evidence of these radiobiologic phenomena as well as of treatment and patient characteristics quantitative methods are desirable. The main task of quantitative clinical radiobiology is therefore to describe the biologic response of human normal tissues and tumors to doses of ionizing radiation in the range of normally employed radiotherapy. Useful information has been gained from retrospective, descriptive studies and from controlled clinical trials. These studies, however, provide only limited insight into biological mechanisms. To improve our understanding of clinical radiobiology, mathematical modeling techniques have been used since several decades. A prerequisite of


7

this approach is the assumption that a quantitative relationship exists between the response to irradiation on one hand and patient and treatment characteristics on the other. In the 1930s consensus was reached that fractionated radiotherapy was, in terms of therapeutic benefit, superior to single irradiations (Fletcher 1988). Consequently, total dose, the dose per fraction or the number of fractions, the overall treatment time and the time interval between fractions became fundamental parameters characterizing any radiotherapy schedule.

1.1.

The Ellis formula

Many researchers attempted to link the total dose that is required to achieve an isoeffect after different treatment times in a purely mathematical way (cf. Thames & Hendry 1987; Willers 1994). A very early basis of these considerations dates back to 1862, which is long before discovery of X-rays in 1895. The Bunsen-Roscoe law I × T = constant stated that the product of light-intensity (I) and exposure time (T) will yield a constant effect in a photochemical process. In 1899 Schwarzschild modified this formula to I × Tq = constant

(Schwarzschild law)

by introducing a parameter q which depends on the given photochemical material and which was smaller than 1. Intensity of light (I) is defined as amount of light (D) divided by exposure time (T), i.e. I = D/T. Replacing intensity I in the Schwarzschild law yields (D/T) × Tq = constant, which is equivalent to Tq-1 × D = constant and can be rearranged to D = constant × T1-q Since q < 1 and 1-q > 0, this formula indicates that for a given isoeffect in total more light is required when exposure time is extended, suggesting some kind of recovery in the exposed photographic material. In the context with radiation exposure of patients, Holthusen (1933) believed that the reduced effectiveness of a radiation dose when applied at a reduced dose rate could be

8

1. INTRODUCTION

adequately described by the Schwarzschild law. In a survey of clinical and experimental data, Liechti (1929) presented evidence for a dose rate effect and values of q less than 1 (and >0) were found. Thus, power-law models, i.e models with the mathematical form y = xz, were introduced because of the analogy between the reduced effectiveness of an exposure to light at lower intensity and the reduced biological effectiveness of a radiation dose applied at lower dose rate. These models predicted a linear relationship between the logarithm of the isoeffective dose and the logarithm of exposure time. Strandqvist (1944) plotted recurrences and complications in patients irradiated for basal and squamous cell carcinomas of the skin and lip as a function of total dose and treatment time. He also documented delayed wound healing and skin necrosis. In 91 patients treated between 1933 and 1937, 15 recurrences and 14 complications were observed. It should be noted that these are rather small numbers and that only one patient's treatment exceeded 14 days. Strandqvist's idea was to establish in a dose-time scattergram an exclusion line that would lie below most of the complications and above most of the recurrences. In a doublelogarithmic plot of total dose versus overall treatment time he drew a straight exclusion line with an exponent of 0.22. Mathematically Strandqvist related the total dose D to overall treatment time T as: D = constant × T0.22 The power law of Strandqvist is identical with the Schwarzschild law supplied with a specific exponent. The difference to the latter is that T is the time between the first and the last session of a fractionated treatment rather than duration of a continuous exposure to light or irradiation. A problem was to place single dose treatments on a logarithmic time scale which has no zero. Strandqvist decided to assign arbitrarily a single dose treatment to an overall treatment time of 0.35 days. With this convention he obtained a slope (or recovery exponent) of 0.22 for the exclusion line (Thames & Hendry 1987). Using the same plot as Strandqvist, Cohen (1949) compared data of normal skin response and recurrences of skin cancer. He followed Strandqvist's convention and assigned a duration of 0.35 days to a single dose treatment for the tumors which also resulted in a recovery exponent of 0.22. For the skin reactions, however, he assigned a treatment time of one day to the single dose treatment. This lead to a higher recovery exponent of 0.33 for normal tissue. The difference of the exponents for tumor and normal tissues was regarded as real and it became widely accepted that recovery occurred more efficiently in normal skin than in squamous cell tumors. If the same convention for "time zero" had been used for tumor and skin data, there would have been no noticeable difference between the two exponents. In other words, the alleged differences between tumor and normal tissue was an artifact. This was clearly pointed out by Liversage as early as in 1971.


9

In 1959, Scanlon stated that " one of the most challenging aspects of radiation therapy today is time-dose effect ... ". The aspect seemed to be solved already in 1963 when THE SYMPOSIUM ON PROTRACTION AND FRACTIONATION came to the consensus that "… there appears to be little doubt that sufficient prolongation of the overall treatment time is the most important factor from the point of view of preservation of normal tissue … . It appears that by prolonging the overall treatment time to more than 6 weeks we can avoid almost all undesirable damage … and in this way eliminate most of the late sequelae of radiation therapy. … it becomes increasingly certain that such prolonged treatment does not significantly alter the possibility of controlling the tumor … . … the prolongation of overall treatment time is one of the most important factors for increasing the differential between effect on the tumor and effect on the vasculo-connective tissue" (Buschke 1963). In 1969 Ellis published a paper with the title "Dose, time and fractionation: a clinical hypothesis". Ellis was inspired by Strandqvist's and Cohen's studies and by experimental data reported by Fowler et al. (1963a) showing that, at least for a range of overall treatment times, the number of dose fractions was more important than time in itself. He changed the Strandqvist law to: D = NSD × N0.24 where NSD (called 'nominal standard dose') is a constant and time T is replaced by the number of fractions N with the argument that usually one fraction per day was given. Nevertheless the original exponent of 0.22 was modified to 0.24 to allow for treatment schedules employing only 5 fractions per week. Ellis suggested that this formula was valid for tumors and that overall treatment time has no impact on tumor control by radiotherapy. He reasoned (Ellis 1969): "Malignant cells are not susceptible to homeostatic control as are normal cells. … We know that some tumours are hormone sensitive to some extent. Inso-far as they are sensitive to hormones they are not behaving like malignant cells. Homeostatic factors depend on time. … ". In other words, malignant cells are not susceptible to time by definition, and if they are susceptible they are not malignant (Bentzen & Overgaard 1993a, Thames & Hendry 1987). Furthermore, Ellis (1969) assumed that the exponent of N is the same for tumors and normal tissues and that the difference of the exponents 0.33 - 0.22 = 0.11 found by Cohen (1949) reflects the impact of treatment time on normal tissues. Thus, Ellis proposed that for normal tissue tolerance the total dose D was related to the number of fractions N and overall treatment time T by: D = NSD × N0.24 × T0.11

.

The merit of Ellis' approach is the separation of treatment time and fractionation. However, there were some similar attempts in earlier years. The importance of dose per fraction was already pointed out by Reisner (1933) and Miescher (1935). Their results failed to reach appropriate attention and Strandqvist (1944) failed to consider them in his famous

10

1. INTRODUCTION

publication which put emphasis on total dose and treatment duration as determinants of both tumor response and normal tissue damage (cf. Willers and Beck-Bornholdt 1996). Curiously Ellis's reinterpretation of the Strandqvist formula, i.e. replacement of time T by number of fractions N, is a rediscovery of fractionation. Nevertheless, several severe points of criticism may be raised with the Ellis model. Firstly, it is based on only very few data. Secondly, the assumption that tumors do not proliferate appears inconsiderate. The paradigm of the 80s and 90s is, on the contrary, that tumor cells proliferate even accelerated during radiotherapy (Hermens & Barendsen 1969; Withers 1988; cf. Perez & Brady 1997). Thirdly, the exponent of T is an artifact due to an inconsistent convention for the time scale for tumor and normal tissue data. A mathematical consequence of the power law by Ellis is that recovery should be fastest at start of treatment and decrease continuously thereafter, as indicated by the decreasing slope of the calculated curve in Fig.1.3. In fact, the Ellis model fails to fit radiobiological data which indicate that compensatory proliferation begins only after a certain time lag, then becomes faster, and finally returns to pre-treatment values (Denekamp 1973; Thames and Hendry 1987; Withers & McBride 1998).

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Notwithstanding almost immediate severe criticism (Liversage 1971) the formalism of Strandqvist and Ellis had profound influence on radiotherapy practice in many institutions

40

Treatment time T (days)

Fig.1.3: Normal tissue reaction and treatment time: Ellis formula and experimental results. Data from Denekamp (1973). The solid curve was calculated from D = 1700×300.24 ×T0.11. The value NSD = 1700 ret does not result from a fit but was arbitrarily chosen from the range of doses suggested by Ellis. Other values would not affect the general shape and position of the curve. The point of the comparison here is that the mathematical form of the Ellis formula cannot reasonably fit the more s-shaped experimental curve.


11

throughout the world in the 1970s and 1980s. This world wide impact is demonstrated by dose-time prescription data from 59 radiotherapy centers (data from Withers et al. 1988) which are plotted in Fig.1.4. The lines are fitted to the data using the Ellis formulae for tumor and normal tissue, respectively. Assuming that 5 fractions were administered per week, the number of fractions N was replaced by treatment time T using N = 5/7 × T. With the dose conversion 1 rad = 0.01 Gy the Ellis formula now looks Dose [Gy] = 0.01 [Gy/ret] × NSDnormal tissue [ret]× (5/7 × T)0.24 × T0.11 for normal tissue and Dose [Gy] = 0.01 [Gy/ret] × NSDtumor [ret] ×

(5/7 × T)0.24

for tumor. The calculated lines (Fig.1.4) and the nominal standard doses resulting from the fit indicate good congruence between actual prescription and the Ellis model. The mean NSD values proposed by Ellis (1969) were NSDtumor = 2900 ret (range 2510 to 3290 ret) and NSDnormal tissue = 1960 ret (range 1670 to 2220 ret). The fit yielded NSDtumor = 2825 ret (95% c.i.: 2770 .. 2880), NSDnormal tissue = 1880 ret (1841 .. 1921)). In addition, as a result of a nationwide fractionation survey, Hendry and Roberts (1991) reported that radiotherapeutic prescriptions in the United Kingdom are in good agreement with the Ellis formula.

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70 60 50 tumor normal tissue

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Treatment time (days) Fig.1.4: Dose-time prescription for treatment of head and neck tumors. Data from Withers et al. (1988). The lines are a fit of the Ellis formulae for tumor and normal tissue, respectively.

The Ellis model implies that both the rate of tumor control and of normal tissue complications are equally dependent on fractionation. Thus with reduced total dose and less fractions, i.e. with less total work, the same therapeutic result should be achievable. "The second assumption, that A (the exponent of N) is a constant … for all tissues, implies that

12

1. INTRODUCTION

the therapeutic ratio is independent of the number of fractions used in a given overall time. This is a particularly dangerous assumption. There are social and economic benefits to be gained by treating patients in, say, six fractions in six weeks, but more evidence is needed before we can forecast which patients would suffer and which might benefit by such a drastic change of fractionation." (Liversage 1971). Disregarding the warning of Liversage, the Ellis model was applied in many institutions and produced an abundance of literature reporting severe late complications in schedules with reduced numbers of fractions that were supposed to be isoeffective according to the NSD formalism. In a study by Singh (1978) on cervix carcinoma the number of fractions was changed from 20 to 5 fractions. This had no effect on early reactions (33% in both schedules) but radiotherapy with five large fractions resulted in a significant increase in late sequelae from 33% to 83% (p=0.001). Singh's results revealed that the Ellis formula underestimates the incidence of late sequelae after large doses per fraction. Overgaard et al. (1987) found by comparison of allegedly isoeffective schedules with two and five weekly fractions in postmastectomy irradiation that the NSD concept is unsuitable to predict either acute lung reaction, or late effects in skin, subcutaneous tissue, lung or bone. A number of variations of the NSD formula have been developed. The Cumulative Radiation Effect (CRE) of Kirk et al. (1971) was a simple rearrangement of the NSD formula. Orton and Ellis 1973 introduced the TDF factors (Time-Dose-Fractionation), mainly to facilitate the use of the NSD concept. Since these formulae are based on the NSD formula, criticism of the NSD concept applies to these variations as well.


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1.2.

The linear-quadratic model

One of the most important contributions of radiation biology to the understanding of radiation effects has been the theoretical description of cell kill as a function of increasing dose, as well as the demonstration of repair of sublethal or potentially lethal damage (Puck & Marcus 1956; Elkind & Sinclair 1965; Elkind 1990). During the 1980s the linear-quadratic model (also named LQ-model or α/β-model) has gained wide acceptance (Douglas & Fowler 1976; Barendsen 1982; Thames et al. 1982; Fowler 1984) as a mathematical description of biological response to irradiation. It is mainly used for the calculation of treatment parameters of schedules supposed to be isoeffective. The LQ model is considered a key concept in modern radiobiology. In 1956 Puck and Marcus reported the first in vitro survival curve of mammalian cells. A quantitative system available to relate absorbed dose with surviving fraction of cells, promised great strides towards better understanding the effect of ionizing radiation on biological materials. A characteristic relationship between single radiation doses and effect in terms of the logarithm of the fraction of surviving cells in vitro is depicted in Fig.1.5. In general, the data do not lie on a straight line. The simplest adequate mathematical description of these data is provided by a linear-quadratic function: ln( SF ) = −α × d − β × d 2 or

SF = e −α × d − β × d

2

(SF: surviving fraction of cells; d: dose) It is assumed that the biological effect of radiation is based on modification of DNAmolecules in the cell nucleus. The underlying molecular mechanisms are not yet entirely understood but there is a hypothesis considering two types of radiation damage that is helpful for understanding. The first type of damage, responsible for the linear component, is assumed to result from a single event. This damage is lethal for the cell if it is not or insufficiently repaired. The probability to produce such a damage is proportional to dose, i.e. = α × d , while its probability to be repaired insufficiently is assumed to be dose independent within the range of clinically relevant doses. The second type of damage, responsible for the quadratic component, is by itself not lethal for the cell. It is a so-called sublethal damage. Only the combination of two such lesions can yield a lethal event for the cell. The probability to produce a single sublethal damage is again proportional to dose. The probability to produce two of such lesions is proportional to the square of dose, i.e. = β × d 2 . Again the probability of insufficient repair is assumed to be dose independent

14

1. INTRODUCTION

Surviving fraction

10 0

10 -1

10 -2

10 -3 0

2

4

6

8

Dose (Gy)

Fig.1.5: Surviving fraction of tumor cells (rhabdomyosarcoma R1H of the rat) after irradiation in vitro as a function of dose. The curve is a fit to the data using the linear-quadratic model with α = 0.091 Gy-1 and β = 0.074 Gy-2 (redrawn from Raabe 1991).

within the range of clinically relevant doses. If a certain dose is given in two or more fractions sublethal damages can be repaired between fractions. This reduces the probability of sublethal lesions to interact leading to a lethal event. Consequently, if a certain total dose is partitioned into more and more fractions the observed biological effect should decrease.

1.2.1.

Fractionation

The surviving fraction after n doses of size d is the product of the surviving fractions after every individual dose. If every dose fraction has the same effect the resulting surviving fraction is SFn, i.e.

[

SF n = e −α ×d − β × d

2

]

n

= e −α × n × d − β × n × d

2

The total effect is then given by total effect = ln( SF n ) = n × ln( SF ) = −α × n × d − β × n × d 2

This yields with D = n × d (D: total dose, d: dose per fraction)

total effect = n × ln( SF ) = −α × D − β × d × D This equation indicates that the total effect depends on both total dose D and dose per fraction d. The assumption that every dose fraction has the same effect means that for n fractions the initial part of the survival curve is repeated n-fold (Fig.1.6). As a


15

consequence, for the same total dose different total effects are achievable depending on the dose per fraction used. For a fractionated irradiation schedule with constant dose per fraction this may be simplified: ln( SF ) = −α × D − β × d × D = −(α + β × d ) × D = −α eff × D The effective radiosensitivity α eff = α + β × d is the slope of the effective dose response relation (dashed lines in Fig.1.6).

Surviving fraction of cells

10 0

10 -1

10 -2

4× 2 Gy

10 -3

2× 4 Gy

10 -4

10 -5

1× 8 Gy 0

2

4

6

8

Dose (Gy)

Fig.1.6: Schematic presentation of an in vitro dose response curve. The total dose of 8 Gy can be given in a single fraction (dotted curve) or in several fractions: here 2× 4 Gy per fraction or 4× 2 Gy per fraction. Cell survival is higher with fractionated doses and increases with decreasing dose per fraction. The effective dose response relationship of a fractionated regimen is linear (dashed lines).

Fig.1.7 shows the results of an experiment in which a measure of a functional damage in mouse kidney is plotted against the total dose given in schedules employing 1 to 64 fractions. The total doses for a certain effect (dashed line) can be read off from the graphs. The reciprocal of these doses is plotted versus the corresponding dose per fraction in Fig.1.8. In good approximation, the data fall on a straight line.

16

14 12 10 8 6 1

4

2

4

8

16

32

64

2

51

Cr EDTA % per ml blood

1. INTRODUCTION

0 0

20

40

60

80

Total radiation dose (Gy)

Fig.1.7: Renal damage measured by an increase in isotope retention. Irradiation was administered in 1 to 64 fractions as indicated. With number of fractions total doses required for a given isoeffect (dashed line) increase from about 18 to 65 Gy. Redrawn from Stewart et al. 1984b.

The linearity between reciprocal total dose and dose per fraction is predicted by the linearquadratic model. Provided that the radiation response of a complex tissue or organ (in terms of the degree of moist desquamation or reduced organ function) correlates with the surviving fraction of a target cell population, it may be written Biological effect = E = − n × ln( SF ) = α × D + β × d × D

Eq.1.1

From this can be deduced

1 α β = + ×d D E E

Eq.1.2

Consequentially, plotting the reciprocal of total dose 1/D versus dose per fraction d should yield a straight line like in Fig.1.8 with slope β/E and intercept α/E.

0.07

-1

1/Isodose (Gy )

0.06 0.05 0.04 0.03 0.02 0.01 0.00 -5 -3

0

5

10

15

20

Dose per fraction (Gy)

Fig.1.8: Plot of the reciprocal total dose versus dose per fraction using the data that are marked by the dashed line in Fig.1.7.


17

The last equation (Eq.1.2) can be rearranged to read E =α + β × d D

,

For D → ∞ follows E D → 0 , and with this

α +β ×d =0 and

d=−

α β

This means that the value of α/β, which is of central importance in the LQ formalism, can be read off from the intercept of the straight line with the abscissa (Fig.1.8). For two isoeffective radiotherapy regimen (i.e. E1 = E2), Eq.1.1 yields

α × D1 + β × d 1 × D1 = α × D2 + β × d 2 × D2

.

From this relationship two important equations can be derived (cf. Thames & Hendry 1987; Steel 1993). Eq.1.3 is used to determine α/β-ratios from isoeffective treatments

α

β=

d 2 D2 − d1 D1 D1 − D2

Eq.1.3

Eq.1.4 is frequently used to calculated from total dose D1 and dose per fraction d1 of a standard treatment the doses D2 and d2 of a new isoeffective radiotherapy schedule

D2 =

α α

+ d1 × D1 β + d2 β

Eq.1.4

Equations 1.3 and 1.4 are intensively discussed in section 4.2.1.1. It should be noted at this point that the LQ formalism was derived from curved in vitro dose response relationships of cells and that it is now applied to the radiation response of a complex tissue in vivo. This implies the idea that the functional changes of an organ, that in general is a composite of different cell types, can be traced back to either the depletion of a certain target cell population or to the destruction of functional units. Such a tissue rescuing unit (TRU) is a hypothetical element capable of independently rescuing the tissue from failure. Further assumptions are: independent survival of TRUs, a random distribution of TRUs and that the linear-quadratic model describes TRU survival (Hendry & Thames 1986). The surviving fraction SF is then identical with the fraction of intact TRUs. For the use of TRUs in the linear-quadratic formalism, it is not a prerequisite to identify TRUs as a certain anatomical structure. In this context, definition of TRUs is purely operational and does not change the formalism.

18

1. INTRODUCTION

The postulated approximately linear relation between dose per fraction d and reciprocal total dose (Fig.1.8) show that these experimental observations are consistent with the linear-quadratic model.

1.2.2.

Tumor control probability

In curative radiotherapy it is of primary interest whether or not a tumor is controlled by a certain radiation dose. For the surviving fraction of tumor cells after total dose D of fraction size d follows from Eq.1.1 SF = e −α × D− β × d × D The surviving fraction SF can be perceived as the probability of a single cell to survive irradiation with total dose D and dose per fraction d. The probability that the cell is inactivated is given by ( 1 − SF ) . The probability that Nc clonogenic tumor cells are N inactivated simultaneously is given by (1 − SF ) c . Thus the probability Pcontrol that a tumor

containing Nc clonogenic tumor cells is inactivated, i.e. controlled, is given by

Pcontrol = (1 − e −α × D− β ×d × D )

Nc

Eq.1.5

Tumor control probability can be calculated from total dose D and dose per fraction d when the tumor related parameters α, β and Nc are known. Fig.1.9 shows this relationship for different values of Nc . The exact equation (Eq.1.5) can be approximated1 by

Pcontrol = e [

− N c ×e − α × D − β × d × D

]

Eq.1.6

The term in brackets [] in Eq.1.6 is equal to the number of cells surviving at the end of irradiation with doses D and d, and, according to Poisson statistics, the expression P = e − N resembles the probability of a certain tumor to contain no viable cell, i.e. to be controlled, with N being the mean number of clonogenic tumor cells per tumor. That tumor control probability follows Poisson statistics was first assumed by Munro & Gilbert (1961), several years before the linear-quadratic model was developed.

1

The first two terms of the Taylor series of the e-function are

x = e −αD− βdD yields 1 − e −αD − βdD ≅ e − e

[1 − e

]

− αD − βdD N c

[

≅ e

− e − αD − βdD

]

Nc

=e

− αD − βdD

e − x ≅ 1 − x . Substitution of x by

. With this the above approximation is obtained:

− N c × e − αD − βdD

.


19


1.0

0.8

1 2 10

106

100 1000

109

0.6

0.4

0.2

0.0 0

20

40

60

80

Dose (Gy)

Fig.1.9: Dose response relationship for tumors containing different numbers of clonogenic cells at begin of treatment (Nc is 1, 2, 10, 100, 1000, 106, and 109, respectively). With increasing cell number more dose is required to reach a given control probability.

The approximation (Eq.1.6) yields practically the same results as the exact formula. It is sometimes easier to handle mathematically and requires less computer precision. The exact formula Eq.1.5 and the approximation Eq.1.6 diverge considerably at very small cell numbers, which frequently occur in evaluation of heterogeneous data.

1.3.

Extensions of the linear-quadratic model

1.3.1.

Linear-quadratic model with time-factor

If tumor cell proliferation is exponential then the increase of cell number with time T is given by N c = N 0 × e γ ×T The factor γ is related to cell doubling time TD by γ = ln( 2) / TD . N0 is the number of clonogenic tumor cells at time T=0. If tumor cells proliferate during the course of fractionated irradiation then tumor control probability will be diminished. This can be accounted for by replacing Nc in the approximated Eq.1.6:

Pcontrol = e − N0 ×e which can be rewritten as

γ ×T

×e− α × D − β ×d × D

20

1. INTRODUCTION

Pcontrol = e − N0 ×e

− α × D − β × d × D +γ × T

Eq.1.7

The same equation is supposed to hold also for the probability of normal tissue complications Pcomplication (Travis & Tucker 1987; Turesson 1989; Turesson & Thames 1989; van Dyk et al. 1989):

Pcomplication = e − N0 ×e

− α × D − β × d × D +γ × T

Eq.1.8

N0 denotes the initial number of tissue rescuing units (TRUs). Eq.1.8 implies that the remaining number of TRUs determines the clinical normal tissue response. More clearly, it is assumed that the probability to produce a certain complication (characterized by α,β, and γ) is related to the number of TRUs remaining after a certain irradiation schedule (described by D, d, and T) by the equation

Pcomplication = e −( number of TRUs at end of treatment )

.

Different doses and treatment times can yield the same probability P for an event (tumor control or complication). Rearrangement of Eq.1.7 (or Eq.1.8) yields ln P = − N 0 × e −α × D − β × d × D +γ × T ln( − ln P ) = ln N 0 − α × D − β × d × D + γ × T D × (α + β × d ) = γ × T + ln N 0 − ln( − ln P )

D=

ln N 0 − ln(− ln P ) γ ×T − α +β ×d α +β ×d

D=

γ ln P ×T − α eff α eff

or

The dose necessary to achieve a tumor control rate P increases linearly with time when tumors proliferate exponentially at a constant rate during treatment. The dose increment per day is given by γ/α(eff). The ratio γ/α(eff) is frequently interpreted as dose lost per additional day when treatment is prolonged (Thames et al. 1990; Bentzen 1993).


21

1.3.2.

The time interval between fractions and incomplete repair

A prerequisite for the validity of the described linear-quadratic formalism is that sublethal damage caused by one fraction is completely repaired before the next fraction is applied. This requires that consecutive dose fractions are separated by a sufficiently long time interval. Usually a minimum interval of 6 hours is recommended (Hall 1994; Sack 1996; Herrmann & Baumann 1997; Perez & Brady 1997). It should be noted that this is a consensus based on a number of assumptions some of which are not yet proven beyond any doubt. Repair of sublethal damage is exponential with time (cf. Dikomey 1986, 1993). Therefore, repair is never complete theoretically. Nevertheless it may be sufficient if the repair halftime is short compared to 6 hours. Experimental half-time values given in the literature (Thames & Hendry 1987; Joiner 1993a; van der Kogel & Ruifrok 1993) range from 0.3 to 2.5 hours which would yield 0.0001 % to 19% residual damage after 6 hours of repair. In addition there are exceptions (skin, spinal cord) which seem to have a second component of repair the half-time of which is almost 4 hours. In general, incomplete repair (with one component) can be described mathematically using the so-called incomplete-repair model (Thames 1985; cf. Thames & Hendry 1987). This model requires repair half time data. However, the precision of presently available experimental half-time data is poor and their transferability to the clinical situation is questionable. For tumor cells, in vivo and in vitro, it has been shown that during time intervals of 1 to 6 hours and 1 to 10 hours, respectively, repair of sublethal damage is superimposed and partially counteracted by some other effects, probably cell cycle effects and/or reoxygenation (Kleineidam et al. 1994; Willers et al. 1997).

1.3.3.

Consequential late damage

Chronic damage of normal tissues such as ulceration and scarring may also occur after very severe early reactions (Baumann 1997; Dubray & Thames 1994; Langberg et al. 1994, 1996; Peters et al. 1988). If an area is completely depopulated of epithelial stem cells, a chronic mucosal or skin ulceration results, and healing depends on migration of epithelial cells from the periphery of the denuded area. Additional factors like trauma and infection may worsen the damage. This kind of injury is termed a consequential late effect because it is not directly attributable to radiation injury of the late responding tissue but occurs as a consequence of the severe acute reaction. Therefore the dependence on dose per fraction

22

1. INTRODUCTION

and on treatment duration of consequential late effects is by definition the same as that of acute reactions and differs from that normally associated with late reactions. Examples for consequential late effects in radiotherapy of head and neck cancer are soft tissue necrosis, chronic mucosal ulcers and mandibular osteoradionecrosis. Such injuries have been reported with clinical fractionation schedules in which treatment duration was shortened (Perrachia & Salti 1981; Maciejewski et al. 1996), with the latter suggesting a correlation of acute and late normal tissue damage in some individual patients. This may represent consequential late effects, but other treatment and patient related parameters like intrinsic radiosensitivity or the time interval between fraction might also explain the correlation. To summarize, some late normal tissue damage might be causally related to and a direct consequence of acute reactions. Thus, acute reactions can be dose limiting events.

1.3.4.

Hypersensitivity

Deviations from the predictions of the linear-quadratic model at low doses have been concluded from in vivo experiments with top-up doses and from in vitro using a computerized microscope (Palcic & Jaggi 1986; Marples and Joiner 1993) for precise measurement of cell survival in the low dose, high survival region of the dose response curve (cf. Joiner et al. 1993c; Marples et al. 1997). Greater than expected radiosensitivity to low doses per fraction (hypersensitivity) has been detected in skin (Joiner et al. 1986) and kidney (Joiner & Johns 1988) and is suggested for lung (Parkins & Fowler 1986). In vitro studies (Marples and Joiner 1993, 1995; Lambin et al. 1993, 1996) revealed dose-response curves that fit to a linear-quadratic model over the dose range 2-5 Gy but that deviate significantly in radiosensitivity at doses below 1 Gy from the prediction extrapolated from a linear-quadratic model fitted to the data at higher doses. Fig.1.10 shows hypersensitivity schematically. A possible explanation for this phenomenon is that radioresistance increases continuously when radiation dose is increased from zero to about one Gy; this might be due to the induction of repair (Joiner et al. 1993c). In a simple modification of the linear-quadratic model it is assumed that α decreases with dose:

{

α = α res × 1 + g × e ( − d d ) c

}

where dc represents the dose at which 63% of induction has occurred, αres is the smallest possible value of α and is approximated by α at high doses. g is the amount by which α at low doses is larger than αres at high doses. The surviving fraction is given by

SF = e

{

− α res × 1+ g × e ( − d

dc )

}× d − β × d 2 .


23

1.0

Induced repair model:

Surviving fraction

SF = exp(-α×d - β×d2) α = αres × (1 + g × exp(-d/dc )) αres = 0.3; β = 0.15; g = 6; dc = 0.3

0.1 0

1

2

3

Dose (Gy)

Fig.1.10: Schematic representation of dose-response curves measured in vitro using computerized microscopy (cf. Palcic & Jaggi 1986; Marples & Joiner 1993). Dashed curve: linear-quadratic model; solid curve: linear-quadratic model including induced repair.

The phenomenon of hypersensitivity, however, has only been demonstrated for a few cell lines and tissues. There is no clinical experience by now. For radiotherapy of tumors that are excessively resistant to conventional therapy, so-called ultrafractionation using doses less than 0.7 Gy per fraction has been proposed (Joiner 1998).

1.4.

Predictions of the linear-quadratic model

According to the linear-quadratic formula (Eq.1.7, Eq.1 8) there should be an impact of the initial number of cells or TRUs, total dose, dose per fraction, and treatment time T on the outcome of clinical radiotherapy. Provided the linear-quadratic model is an appropriate description of tumor and normal tissue reaction to irradiation, it should, to be a useful tool in clinical radiotherapy, make possible the design of optimized treatment schedules.

1.4.1.

Total dose

It is axiomatic in radiation therapy that higher doses of irradiation produce better tumor control and higher rates of normal tissue damage. Positive dose response relationships have been demonstrated experimentally (e.g. Baumann et al. 1994; Petersen et al. 1998; cf. Steel 1993) and clinically (Thames et al. 1991; cf. Bentzen 1994; cf. Baumann & Liertz 1995) for a variety of late responding normal tissues and tumors, albeit with considerable

24

1. INTRODUCTION

variation in steepness between studies. The steepness can be quantified as the normalized dose response gradient, which is the increase of response probability, in percentage points, for a 1% increase in total dose (normalized dose response gradient; Brahme 1984). Bentzen (1994) compiled data from radiotherapy of head and neck tumors. The response gradient of which varied from 0.5 to 2.8. That means, a dose escalation by 10% will translate into an increase of 5 to 28% in tumor control rate. Late normal tissue response increases with dose with a response gradient ranging from 1 to 4.8. Similar values were reported by Thames et al. (1992). The steepness of clinical dose response curves is lower than expected from in vitro data and from the linear-quadratic model. This may be understood in terms of population heterogeneity, e.g. differences in intrinsic radiosensitivity, cell number, hypoxic fraction etc. (Thames et al. 1992). Due to heterogeneity modest dose escalation may remain undetected in clinical trials. Apart from the phenomenon of hypersensitivity at very low doses, experimental in vitro and in vivo studies leave little doubt that, other factors being equal, more dose translates into a correspondingly higher biological effect. For the present study it is therefore assumed that there is an underlying dose response relationship on a cellular level that, if it is not detectable on the clinical level, is confounded by other variables. The Holthusen plot (Fig.1.2) illustrates that dose escalation is beneficial up to a certain optimum, and detrimental if dose is further increased. Obviously, to increase tumor dose while the dose to the normal tissue is kept constant or even is reduced is the strategy applied for improving the results of radiotherapy: minimization of normal tissue dose relative to the tumor dose, mainly by improving physical treatment planning.

1.4.2.

Number of clonogenic tumor cells

Assuming other factors being equal, tumors with a higher number of clonogenic cells should have a lower control probability or require a higher total dose for the same rate of control. Tumor control probability according to the linear-quadratic formula (Eq.1.6)

Pcontrol = e

− N c ×e− α × D − β ×d × D

=e

− N c ×e

− α eff × D

is depicted schematically in Fig.1.11. The curve drawn was calculated using the parameters assuming αeff = 0.3 Gy-1 and D = 70 Gy.


25


1.0

0.8

0.6

0.4

0.2

0.0 106

107 108 109 1010 1011 Number of clonogenic tumor cells

Fig.1.11: Tumor control probability as a function of the number of clonogenic tumor cells per tumor. This schematic graph was calculated according to the linear-quadratic model (Eq.1.6) using the parameters αeff = 0.3 Gy-1 and a total dose of D = 70 Gy.

In the clinical setting it is difficult and ethically questionable to monitor cell numbers. Yet a higher number of cells will surely occupy a larger volume and, accordingly, large tumor should contain, on average, more cells then small ones. It is therefore hypothesized here that, as a consequence of the linear-quadratic model, larger tumors should require a higher dose for the same control rate, or that larger tumor are less likely to be controlled with a certain dose than smaller tumors. From Eq.1.6 follows that the dose D necessary to achieve a given tumor control rate P is described by D=

ln N c ln( − ln P ) 1 1 − = × ln( N c ) − × ln( − ln P ) α +β ×d α +β ×d α eff α eff

Thus, there is a linear relationship between dose D and the logarithm of the number of clonogenic tumor cells (ln Nc) at the beginning of treatment. This relationship has been experimentally verified for human tumor cell xenografts (FaDu) growing on nude mice (Baumann et al. 1990).

1.4.3.

Dose per fraction

Formally, according to the linear-quadratic formula, the effect of fractionated irradiation depends on the dose per fraction, with smaller doses being less effective per unit dose than larger ones (Fig.1.12).

26

1. INTRODUCTION

Response probability

1.0

0.8

0.6

0.4

0.2

0.0 0

1

2

3

4


Fig.1.12: Response probability (tumor control or normal tissue reaction) as a function of dose per fraction. This schematic graph was calculated according to the linear-quadratic model (Eq.1.6) using the parameters α= 0.3 Gy-1, β = 0.15 Gy-2, a total dose of D = 70 Gy and a total number of clonogenic tumor cells or tissue rescuing units, respectively, of N0 = 109.

The clinical application of smaller doses per fraction, termed hyperfractionation, has a long history during which it was based on different rationales. The original meaning of the term hyperfractionation is the application of a larger number of smaller fractions than in standard treatment. This originates from the Strandqvist and Ellis formalism (Strandqvist 1944; Ellis 1969). Hyperfractionation is and was based on various radiobiological rationales (Withers 1993): Redistribution of surviving tumor clonogens through the division cycle gave rise to the idea to increase the number of interfraction intervals. This might enhance redistribution and the probability to irradiate more tumor cells in sensitive phases of the cell cycle. Since only a very small fraction of cells proliferates in late reacting normal tissues, a differential radiation effect was expected (Withers 1975, Shukovsky et al. 1976, Withers et al. 1982). Another rationale to administer smaller dose fractions was that the oxygen effect is less pronounced at low doses. Thus, hypoxic tumor cells would be less radioresistant (Powers & Tolmach 1963; Littbrand et al. 1975; Horiot 1991). If there is sufficient reoxygenation between fractions, a small hypoxic tumor subpopulation would have less influence on response to a sequence of small dose fractions as compared to high dose fractions (Withers & Peters 1980). Hypofractionation studies in the 1960s and 1970s revealed poor tolerance of late responding normal tissue to high dose fractions (Horiot et al. 1992). From this, the converse was concluded that smaller-than-standard doses per fraction are better tolerated


27

by late responding tissues but not by acute reacting tissues and tumors. The initial assumption of selective sensitization of the tumor cells by exploiting cell cycle effects and reoxygenation was replaced by assuming a selective increase of normal tissue tolerance with smaller dose fractions. This was formalized by the linear-quadratic model only long after hyperfractionation studies had already been initiated (Withers 1993). The anticipated difference in reaction to dose fractionation between late-responding and early responding tissues and most tumors is now interpreted as a consequence of different shapes of the underlying survival curves of the respective target cells, characterized by different α/βratios (Fowler et al. 1963; Withers et al. 1983; Fowler 1984). Fig.1.13 shows plots of reciprocal total isoeffective dose versus dose per fraction, so-called Fe-plots (Fowler and Stern 1963), of various normal tissue data. The intersections of extrapolated regression lines indicate different α/β-ratios. Smaller α/β-values reflect larger changes of tolerance with changes of dose per fraction. The dose tolerance of late reacting tissues (right panel of Fig.1.13) like spinal cord appear to depend markedly on dose per fraction. This is much less pronounced in acute reacting tissue (left panel). α/β-ratios derived from Fig.1.13 are depicted in Fig.1.14. It appears that acute and late responding tissues have different α/β-values and, consequently, that late responding tissues depend much more on fractionation than acute responding normal tissues.

0.06

1 / isoeffective dose (Gy -1 )

1 / isoeffective dose (Gy -1)

It has been assumed that tumors behave similar to acute reacting normal tissues and, consequently, that tumor control probability depends less on fraction size than late complications. A therapeutic advantage is thought to derive from a more rapid increase in

0.04

0.02

0.06 skin (acute) colon testis jejunum

0.04

spinal cord skin (late) skin (late) lung kidney

0.02

0.00

0.00 -12-10 -8 -6 -4 -2 0 2 4 6 8 10 Dose per fraction (Gy)

-12-10 -8 -6 -4 -2 0 2 4 6 8 10 Dose per fraction (Gy)

Fig.1.13: Reciprocal total isoeffective dose 1/D and dose per fraction d (Fe-Plot). Redrawn according to Thames et al. 1982. Left panel: acute reacting tissue; right panel: late reacting tissue. The lines in the right hand figure are steeper, suggesting a larger sparing effect from reduction of dose per fraction.

28

1. INTRODUCTION

14 12 colon testis jejunum

spinal cord

α /β -ratio (Gy)

skin (acute)

10 8 6 4

skin (late)

2

skin (late)

0

lung kidney

-2 Acute reacting tissue

Late reacting tissue

Fig.1.14: α/β-ratios derived from intersection of regression lines with x-axis in Fig.1.13

tolerance with decreasing dose per fraction for late responding normal tissues than for tumors, thus even allowing to escalate total dose without increasing late complication rates (Thames et al. 1982; Joiner 1993b; Withers 1993; cf. Hall 1994; Perez & Brady 1998). Experimental tumor data on dose fractionation do not unequivocally support this concept. For illustration, experimental data of four different tumors are shown in an Fe-plot (Fig.1.15). Two tumors, the R1H- and the FaDu-tumor are not affected by fraction size, whereas isoeffective total doses for a fibrosarcoma and the GL tumor increase (i.e., their reciprocals decline) with decreasing dose per fraction. Therefore these data suggest that there could be a differential effect which could lead to a therapeutic gain from lower doses per fraction for certain tumors in certain locations, but a benefit cannot be expected in general. Notwithstanding these limitations, it is widely accepted that hyperfractionation permits to improve tumor control rates by increasing the total tumor dose without increasing the risk for late complications (Horiot 1991, 1992, 1993; Withers 1992; Steel 1993; Hall 1994; Sack et al. 1996; Perez & Brady 1998) and that it is possible to determine adequate doses of new hyperfractionation schedules using the linear-quadratic formula, setting out from an approved conventional treatment schedule (e.g. Dubben et al. 1992b). α/β-ratios of many different normal tissues required for this calculation can meanwhile be obtained from tables in the literature (Thames et al. 1982; Fowler 1984; Thames & Hendry 1987; Joiner 1993). It should, however, be noted that there are many data from schedules employing more than 2 Gy per fraction, which indicate that large doses per fraction should be avoided, but there are too few data below 2 Gy for drawing reliable conclusions on the clinical effect


29

FaDu-tumor R1H-tumor GL-tumor fibrosarcoma

Reciprocal isoeffective dose (Gy-1)

0.10

0.08

0.06

0.04

0.02

0.00 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Dose per fraction (Gy)

Fig.1.15: Reciprocal isoeffective total doses applied with different doses per fraction: FaDu and GL (Petersen et al., 1998), fibrosarcoma (Thames et al. 1982) and R1H (Beck-Bornholdt et al 1989).

at clinically relevant doses (Fig.1.13 and Fig.1.15). Human data reveal low α/β-ratios also for some tumors (Thames et al. 1990; Ang et al. 1997). In fact, the data for whole classes of tumors are inadequate for reliable prognostication of the outcome of hyperfractionated radiotherapy (Thames et al. 1990; cf. Table 4.1 in Withers 1993). The term "hyperfractionation" is used inconsistently in the literature. The dose per fraction in standard radiotherapy regimen is 1.8 to 2 Gy. For the purpose of a clear definition, hyperfractionation denotes a treatment with doses per fraction significantly lower than in standard regimen. Therefore only doses smaller than 1.8 Gy will be considered as hyperfractionated.

1.4.4.

Duration of treatment

The manifestation of late normal tissue reactions after long times is attributed to the very slow or missing cell turnover in these tissues. As a consequence, there is no considerable cell production during a radiotherapy treatment of a few weeks duration. It is therefore assumed that changes in treatment time do not substantially affect the incidence of late reactions. Acute reacting tissues show a proliferative response already at short times after the radiation insult. Changes in treatment duration might well influence the incidence and severity of acute radiation damage. Since this kind of damage usually is temporary it is not

30

1. INTRODUCTION

regarded as dose limiting. This view, however, is only true as long consequential late effects do not occur. In many editorials, reviews and textbooks ( Steel 1993; Bentzen 1994; Hall 1994; Scherer & Sack 1996; Ang 1997b; Horiot 1997; Perez & Brady 1997) it is advocated that retrospective analyses by Withers et al. (1988), by Overgaard et al. (1988), and by Fowler & Lindstrom (1992) have demonstrated decreasing tumor control probability with increasing overall treatment time, caused by tumor cell repopulation. Based on the linearquadratic model, time-factors for tumors were calculated. From these assertions and model calculations it has been deduced that shortening treatment time could yield a therapeutic gain. The idea of this so-called accelerated radiotherapy is to reduce the protective effect of the anticipated tumor-cell repopulation during radiotherapy. This idea includes that treatment interruptions have to be avoided because only proliferating tumor cells but not non-proliferating dose limiting normal tissue would profit from it. The term "accelerated fractionation" is used inconsistently in the literature. Originally, accelerated fractionation was defined as the shortening of overall treatment time while keeping the other treatment parameters like total dose, number of fractions, and dose per fraction constant. In practice, total dose and/or fraction size were lowered simultaneously. Therefore, dose intensity, i.e. the dose applied per time interval like dose per week, rather than treatment duration is the more adequate parameter to describe and quantify acceleration. Standard treatments correspond to 5 x 1.8 Gy = 9 Gy per week or 5 x 2.0 Gy = 10 Gy per week. Accelerated fractionation denotes a treatment with more than 10 Gy per week. Hyperfractionation is nowadays usually applied in connection with a moderate acceleration. Provided acceleration alone and hyperfractionation alone are beneficial it is logic to assume that a combination of both is even more beneficial. This was the rationale of the CHART trial (Continuous Hyperfractionated Accelerated RadioTherapy; Saunders et al. 1997; Dische et al. 1997) which will be commented on later.

1.5.

Check of the linear-quadratic model

1.5.1.

Quality assurance and Evidence Based Medicine

Radiotherapy requires careful and accurate operation of complex equipment and procedures for planning and performing of treatment. The success of radiotherapy, in terms of the probability of local control of the tumor, depends on an adequate dose of radiation


31

being delivered to the target volume. At the same time, the probability of radiation-induced damage to normal tissues is a dose-limiting factor. The most serious complications, late effects, normally occur after a latency period and may develop progressively throughout the rest of the patient's life. Both tumor control and normal tissue complications make strong demands on the accuracy and precision of the treatment delivered to the patient. This in turn leads to strong demands on quality assurance on all of the steps, processes and equipment contributing to radiotherapy treatment. In particular, because of the potential for long-term irreversible damage, which may occur after a delay of months or years, there has traditionally been a great emphasis on applying quality assurance in radiotherapy to prevent, or minimize, such damage and also on establishing careful long term follow-up. Thus quality assurance approaches have long been recognized as important and have been widely applied, but until recently they have often been limited in concept to quality assurance of the physical and technical aspects radiotherapy. More recently it has become appreciated that the concept of quality assurance in radiotherapy is more than a definition of technical maintenance and quality control of equipment and treatment delivery. Instead it should encompass all activities in the radiotherapy department, from the patient's first visit to the end of treatment, and also extending into the follow-up period. The comprehensive approach is favorable because it is recognized that organizational improvement of only some of the key steps in the radiotherapy process is not sufficient to guarantee that each patient will receive the best care available for his disease. The principles and structure of a comprehensive radiotherapy quality system have been summarized in the report 'Quality Assurance in Radiotherapy' (QART) of the Quality Assurance Committee of ESTRO (Thwaites et al. 1995). Many radiotherapy trials are based on considerations using the linear-quadratic model. It influences clinical decisions when individual treatments are altered in dose and/or fractionation, e.g. because of an unplanned interruption. As it is a basic tool in radiotherapy it should also be subjected to quality assessment. The linear-quadratic model appears plausible in many instances but does not necessarily describe irradiation effects correctly on a clinical level. Similar to the Ellis model, there are some gaps in the line of evidence and a large number of assumptions was necessary for the derivation of the linear-quadratic model. For doses greater than 2 Gy per fraction, the linear-quadratic model probably does reasonably describe the fundamental radiation response of normal tissues, but identifiable factors operating between fractions like incomplete repair of sublethal damage, changes in oxygen tension, cellular proliferation or redistribution of cells in the cycle may modify radiation response to such an extend that the linear-quadratic model may become deficient in summarizing the overall fractionation response in detail. A new paradigm of clinical practice and research is "Evidence Based Medicine". The basic concept is that any recommendation of a specific medical procedure should rely on empirical evidence.

32

1. INTRODUCTION

"Evidence-based medicine is the conscientious, explicit and judicious use of current best evidence in making decisions about the care of individual patients" (Sackett et al. 1996). In practice it is understood as integrating individual clinical expertise with the best available external clinical evidence from systematic research. Evidence Based Medicine is not restricted to randomized trials and meta-analyses but involves tracking down the currently best evidence available for answering a specific clinical question. As a consequence, Evidence Based Medicine distinguishes different classes of evidence: class I evidence is derived from one or more well-designed, randomized, controlled clinical trials; class II evidence from at least one well-designed clinical study, such as case-control or cohort studies; class III evidence is derived from experts opinions, non-randomized historical controls, or case reports (Shaw 1997). This is not the only evidence system. The START project, launched by the European School of Oncology, involves approximately 170 leading European oncologists. Its objective is to maintain a concise database on state-of-the-art treatment of human malignant tumors (START 1998) with statements on main clinical options being accompanied by their "type of basis". In the START project, types of basis are ranked in five levels. A Type C basis is seen in a widespread consolidated consensus. Randomized trials have not been carried out or have been inadequate, but the issue is settled without major controversy. Currently, no (further) experimental evidence is felt to be needed. Type 1 evidence is concluded from consistent results provided by more than one randomized trials, and/or a reliable meta-analysis. In some instances, one randomized trial is considered sufficient to support this type of evidence. Further confirmatory trials are not regarded as necessary. Type 2 evidence of the START system requires that one or more randomized trials have been completed, but the evidence they provide is not considered definitive (the results are not consistent, and/or the studies are methodologically unsatisfactory, etc.). Some controlled evidence has been provided, but confirmatory trials would be desirable. Type 3 evidence is assumed to be available from non-randomized studies, with external controls allowing comparisons. Some uncontrolled evidence has therefore been provided, but trials would be desirable. The basis is denoted Type R when there is little or no direct evidence from clinical studies. Yet clinical conclusions can be rationally inferred from available data and knowledge (e.g. by rationally combining pieces of information from published studies and observations; for a rare neoplasm, or presentation, through analogy with a related, more common tumor, or presentation; etc.). The inference can be more or less strong, and trials may, or may not, be desirable (START 1998). Presently there are different evidence systems in use. For the future, it can not be ruled out that assessment of treatment options and decisions in cancer therapy are made according to uniform criteria of Evidence Based Medicine.


33

The clinical question in the context of radiotherapy and the linear-quadratic model is which dose, fractionation and treatment time can yield optimum benefit in the care of an individual patient. A more general question is whether or not the predictions of the linearquadratic model are supported by clinical data. Present research on predictive assays which measure radiosensitivity or tumor cell kinetics relies on the validity of the linear-quadratic model. There is an increasing number of trials on combined radio-chemotherapy but less trials on radiotherapy alone, leading to the impression that radiotherapy is completely and definitely understood. Yet it appears wise to have a critical look at those issues that are on the edge of becoming standard knowledge in radiotherapy and clinical radiobiology since "one cannot build another level of useful information without having a solid ground to build on" (Fletcher 1988).

1.5.2.

Aim of this study

Understandably, authors generally evaluate and interpret their results from a certain point of view and sometimes leave other qualified approaches unnoticed. Indications provided by single publications can be limited while combined assessment of several studies might enhance the overall evidence for a certain issue. Solid scientific information, that constitutes a solid ground for future research, might be identified and distinguished from mere hypotheses, plausible assumptions and opinions. According to the considerations outlined above, the aim of the present study is to check the linear-quadratic model by applying it to data sets from different studies and to detect possible inconsistencies which could enhance our understanding of radiobiology. In particular, the present study is concerned with the following questions: − Is there clinical evidence for an impact of tumor cell number on treatment outcome? − Is there clinical evidence for a benefit from hyperfractionation? − Is there clinical evidence for a benefit from short treatment times? − Is the linear-quadratic model consistent with clinical experience?

34

1. INTRODUCTION


35

2.

Materials and Methods

2.1.

Identification of trials

The analysis of the clinical results was based on published data. No attempt was made to obtain data on individual patients. Publications were identified in a Medline database by searching for appropriate keyword combinations in titles and abstracts. In addition, the reference lists of the papers found in Medline were examined for further publications. All randomized trials on hyperfractionation, split-course radiotherapy, and hyperfractionated accelerated radiotherapy applying radiotherapy alone in both trial arms found in this way were included. Some frequently quoted review articles were reassessed and discussed because of their high impact on current opinion and treatment practice.

2.2.

Assessment criteria of clinical studies

For statistical and methodological assessment, the following aspects were evaluated and discussed where appropriate: − A priori hypothesis: The principle of a priori hypothesis testing is critical because testing for statistical significance remains valid only if hypotheses are stated in advance. − Post hoc patient exclusion: post hoc exclusion of patients is critical. The likelihood for a statistically significant result increases when some (unfavorable) patients are excluded later. Intention-to-treat analysis with all eligible patients who entered a trial should be the primary analysis (Simon 1993). − Therapeutic gain: A therapeutic gain is defined by a better relation between local tumor control and normal tissue reactions. Despite the fact that late normal tissue morbidity is the most critical element in the conduct of radiotherapy, side effects are often not or insufficiently reported. Clinical studies not reporting both endpoints provide no information about therapeutic benefit and are to be considered as incomplete (Overgaard & Bartelink 1995). In order to compare the effectiveness of different radiotherapy schedules the number of events (e.g. local failures or deaths, late complications) was estimated from the published data whenever possible. As a measure of therapeutic gain the rate of uncomplicated controls was calculated according to Holthusen (1936) from tumor control rate × (1 complication rate). − Balanced groups: The distribution of patients in the various treatment arms concerning known predictive parameters is crucial for the validity of a study. Imbalances for important prognostic factors can have a large effect on the comparison of treatments with regard to

36

2. MATERIALS AND METHODS

outcome (Simon 1997). Therefore imbalances were assessed for their potential to have biased the results. − Actuarial analysis: Although it has been questioned recently (Caplan et al. 1994, 1995) actuarial analysis (Kaplan & Meier 1958) is considered to be essential for the assessment of the efficacy of a treatment (Bentzen et al. 1995). It was checked whether both tumor and normal tissue response were reported in an actuarial manner. − Type I error: Type I error characterizes the risk to obtain a significant result by chance (Simon 1997). The risk of committing a type I error increases rapidly with the number of statistical tests performed (Beck-Bornholdt & Dubben 1994, 1995). Therefore, the significance levels of stated significances were examined for multiple testing. − Type II error: Type II error characterizes the risk to overlook an existing difference in a study. Trials that are too small and accordingly do not find statistical differences generally have to be considered "indeterminate" but not "negative" (Freiman et al. 1992; Simon 1997). Furthermore, if a small trial reaches significance, then the observed difference is most likely overestimated (Bentzen 1994). Power and sample size estimates were calculated according to Rosner (1995). − Consistency: The consistency of data within a publication and also between preliminary and final analyses of the same patients was explored. Inconsistency is an indicator of data management quality.

2.3.

Metaanalysis and odds ratios

Metaanalyses were performed by pooling the data of different trials on tumors of the same site. No attempt was made to check the data for homogeneity. Since trials, in general, were performed in different institutions and countries and at different times it is very likely that data are not comparable and should not be pooled. Thus there is a high risk of obtaining spurious positive results (LeLorier 1997). Some merits and pitfalls of metaanalyses are discussed in section 4.4. Odds ratios and 95% confidence interval estimates (Woolf method) were calculated according to (Rosner 1995). The occurrence of events in two groups of patients can be written

Group I Group II

Number of patients with event without event a b c d


37

The odds in favor of an event are a/b in group I and c/d in group II. The odds ratio OR is defined as a b a×d OR = = c d b×c An approximate two-sided 95% confidence interval for the odds ratio OR is given by ( e cI .. ec II ), where cI = ln( OR ) − 1.96 × c II = ln(OR ) + 196 . ×

1 a

+ b1 + 1c + 1 a

1 d

+ b1 + 1c +

1 d

.

38

2. MATERIALS AND METHODS


39

3.

Results

3.1.

Tumor volume1

One parameter in the linear-quadratic formula is the number of clonogenic tumor cells that have to be sterilized for tumor control. Apparently fewer cells occupy a smaller volume than many cells and, in general, a small tumor is more easily controlled with a certain radiation dose than is a larger tumor. In fact, survey of clinical literature indicates that treatment outcome is closely related to the volume of tumors at the beginning of treatment, and the evidence continues to grow: (1) Cervix: for stage IB squamous cell carcinoma of the uterine cervix central and pelvic tumor control and disease-specific survival correlated strongly (p100 0.5 - >113 >226 >226 0.065 - 15 0.5 - 180 180 500

>6 >8 14

Ib - IVa III, IV I-IV IB 0.5 - >113 0.5 - >113 T1 I-IV

>16 >16 39 >100 >226

230 360 >360 >1000(a)

44

3. RESULTS

stages (in which volume varied considerably; see Table 3.1) was reported by Mendenhall et al. (1994) for cervix carcinoma (Fig.3.3F). Tumor size was again given as diameter. Fig.3.3G is based on 44 patients with T3 squamous cell carcinoma of the larynx who were treated with definitive radiotherapy. To determine tumor volume, the primary lesion was outlined on each CT slice that showed part of the tumor. This data was used to calculate tumor volume in cubic centimeters. Relapse-free survival rate of cervix carcinoma patients (Fig.3.3H) was read off from Kaplan-Meier curves in a publication by Magee et al. (1991). Tumor diameters were assessed using transrectal ultrasonography.

1.0

0.8

0.6

0.4

0.2

A 0.0

Tumour control probability

1.0 Locoregional control probability

Tumour control probability

1.0

0.8

0.6

0.4

0.2

1

10

100

1000

0.1

C

1

10

100

1000

0.1

0.8

0.6

0.4

0.2

1.0

1.0

0.8

0.8

0.6

0.4

0.2

100

1000

0.4

0.0 0.1

Volume (cm 3 )

1

10

100

1000

Volume (cm 3 )

1.0

0.8

0.8

Relapse free rate

1.0

0.6

0.4

1000

F

0.0 10

100

0.6

E

1

10

0.2

D 0.0

1

Volume (cm 3)

Relapse-free survival

Local control probability

Complete response probability

0.2

Volume (cm 3 )

1.0

Local control probability

0.4

0.0

Volume (cm 3 )

0.1

0.6

B 0.0

0.1

0.8

0.1

1

10

100

1000

Volume (cm 3 )

0.6

0.4

0.2

0.2

H

G 0.0

0.0 0.1

1

10

100

Volumen (cm 3 )

1000

0.1

1

10

100

1000

Volume (cm3)

Fig. 3.3: Clinical data on the impact of tumor volume on tumor response probability. The calculated curves correspond to Fig.3.1; only its horizontal position was fitted by eye. Vertical bars represent 95% confidence intervals, horizontal bars indicate the range of volume strata when available and larger than dot size. A: Laryngeal carcinoma (Hjelm-Hansen et al., 1979). B: Advanced head and neck cancer (Van den Bogaert et al. 1995). C: Head and neck carcinoma (Johnson et al. 1995a). D: Melanoma, complete response (Overgaard et al. 1986). E: Breast cancer (Arriagada et al. 1985). F: Cervix carcinoma (confidence intervals were not available), relapse-free survival (Mendenhall et al. 1994). G: T3 glottic larynx carcinoma (Pameijer et al. 1997). H: Cervix carcinoma (vertical errors were not available), relapse-free rate (Magee et al. 1991).


45

TUMOR VOLUME

It should be noted that the calculated curves in Fig.3.3A-H do not represent a fit to the data. The data may be well described by the curve from Fig.3.1 which was only shifted horizontally to fit the clinical volume data given in absolute units. Fig.3.4 shows a

1.0


0.8

0.6

0.4

0.2

0.0 0.01

0.10

1.00

10.00

100.00

Relative volume Expected response probability Head and neck [Hjelm-Hansen et al. 1979] Head and neck [Van den Bogaert et al. 1995] Head and neck [Johnson et al. 1995a] T3 glottic larynx [Pameijer et al. 1997]

Melanoma [Overgaard et al. 1986] Breast cancer [Arriagada et al. 1985] Cervix cancer [Mendenhall et al. 1994] Cervix cancer [Magee et al. 1991]

Fig.3.4: Superposition of the clinical data plotted in Fig.3.3A-H on a relative volume scale. Dashed curves represent fits to the individual data sets.

superposition of all data of Fig.3.3 in a single plot. The solid curve is again taken from Fig.3.1. The dashed curves are fits to the data in which not only the horizontal position but also the steepness was fitted.

3.1.4.

Discussion

The clinical volume response data (Fig.3.3A-H, Fig.3.4) agree well with the theoretical curve in Fig.3.1 but the relationship generally appears to be less steep than expected. This is likely due to a variety of sources of heterogeneity, including inaccuracies in volume measurement, variations in treatments administered, differences in primary site, and biological variability e.g. in radiosensitivity. In some of the studies tumor diameters were

46

3. RESULTS

measured using rather crude methods and volume was calculated from mean diameters assuming spherical tumors. Assessment by ultrasound (Magee et al. 1991) is likely to be more accurate. Probably the most accurate way to measure tumor volume, based on CT and/or MRI, is described by Freeman et al. (1990). The most precise data, i.e. those determined from CT-scans (Fig.3.3C and Fig.3.3G) or using ultrasound (Fig.3.3H) and the experimental data (Fig.3.2), yielded the steepest relationships. It is well recognized that inter-tumor heterogeneity yields dose response curves that are less steep than curves based on homogeneous data (Bentzen 1992). The same considerations hold for volume response curves. The discrepancy between data and curve in Fig.3.4 can also be explained by heterogeneity in other parameters, including variation in treatment parameters and biological variability between patients, that influence tumor response. Heterogeneity is strongly reduced in the experimental setting. Accordingly, the experimental data are in best agreement with the theoretical expectation (Fig.3.2). An estimate of the other treatment and biological factors contributing to heterogeneity of response from the deviation of the actual curves from the predicted curve would be useful. Unfortunately this is seriously complicated by simultaneous variation of treatment parameters, especially of total dose, in some of the studies evaluated here. The number of clonogenic tumor cells was assumed to increase linearly with tumor volume. This is not necessarily true, e.g. due to an increased fraction of necrotic regions in larger tumors or volumes of tumor infiltration where the proportion of tumor cells is small. This deviation from linearity might also modify the volume response but it is obviously not of crucial importance since the relationship is not obscured. These results are in agreement with a recent report of Bentzen and Thames (1996), who found evidence for a highly significant reduction of tumor control probability with increasing tumor volume. Because of heterogeneity in patient and tumor characteristics the volume effect was less pronounced than would be expected from a simple proportionality between number of clonogens and tumor volume. However, reanalysis of local control data of oropharyngeal cancer patients revealed that when heterogeneity in intrinsic radiosensitivity was explicitly allowed for in the model analysis, the relationship between volume and number of clonogen cells did not differ significantly from linearity. This is in agreement with conclusions of Brenner (1993).

3.1.5.

Conclusion

Tumor volume appears to be an important factor in radiotherapy. This is confirmed by experimental and clinical data. Concerning tumor volume and associated number of clonogenic tumor cells per tumor, the linear-quadratic model makes accurate predictions on the outcome of clinical radiotherapy.


47

3.2.

The dose per fraction in hyperfractionated radiotherapy1

In this section, the literature on primary hyperfractionated radiotherapy of solid tumors is reviewed with emphasis on biostatistics and radiobiology. Clinical and physical aspects are at least equally important for overall judgment of this new treatment modality but have been considered less here. Studies on combined radio-chemotherapy were consistently excluded. The analysis of the clinical results was based on published data. No attempt was made to obtain data on individual patients.

3.2.1.

Experimental evidence for sparing of late reactions by hyperfractionation

Experimental data about the influence of dose per fraction on radiation tolerance were compiled by Thames et al. (1982). From these data, Fowler (1984) derived α/β-values which were more recently presented again by Joiner in a text book (Joiner 1993). Thames et al. (1982) concluded "that the sparing that can be achieved by the use of doses smaller than the conventional 200 rad [2 Gy] per fraction is greater for late than for early effects, for which it might be negligible ...". A therapeutic gain from reduced doses per fraction seemed conceivable "if it is assumed that tumors have the same dose survival characteristics as acutely responding tissues, and that late responding tissues are dose limiting" (Thames et al. 1982). However, among the data compiled by Thames et al. (1982) there are very few tolerance measurements of late reacting tissues at clinically relevant doses of less than 2 Gy per fraction (see Fig.1.13; introduction)). On the other hand, experiments on kidney and skin demonstrated an increasing sensitivity to radiation when dose per fraction was reduced below 1 Gy (Stewart et al. 1984; Joiner et al. 1986; Parkins & Fowler 1986; Joiner & Johns 1987, 1988; Joiner 1989; Joiner et al. 1993). These observations clearly do not fit the linear-quadratic model. Tolerance was observed to decrease by a factor of two in a narrow dose range. Increasing sensitivity below 1 Gy per fraction is, however, not observed in spinal cord (Wong et al. 1992, 1993). For comparison of hyperfractionated with standard radiotherapy only the dose range from 1 to 2 Gy per fraction is clinically relevant. Experimental data within this range are sparse. The experimental data mentioned above indicate that radiation tolerance of late reacting normal tissue declines below and above this range. Consequently, an optimum between 1 and 2 Gy should be expected. If the optimum is closer to 1 Gy, as it seems to apply to skin and kidney but not for spinal cord, lowering the dose per fraction below 2 Gy might be beneficial. With the optimum close to 2 Gy it might be detrimental.

1

Main parts of this chapter are published in: Dubben et al. 1996a; Beck-Bornholdt et al. 1997, 1998ab; Willers et al. 1998.

48

3. RESULTS

In summary, experimental data on late reactions of normal tissue do not provide unequivocal evidence for a therapeutic gain from hyperfractionation in the relevant dose range. Since interfraction intervals are usually reduced below 24 hours in hyperfractionated irradiation treatment, repair kinetics became an important issue. The experimental data have been reviewed recently by Joiner (1993a) and Bentzen et al. (1996c). In clinical practice, hyperfractionation is usually performed using a higher total dose in approximately the same overall treatment time. Consequently, treatment is slightly accelerated at the same time, which in turn causes higher acute reactions. At first glance, this appears to be no problem, since not acute but late reactions are considered as dose limiting. However, consequential late reactions that arise from severe acute sequelae cannot be ruled out (Peters et al. 1988; Bentzen et al. 1991; Peck et al. 1994).

3.2.2.

Response of experimental tumors to hyperfractionation

In most radiobiological studies on experimental tumors, fractionation is generally extended to a maximum of only 5 to 8 fractions. Table 3.2 summarizes publications on fractionated irradiation of experimental tumors involving 10 or more fractions. The upper part of the table shows the hyperfractionation studies, i.e. those reports that include treatments with doses per fraction of 1.8 Gy or less. The lower part of the table shows the studies with larger doses per fraction. The number of studies relevant for hyperfractionation is rather limited. In the following, a brief summary of these studies is given. Kob et al. (1976, 1977) investigated tumor cell viability in a solid murine Ehrlich carcinoma and a murine mammary carcinoma on the basis of histological criteria and the tumor size at the nadir after end of treatment. They compared 40 fractions of 1.5 Gy, 20 fractions of 3 Gy and 5 fractions of 12 Gy. No established quantitative endpoints like local tumor control or growth delay were determined. Gonzalez and Haveman (1982) studied the effects of different fractionation schedules of irradiation in an experimental murine mammary adenocarcinoma. They varied the number of fractions per day from one to three, keeping the daily dose constant, and found that an increase in the number of fractions per day did not necessarily lead to a decrease in tumor response. Pfersdorff and Sack (1986) compared the response of a murine adenocarcinoma to either one fraction of 2 Gy per day or 3 fractions of 1.6 Gy per day. In the two schedules, the total dose of 24 Gy was applied within 11 or 5 days, and in 12 or 15 fractions, respectively. A


THE DOSE PER FRACTION IN HYPERFRACTIONATIONATED RADIOTHERAPY

49

higher efficacy of the multiple daily fraction regimen was found. It cannot be discriminated whether the increased tumor response observed in the hyperfractionated arm is due to the smaller doses per fraction or to acceleration. The kinetics of cellular inactivation by fractionated irradiation in the R1H-tumour of the rat was studied by Vogler and Beck-Bornholdt (1988) in the dose range of 1.07 to 12.5 Gy per fraction. The number of clonogenic tumor cells per tumor in the course of the different treatment schedules was determined using an in vitro colony assay. The cellular response was found to be the same, no matter whether the weekly dose was applied in 1, 3, 5, 7, or 10 fractions. Corresponding results were reported for the same tumor system using the endpoints net growth delay and local tumor control (Würschmidt et al. 1988). In a later study of the same group (Beck-Bornholdt et al. 1989), the effect of hyperfractionation with 126 fractions of X-rays, applied in 3 fractions per day with a time interval of 8 hours between fractions on 7 days per week during 6 weeks was investigated. The response to the hyperfractionated treatment was found to be slightly more effective as compared to the results obtained with 6, 18, 30 and 42 fractions. A caveat of this study is that the results are compared with those from previous experiments, i.e. with "historical controls". The response of the R1H-tumour to hyperfractionated irradiation with different time intervals between the two daily fractions has also been investigated (Würschmidt et al. 1992; Kleineidam et al. 1994). A standard treatment of 30 fractions was compared with a hyperfractionated schedule of 60 fractions with two daily fractions separated by 1 to 6 hours. A significant reduction of response was observed for the tumors treated with two daily fractions separated by 2 hours (Würschmidt et al. 1992). By contrast, a considerable and significant increase in tumor response was observed for time intervals of 5 and 6 hours (Kleineidam et al. 1994). A caveat of this study is that the data were not obtained in a single experiment, and that due to slight changes of radiosensitivity of tumors between different experiments it was necessary to quantify tumor response using the rather artificial parameter "relative net growth delay". In the Gray Laboratory a large series of experiments was carried out to investigate the effect of normobaric oxygen or carbogen alone or in combination with nicotinamide on the outcome of a fractionated irradiation treatment (Rojas et al. 1990, Kjellen et al. 1991, Rojas et al. 1992a). Although performed with small fraction sizes, the experiments were not aimed for investigating the effect of dose per fraction and they do not provide information on it. In the experiments by Baumann et al. (1992, 1994) and by Wolf et al. (1997) human tumor xenografts on nude mice were investigated. The purpose of the experiments was to determine the TCD50 of different tumor cell lines, to investigate the impact of overall treatment

50

3. RESULTS

Table 3.2: Publications on fractionated irradiation of experimental tumors involving treatments with 10 or more fractions. Upper part: hyperfractionation studies including doses per fraction of 1.8 Gy or less. Lower part: fractionation studies with doses per fraction of more than 1.8 Gy. Authors

Year


Kob et al. Kob et al. Gonzalez & Haveman Pfersdorff & Sack

1976 1977 1982 1986

1.5 - 12 1.5 - 12 0.7 - 7.5 1.6 - 2

Vogler & Beck-Bornholdt Würschmidt et al Beck-Bornholdt et al. Rojas et al. Kjellen et al. Beck-Bornholdt et al.

1988 1988 1989 1990 1991 1991a

1.07 - 12.5 1.07 - 12.5 0.43 - 0.71 1.2 - 55 1.5 - 13 1.50 - 2.67

Würschmidt et al.

1992

1.23 - 2.67

Rojas et al. Kleineidam et al.

1992a 1994

0.3 - 20 0.92 - 2.75

Baumann et al.

1992

≈1.5 - 4

Rojas et al. 1993 Dubben & Beck-Bornholdt 1993

1.75 - 5.4 1.65 - 12.5

Baumann et al.

1994

1.4 - 4.8

Wolf et al.

1997

0.67 - 3.3

Appold et al. Petersen et al.

1998 1998

1.06 - 12.7 0.33 - 7.9

Barendsen & Broerse Fischer & Reinhold Fowler et al. Moulder et al. Fowler et al.

1970 1972 1975 1976 1976

2-4 2.5 - 10 3 - 9.4 4.3 - 36 3 - 15

Suit et al.

1977

≈4.8 - 75

Martin et al. Unger Kummermehr & Trott Unger Beck-Bornholdt et al. Kummermehr Looney & Hopkins Reghebi et al. Weinberg & Rauth

1980 1982 1982 1983 1985 1985 1986 1986 1987

≈8 - 11 1.67 - 12.5 10 - 25 1.67 - 12.5 2.3 - 6.5 7 2.5 ≈3 - 12 2.5 - 10

Suit et al. Pavy et al. Würschmidt et al.

1988 1990 1991

7 - 23 3.4 2.3 - 2.7

Rojas et al. Allam et al.

1992b 1995

3-8 2.0 - 2.5

Remarks Only histological endpoint. Only histological endpoint. Reduced doses per fraction lead to essentially identical tumor responses. Small doses per fraction were more effective, but also reduced overall treatment time. Tumor response was found to be independent of dose per fraction. Tumor response was found to be independent of dose per fraction. Small doses per fraction were more effective as compared to historical control. Study was designed to investigate the effect of Carbogen and Nicotinamide. Study was designed to investigate the effect of Carbogen and Nicotinamide. Influence of overall treatment time was investigated. Impact of dose per fraction not tested. Time interval of 2 hours yields reduced tumor response. Impact of dose per fraction was not tested. Study was designed to investigate the effect of Carbogen and Nicotinamide. Time interval of 5-6 hours yields increased tumor response. Impact of dose per fraction was not tested. Determination of TCD50 of different xenografted tumors. Total dose increases with dose per fraction. Study was designed to investigate the effect of Carbogen and Nicotinamide. All doses per fraction in boost treatment were isoeffective, but large error margins. Total dose increases with dose per fraction. Impact of overall treatment time on response of FaDu-tumor was investigated. Total dose increases with dose per fraction. Designed to investigate the impact of treatment breaks. Impact of dose fractionation on response of FaDu-tumor was investigated. No impact of dose per fraction on FaDu-tumor but marked fractionation effect on GL-tumor (α/ß = 3 Gy). Mechanisms other than recovery from sublethal radiation damage and repopulation of clonogenic tumor cells may importantly impact on treatment outcome when the number of fractions is changed in clinical radiotherapy. Number of fractions and overall treatment time were varied simultaneously. Number of fractions and overall treatment time were varied simultaneously. Changes in dose per fraction associated with changes in total dose. Number of fractions and overall treatment time were varied simultaneously. Effectiveness estimated by comparing local tumor control that could be achieved for a given skin reaction. Tumor response independent of dose per fraction when ≥10 fractions were applied (ambient conditions). Impact of dose per fraction was not tested. Only histological endpoint. Isoeffect doses increased with decreasing dose per fraction (clamped hypoxia). Only histological endpoint. Small doses per fraction were isoeffective. Dose per fraction was not varied. Impact of dose per fraction was not tested. No impact of fractionation on clamped TCD50. No significant difference in tumor response was observed between schedules of 5 or 10 fractions. Tumor response was found to be independent of dose per fraction. Study was designed to study the influence of overall treatment time. Influence of gaps on treatment outcome was investigated. Impact of dose per fraction was not tested. Study was designed to investigate the effect of Carbogen and Nicotinamide. Influence of overall treatment time was investigated. Impact of dose per fraction not tested.



51

time or the impact of treatment interruptions, respectively. Conclusions about the impact of hyperfractionation cannot be drawn since total dose was given in a constant number of fractions. The impact of dose fractionation in FaDu tumor xenografted to nude mice was investigated by Appold et al. (1998). Tumor control rate appeared to be independent from dose per fraction. In a study by Petersen et al. (1998), the influence of different numbers of fractions on local tumor control in two human head and neck squamous cell carcinomas grown in nude mice was investigated. The TCD50 values for the poorly differentiated FaDu-tumors irradiated with 12, 30, and 60 fractions over 6 weeks were 69.5 Gy, 59.6 Gy, and 72.6 Gy, respectively. The effective α/β-ratio derived form these data by direct analysis was infinite with a lower 95% confidence limit of 52 Gy. In contrast, the TCD50 values of the moderately well differentiated slowly growing GL-tumors after 12, 30, and 60 fractions increased from 35.2 Gy, to 44.4 Gy, and 56.4 Gy, respectively. Thus, when irradiated under ambient conditions over 6 weeks, the TCD50 of FaDu-tumors did not depend on dose per fraction, whereas in GL-tumors TCD50 increased with decreasing dose per fraction. These data and those of two other experimental tumors are depicted in Fig.1.15. The effective α/β-ratio derived from these data was 3 Gy (0.6 - 12 Gy) which is in contrast to α/β-ratios determined from local tumor control data after treatment with single doses and 2, 4, and 8 fractions under clamp hypoxia (Petersen et al. 1998). After correction for an oxygen enhancement ratio of 2.7 the α/β-ratios were 15 Gy (95% CI 9 .. 24 Gy) for FaDu and 49 Gy (26 .. 122 Gy) for GL. The results support the view that mechanisms other than recovery from sublethal radiation damage and repopulation of clonogenic tumor cells may substantially affect treatment outcome when the number of fractions is changed in clinical radiotherapy. In summary, due to parallel variation of several parameters like number of fractions and overall treatment time most studies do not allow to separate the influence of every individual parameter. Furthermore, most experimental settings appear rather artificial. The number of fractions was generally kept small, probably for reasons of convenience, leading to relatively high doses per fraction. Overall treatment time usually was extremely short. In several studies the tumors were clamped during irradiation (Suit et al. 1977; Martin et al. 1980; Gonzalez & Haveman 1982; Kummermehr & Trott 1982, 1993; Kummermehr 1985; for discussion see Beck-Bornholdt et al. 1991b, 1993), and in most studies, animals were anaesthetized during irradiation, which may lead to uncontrolled irradiation conditions (Zanelli et al. 1975; cf. Johnson et al. 1976, Kal & Gaiser 1980). It appears that no general conclusions can be drawn from these studies concerning whether and to which extent tumor response depends on fraction size.

52

3.2.3.

3. RESULTS

Clinical studies

For statistical and methodological assessment of clinical studies, the criteria in outlined in chapter 2 were applied. 3.2.3.1.

Historical results

It has been claimed that non-standard fractionation techniques such as multiple fractions per day were already used in the 1920s and 1930s, for instance by Coutard (Reinhold & Visser 1986; Thames & Hendry 1987; Stillwagon et al. 1989). In fact, in the first decades of the century it was not uncommon to give more than one radiation treatment per day to head and neck cancer patients (Nielsen 1935; Schwarz et al. 1937). Coutard, for example, delivered a surface dose of approximately 1.5-2 Gy twice daily to a total dose that could exceed 80 Gy (Coutard et al. 1937). However, in each sitting only one radiation field out of a total of two or more was irradiated. Furthermore, Coutard delivered the dose at a very low dose rate. As a result, one to two hours were needed to complete each irradiation. It must be concluded that a parameter "dose per fraction" did not exist: a "fraction" which today does consist of the irradiation of multiple fields in one short sitting was given over a considerably extended period of time. Therefore, hyperfractionated radiotherapy cannot be regarded as having been clinically used already during the first decades of the century. Early exploratory studies on hyperfractionation were published in the 1970s. In 1973, Bäckström et al. (1973) reported on 17 patients with advanced floor of mouth carcinomas who underwent preoperative irradiation or radiotherapy alone. Treatments were given at 1 Gy per fraction thrice daily with intervals of 4 hours. Subsequent studies on head and neck cancer also involved similarly small numbers of patients (Shukovsky et al. 1976; Jampolis et al. 1977; Arcangeli et al. 1979). The results of a RTOG pilot study investigating hyperfractionation for head and neck and esophagus tumors were only published in abstract form by Marks et al. (1978). Preliminary results for 45 patients with bladder carcinoma randomized either to hyperfractionation with 84 Gy at 1 Gy per fraction given thrice daily or to conventional irradiation with 64 Gy were published in 1975 by Littbrand et al.. In 1979, Arcangeli et al. reported on clinical observations in various anatomical sites like head and neck, lung, breast, or bone. All of these studies claimed promising or favorable results for hyperfractionated radiotherapy, although the statistical basis was insufficient.

3.2.3.2.

Head and neck cancer

3.2.3.2.a Head and neck cancer: Non-randomized studies Table 3.3 provides an overview on non-randomized clinical studies investigating hyperfractionated radiotherapy for head and neck tumors that have been published since the early 1970s. Combined hyperfractionated and accelerated radiotherapy, like CHART, has



53

not been considered here (e.g. Svoboda 1978; Perrachia & Salti 1981; Wang et al. 1986) with the exception of two reports on split-course treatment (van den Bogaert et al. 1985; Nguyen et al. 1985, 1988). In general, hyperfractionation was tested in tumors of advanced stages including various primary sites. A wide range of total tumor doses was used. Doses per fraction usually were 1.1 or 1.2 Gy given twice daily with interfraction intervals of at least 4 hours. In most of the studies, numbers of patients were small. Particularly the early reports involved only few patients and appear to be only of historical interest (e.g. Bäckström et al. 1973; Shukovsky et al. 1976; Jampolis et al. 1977; Medini et al. 1980). Probably the largest experience has been published by the M. D. Anderson Hospital (MDAH) (Shukovsky et al. 1976; Meoz et al. 1984; Wendt et al. 1989; Garden et al. 1995) and the University of Florida (Parsons et al. 1984, Parsons et al. 1988, Parsons et al. 1993). Parsons et al. (1988, 1993) compared the results of hyperfractionated radiotherapy at the University of Florida to conventionally fractionated historical controls. For the hyperfractionated treatments, the data were documented prospectively. For T2-T3 tumors located in the larynx, hypopharynx and oropharynx, crude local control rates were observed to be 1020% higher in 6 out of 8 twice-a-day fractionation groups compared to once-a-day fractionated controls (Parsons et al. 1988). However, none of these differences reached statistical significance. In a later report based on more than 400 patients (Parsons et al. 1993), an analogous comparison was made for various sites and stages. Crude local control rates for T2-T3 larynx and hypopharynx carcinomas gave a p-value of less than 0.05, whereas a significant improvement for oropharyngeal cancers was not seen. In summary, Parsons et al. reported on very heterogeneous data and general conclusions from their analysis appear to be limited. For 41 patients with supraglottic larynx carcinoma treated at MDAH, Wendt et al. (Wendt et al. 1989) found a significantly higher locoregional control rate when compared to a conventionally fractionated group irradiated in a preceding treatment period. However, this difference did not translate into an improvement in survival. It is important to note that the median follow-up time in this analysis was less than two years. Most of the studies listed in Table 3.3 involved interfraction intervals of more than 4 hours. It is remarkable that already in the 1970s intervals of 6 or 8 hours apparently were considered to be adequate by some authors (Shukovsky et al. 1976; Jampolis et al. 1977). In contrast, Nguyen et al. (Nguyen et al. 1985, 1988) investigated a fractionation schedule consisting of multiple daily fractions of small size separated by only two hours. As a result, hazardous late normal tissue toxicity was observed including 16% fatal complications. Recently, Garden et al. (1995) analyzed the impact of interfraction intervals of ≥ 4 versus

54

Table 3.3: Non-randomized clinical studies on head and neck tumors First author Study No. of Total dose Dose per Interval Minimum & origin characteristics patients (Gy) fraction (hours) follow-up [2] (Gy)[1] (years)

Actuarial[3] LC or LRC rate

Actuarial[3] severe late complication rate

Comments

Bäckström 1973 Stage III-IV Stockholm/Sweden floor of mouth

9

84

1.0 tid

4

1*

crude 78% LRC

no

5 patients also had surgery

Shukovsky 1976 Houston/USA

almost all T4 or N3

24

60-75

1.1-1.2

8

1

crude 79% LRC at 2 years

crude 13%

long interfraction interval remarkable

Jampolis 1977 Dijon/France

advanced T4

24

69.6 or 72

1.2

6-8

1.1

crude 61% LRC at 1.5 years

crude 13% ("marked neck fibrosis")

also long interfraction interval

Medini 1980 Minneapolis/USA

Stage III-IV prospectively

15

75

1.1

4

0.6*

53% complete remission of primary

crude 7%

very short follow-up

Meoz 1984 Houston/USA

Stage III-IV

65

60-75

1.1-1.2

3-6

1.5

crude 53% LC at 2 years

crude 17%

Parsons 1984 Gainesville/USA

Stage III-IV prospectively

57

74.4-76.8

1.2

4-6

2 (?)

crude 45% LC at 2 years

crude £ 6%

7 patients had preoperative radiation

v.d. Bogaert 1985 EORTC group

all stages, pilot study 179 misonidazole tested

67.2 or 72

1.6 tid.

4

3

34% LRC at 3 years

crude 9% dead (early & late complications)

split-course technique

Nguyen 1985/88 Reims/France

Stage III-IV

178

66 or 72

0.9/1.1#

2

2

crude 45 or 55% LRC at 2 years

crude 69% (16% dead)

short interval hazardous, split-course technique


Stage II-IV prospectively

144

60-81.6

1.2

4-6

2

32-78% LRC at 4 years

crude 5%

very heterogen. data, results superior to historical control

Wendt 1989 Houston/USA

supraglottic larynx T2,3

41

72-79

1.1/1.2

≥4

1.8*

87% LRC at 2 years

5% at 2 years

short follow-up, results superior to historical control


Stage I-IV prospectively

419

74.4-81.6

1.2

4-6

2

40-83% LRC at 5 years

crude 5%

very heterogen. data, results superior to historical control

$

Garden 1995 almost all Stage II-IV 78 72.0-79.7 1.2 ≥4 3.8* 77% LC at 2 years 15% at 3 years trend towards reduced toxicity Houston/USA incl. chemotherapy 158 71.8-78.4 1.2/1.1 ≥ 6 1.5* 74% LC at 2 years 8% at 3 years with longer intervals suggested [1]: fractions were given twice daily, if not otherwise stated, tid.: thrice daily. [2]: time interval between fractions. [3]: if not otherwise indicated. LC: local tumor control. LRC: locoregional tumor control. *: median follow-up, $: doses for 50 patients without surgery. #: 6 x 1.1 and 8 x 0.9 Gy daily.


55

≥ 6 hours on local control and normal tissue reactions. A trend towards reduced normal tissue toxicity was suggested when intervals of at least 6 hours and doses per fraction of 1.2 and 1.1 Gy were used. The authors evaluated more than 200 patients including a considerable portion of patients who also underwent chemotherapy. In some reports, hyperfractionated radiotherapy led to increased acute normal tissue toxicity (Shukovsky et al. 1976, Wendt et al. 1989; Parsons et al. 1993). In most of the studies listed here, no significant increase in severe late complications with twice-a-day fractionation seemed to have occurred. Numbers of patients at risk after two or more years of follow-up generally were small and use of crude rather than of actuarial rates was the rule (Table 3.3). Therefore, conclusions with respect to the impact of altered fractionation schemes on late normal tissue toxicity can hardly be drawn. In summary, conclusions from these retrospectively analyzed data are limited.

3.2.3.2.b

Head and neck cancer: Controlled randomized trials

There is a large number of randomized trials using hyperfractionation. Some are dose escalation studies without control group, i.e. patients were only randomized to hyperfractionated treatment with different total doses. Others compared hyperfractionated irradiation with and without additional agents like misonidazole. Six trials have been published so far in which patients were randomized to either a control arm with standard irradiation or to an experimental arm with hyperfractionation (van den Bogaert et al. 1986, 1995; Marcial et al. 1987; Datta et al. 1989; Sanchíz et al. 1990; Pinto et al. 1991; Horiot et al. 1992). These trials are summarized in Table 3.4. The first study was performed by the EORTC Cooperative Group of Radiotherapy and published by van den Bogaert et al. (1986, 1995). A total of 487 evaluable patients had been randomized either to a standard treatment protocol (CF: 2 Gy per fraction, 5 fractions per week, 70 Gy within 7 weeks), to hyperfractionation (HF: 1.6 Gy per fraction, 3 fractions per day for 10 days, 3 weeks rest, followed by a boost to 67.2 or 72 Gy, interfraction intervals of 4 hours), or to a third arm that is not considered here because it is a combination of radiotherapy plus misonidazole. The experimental arm tested in this trial is not only hyperfractionated (1.6 Gy per fraction) but is also a split-course treatment with two accelerated (4.8 Gy/day) components, and is therefore not typical for hyperfractionated schedules. The distribution of prognostic factors like primary tumor site, stage, and nodal status, between the treatment arms was not reported. Therefore, balance between the arms cannot be checked. Maximum follow-up time was 8 years. Actuarial analysis revealed 5year local control rates of 27% (CF) and 22% (HF). Evaluation of pooled grade 2 and 3 late side effects using the Kaplan-Meier method yielded no significant difference in xerostomy

56

3. RESULTS

and fibrosis but a significant increase of edema in the experimental arm. For serious late side effects (grade 3 alone) crude incidences are reported: 14/88 (16%) in the conventional and 37/94 (39%) in the experimental arm. These serious complication rates differ significantly (p = 0.0003), indicating a considerable therapeutic loss. In a preliminary publication, van den Bogaert et al. (1986) reported that differences in late effects did not occur, even though the early crude rates of trismus and chronic ulceration already amounted to 3% (2/74) in the standard arm and to 7% (6/81) in the experimental arm. Therefore, early results should be considered very carefully. They may be misleading like in this trial, because follow-up time is insufficiently long and the statistical power for differences in late reactions is usually very low in early reports. A subsequent trial (EORTC 22851) that was based on an incautious interpretation of EORTC 22811 lead to disastrous late side effects; this will be discussed in section 3.5.4. In summary, there was no difference in local control but a considerable increase in serious late side effects in the experimental arm. The results of this study do not provide any support for the hypothesis that hyperfractionation, as used in this trial, offers a therapeutic gain in treatment of head and neck cancer. Several authors (Stuschke & Thames 1997ab, 1998; Baumann et al. 1998) argue that the EORTC 22811 trial is not a hyperfractionation trial. Indeed, not only the dose per fraction but also the dose per day was changed and a treatment break of 3 weeks was introduced. The study design allows only to speculate about possible causes of increased late toxicity. Proliferation is a very unlikely cause since late reacting tissue probably does not proliferate noticeably during several weeks and because treatment time was the same in both arms. Total dose was approximately the same in both arms. The break itself is unlikely to produce late damage. Thus short interfraction intervals, which are an intrinsic problem in hyperfractionation when treatment time is kept constant, and dose per fraction remain as potential causes. Therefore, to be on the safe side when assessing the effect of hyperfractionation the EORTC 22811 trial must not be excluded from analysis. In 1987, a preliminary report of a RTOG hyperfractionation study was published (Marcial et al. 1987). A total of 187 patients was randomized either to a standard protocol (1.8 to 2 Gy per fraction, 5 fractions per week, total dose 66 to 73.8 Gy), or to hyperfractionation (1.2 Gy per fraction, 2 fractions per day, time interval between daily fractions of 3.5 to 7 hours, total dose 60 Gy). There was a slight imbalance in the prognostic factors favoring hyperfractionation; in the standard arm there were 40% T4 and 37% N3 tumors, and 34% of patients with Karnofsky performance score of 90-100, whereas the corresponding figures in the hyperfractionation arm were 34%, 27% and 50%, respectively. According to the Medline database (July 1998) this preliminary report has not yet been succeeded by a later analysis, so that the median follow-up time still amounts to approximately 15 months,


57

Table 3.4: Summary of the main results of all controlled randomized trials on hyperfractionated radiotherapy of head and neck cancer. Total doses (Gy) Number of Distribution Median Tumor response Severe late Trial (dose/fraction) patients of prognostic follow-up [actuarial]; complications factors (years) Endpoint (at years) [crude] RTOG (79-13) Marcial et al. 1987

CF

70

93 In favor of HF

HF

60 (1.2)

94

Datta et al. 1989

CF

66

85

HF

79.2 (1.2)

91

Sanchíz et al. 1990

CF

60

227

HF

70.4 (1.1)

282

Pinto et al. 1991

CF

66

48

HF

70.4 (1.1)

50

EORTC 22791 Horiot et al. 1992

CF

70

176

HF

80.5 (1.15)

180

EORTC 22811 van den Bogaert et al. 1995

CF

70

168

70.4 163 (1.6) CF = conventional radiotherapy with 2 Gy per fraction. HF = hyperfractionation HF

1.3 Preliminary report

29%   n.s. 30%  Local control (2)

16%   p=0.059 30% 

33%   p4.5 hours, the cumulative incidence of "grade 3 or more" reactions at 2 years was 17% and 10% and for grade 4 reactions the incidence was 6% and 2%, respectively. These results have been subjected to considerable discussion in the most recent literature (Fu et al. 1995b; Herrmann 1995, Withers & Taylor 1995; Bentzen and Thames 1996b; Fu et al. 1996). In summary, it must be considered unexpected that RTOG study 83-13 was not able to demonstrate a dose-response relationship for late normal tissue reactions. It is surprising that the interfraction interval rather than total dose appears to be the most important prognostic factor for late complications (Bentzen and Thames 1996). There might be other factors at work that contributed to the development of the late effects observed. In this context, some important issues regarding study design and analysis of RTOG trial 83-13 should be mentioned. First, it must be emphasized that there is only sparse information provided on the distribution of the actual interfraction intervals and their grouping. Second, it has to be considered that the four different treatment arms were not open at the same time. The trial was started with an 1:1:2 unequal randomization between the 67.2, 72.0, and 76.8 Gy arms, and continued with an 1:3 randomization between the 72.0 and 81.6 Gy arms. Over time, the proportion of short intervals (≤4.5 hours) dropped from 68% for 67.2 Gy to 29% for 81.6 Gy. Third, it could be questioned whether a similar time-related shift in treatment techniques or patient selection could have biased the results (Bentzen and Thames 1996). Another randomized study without a control arm was reported by Panis et al. (1984). Fiftytwo patients were randomized either to hyperfractionated radiotherapy alone or to hyperfractionated radiotherapy plus misonidazole. A split-course technique delivering 66 Gy to

66

3. RESULTS

various head and neck sites was used. Fractions of 1.1 Gy were given six times daily separated by 2 hours. Overall treatment time was six weeks. There was a high incidence of severe acute toxicity. Since the results from the radiotherapy alone and the combination arm were pooled, no firm conclusions on the toxicity of the chosen hyperfractionation regimen can be drawn.

3.2.3.3.

Non-small-cell lung cancer

Local tumor response is difficult to assess in radiotherapy of inoperable non-small-cell lung cancer (NSCLC) due to the difficulties in separating radiation effects from persisting or recurring tumor (Green et al. 1994; ARO 1997). Accordingly, overall survival has become a widely used endpoint in analysis of the efficacy of locoregional treatment, inevitably neglecting the well known fact that distant metastases have a considerable influence on survival. Hyperfractionated radiotherapy for Stage II-IV NSCLC was tested by RTOG Protocol 8108 (Seydel et al. 1985; Cox et al. 1991a). Using a dose per fraction of 1.2 Gy and interfraction intervals of 4-6 hours the total dose was escalated from 50.4 to 60.0, 69.6 and 74.4 Gy. All of the 41 patients assigned to receive 50.4, 60.0, or 74.4 Gy died before 5 years, whereas for the 79 patients of the 69.6 Gy arm, the 5-year survival rate was approximately 7%. This result obviously was due to a striking imbalance in pre-treatment characteristics among the four dose groups as can be estimated from Table 3.6 which has been produced setting out from Table 1 in the paper of Cox et al. (Cox et al. 1991a). When comparing all 120 patients (column I) to the 79 patients assigned to 69.6 Gy (column II), a balanced distribution of prognostic factors seems to exist. But, when the 69.6 Gy group is compared to the other 3 groups (column III), it becomes obvious that these groups included a considerably higher portion of unfavorable prognosticators. Table 3.7 shows the results of a subgroup analysis performed on 48 clinical Stage II and III patients who were assigned to receive 69.6 Gy. Their 5-year survival rate of 8.3% was similar to the 5.6% survival rate of the control group which consisted of conventionally fractionated RTOG Protocols 78-11 and 79-17. To avoid confusion, the other dose groups are not displayed again in Table 3.7. RTOG Protocol 83-11 randomized 884 patients between total doses of 60.0, 64.8, 69.6, 74.4, and 79.2 Gy given at 1.2 Gy per fraction with interfraction intervals of at least 4 hours (Cox et al. 1990a). When analyzing the 2-year survival rates according to assigned treatment arm no difference between the dose groups could be observed. In a retrospective subgroup analysis of 350 patients with favorable prognostic factors (meeting the inclusion


67


Table 3.6: Pre-treatment characteristics of non-small-cell lung cancer patients in the RTOG 81-08 trial (Cox et al. 1991a). Column I and II are as presented by Cox et al. (1991a), indicating balanced characteristics. Comparison between column II and III shows an imbalance in prognostic factors. I all dose groups (50.4, 60.0, 69.6, and 74.4 Gy)

II dose group 69.6 Gy only

III dose groups 50.4, 60.0, 74.4 Gy separately

T-Stage

T1 T2 T3 T4

1% 35 % 27 % 37 %

0% 39 % 28 % 33 %

3% 27 % 24 % 46%

N-Stage

N0 N1 N2 N3

22 % 15 % 49 % 14 %

28 % 19 % 44 % 9%

10 % 7% 59 % 24 %

n = 120

n = 79

n = 41

No. of patients:

*: not shown in the original publication of Cox et al. 1991

criteria of CALGB Protocol 84-33; Dillman et al. 1990), patients who received 69.6 Gy (± 2.4 Gy) had a superior 2-year survival rate of 35% compared to all other dose groups (range, 13-27%). (In Table 3.7 only results for 60.0 and 69.6 Gy are given). For the difference between the three lower dose groups a p-value of 0.02 was obtained by logrank test, suggesting a dose-response relationship between 60.0 and 69.6 Gy in this favorable subgroup. There are particularly three issues to consider: First, the corresponding p-value of 0.02 can hardly be regarded as reflecting a statistically significant difference when the large number of tests performed is considered (Beck-Bornholdt & Dubben 1994). Second, it remains unclear why no further improvement in survival was observed with higher total doses. Finally, the survival advantage found retrospectively for 69.6 Gy was lost beyond 3 years. The long-term results did not show any difference in 5-year survival rates between the five dose groups: Survival ranged from 6% to 8% for all patients and from 8% to 12% for the subset with favorable prognosticators (see Table 3.7) (Byhardt et al. 1995). A controlled clinical trial randomizing 109 patients between hyperfractionation (69.6 Gy at 1.15-1.25 Gy per fraction twice daily with intervals of ≥ 6 hours) and conventional irradiation (63.9 Gy at 1.8-2.0 Gy per fraction) was conducted in China and published in Chinese (Fu et al. 1994). There appears to exist only an English written abstract, which reported that there was no significant difference in overall survival but in local control between the two arms. In a subgroup analysis on Stage I-IIIA patients, however, 2-year survival and local control rates were enhanced in the hyperfractionation arm: 32% vs. 6% and 28% vs. 13%,

68

3. RESULTS

respectively (p 60 Gy

Frequency of edema (%)

30

10

4

20

10

208

97 24 42

0

4 12

55

46 43

51

60

37

6 5 1

14 9

65

70

Total dose (Gy) Fig.3.9: Frequency of edema after radiotherapy for carcinoma of the larynx. : data published by Hjelm-Hansen (1980). : pooled data published by Overgaard et al. (1988). Numbers indicate the number of patients the data points are based on. 198 patients and 110 patients who received according to Hjelm-Hansen (1980) ≤ 60 Gy or >60 Gy , respectively, were pooled by Overgaard et al. (1988) to 208 and 97 patients who received 57 Gy or 60 Gy. There is, however, no way to reconstruct these pooled data points () from the underlying data ().

textbook as evidence against split-course and against protraction (e.g. Bentzen & Overgaard 1993; Bentzen 1993; Ang et al. 1998; Withers & McBride 1998). For the reasons outlined the evidence provided by this study appears somewhat overestimated. Evidence derived from retrospective studies is currently considered to be of low quality (Shaw 1997; START 1998; Royal College of Radiologists 1996). In all but one of the nonrandomized studies evaluated by Fowler & Lindstrom (1992) it is explicitly stated that patient allocation was biased, e.g. "split-course was initially used only for patients who were in poor condition" (Budihna 1980). Unfortunately retrospective studies of this kind, which are not even well-designed, represent the basis of the guidelines given by the Royal College of Radiologists (1996) which were claimed to be based on the best current evidence, but the results of the randomized studies were ignored.

96

3.3.6.

3. RESULTS

Time dependence of clinical results

Fraction of "positive" publications (%)

A total of 77 publications (2, 3, 10, 11, 15, 51, 62, 67-8, 71, 77, 89, 92, 121, 131, 136-7, 158, 171, 173, 176-7, 179, 190-4, 214-5, 217, 228, 232-3, 237-8, 258, 261-2, 264, 268-9, 273, 276-80, 282, 294-5, 309, 321-2, 329-30, 332-3, 339, 341, 361, 369-71, 380-1, 383, 387, 389, 391, 393-4, 413, 435, 439, 443, 475) on split-course radiotherapy during 1966 to 1998 were found in the Medline data base, most of which are non-randomized and retrospective. Most frequently read sections like title, abstract, and in case there was no abstract, the last part of the conclusions were examined for statements of the respective authors about their treatment results. It was not verified whether statements were indeed supported by the data. Each publication was classified as "positive" (split course gives a better result as compared to continuous), "inconclusive" or "negative". The fraction of positive papers as a function of year of publication is displayed in Fig.3.10. The decrease of this fraction with time is highly significant (p 1982; χ2-Test).


TREATMENT DURATION I: SPLIT-COURSE RADIOTHERAPY

97

This development is paralleled by a change in paradigm about the impact of treatment interruptions. In the 60s there was a consensus that the prolongation of overall treatment time is one of the most important factors for increasing the differential effect between tumor and normal tissue (Consensus of the American Radium Society: Buschke 1963; Sambrook 1964). „During the rest interval, normal tissue proliferates. … In malignant cells … there is very little regrowth during a rest interval of two to three weeks“ (Holsti et al. 1969). Nowadays the opposite is advocated: tumor cells may proliferate even during continuous treatment and normal tissues, the reactions of which are dose-limiting, do not profit from treatment prolongation. It is not reasonable to assume that the effect of a break in radiotherapy on clinical outcome has, in fact, changed from beneficial to detrimental within 20 years. The time-dependent change in treatment outcome (Fig.3.10) is more likely due to publication bias. Therefore it could not be expected to obtain relevant scientific information from re-assessing these earlier papers or to perform a metaanalysis.

3.3.7.

Conclusion

There might be a number of logical or radiobiological ideas or arguments to believe that continuous radiotherapy is superior to split-course treatment. However, a detrimental effect of a break in split-course radiotherapy cannot be derived from non-randomized trials since prescription bias and patient selection bias are very likely explanations for the results observed (Beck-Bornholdt & Dubben 1992, 1996). In particular, the assumption of a 14% loss of tumor control rate per week (Fowler & Lindstrom 1992) that was deduced from a selection of retrospective studies is incompatible with the outcome of randomized trials. All randomized trials on split-course radiotherapy found in a literature search, i.e. all available data that could potentially provide type I evidence, were critically assessed, including a meta-analysis. In terms of local control, or survival if adequate, late normal tissue complications and uncomplicated tumor control rate no evidence favoring continuous or split-course irradiation could be demonstrated. This does not necessarily mean that there is indeed no significant and relevant difference but it implies that the trials performed by now did not adequately address the question. On the basis of presently available data the dose necessary to compensate for a treatment interruption of one week cannot be specified.

98

3. RESULTS


99

3.4.

Treatment duration II: Tumor control dose TCD50 and dose-time prescription1

3.4.1.

Introduction

Provided the time-factor in clinical radiotherapy is caused by proliferation, it is indispensable to distinguish clearly between three time points at which repopulation might occur (Beck-Bornholdt & Dubben 1992): after end of treatment; during the gap in a splitcourse regimen; or during continuous fractionated radiation treatment. In the literature, these different types of repopulation have often been confused. Fast repopulation kinetics after end of treatment and/or the negative impact of treatment prolongation due to a gap has been repeatedly interpreted as evidence of accelerated repopulation during fractionated irradiation. The experimental data published by Hermens & Barendsen (1969) are regularly quoted as a good piece of evidence for accelerated repopulation (Steel 1993; Hall 1994; Perez & Brady 1998). For an experimental tumor, the authors measured the surviving fraction of tumor cells as a function of time after a high single dose irradiation. The results show a dramatic increase of the surviving fraction 5-9 days after treatment. In the textbook by Hall (1994), these data are quoted as evidence for accelerated repopulation: "The important point to note is that, during the time that the tumor is overtly shrinking and regressing, the surviving clonogens are dividing and increasing in number more rapidly than ever". In fact, the clonogen fraction increased but the conclusions drawn seemed to show that the number of clonogenic tumor cells increased. A decade later, the experiments were repeated, and due to more modern techniques it was possible to really measure the number of clonogens in the same tumor system (Beck et al. 1981, Jung et al. 1981, 1990). Apart from a lag period, repopulation kinetics after irradiation did not differ from that of comparable untreated tumors. The experiments clearly showed that the steep increase in surviving fraction was not only due to repopulation of clonogens, but is primarily caused by the depopulation of inactivated tumor cells. The combination of both leads to the dramatic increase in surviving fraction (Jung 1983). Another problem is that the time interval between treatment and recurrence in squamous cell carcinomas is often considered an indicator for accelerated repopulation (cf. Thames et al. 1993). Time to recurrence, however, is obviously a measure of repopulation after end of treatment. Even if repopulation after end of treatment would be found to be accelerated, this would not provide evidence for accelerated repopulation during a continuous fractionated irradiation regimen. 1

Main parts of this chapter have been published in: Beck-Bornholdt & Dubben 1992, 1996b; Dubben 1992a, 1993, 1994ab, 1995a; Dubben & Beck-Bornholdt 1996b.

3. RESULTS

100

For logic reasons tumor cell repopulation during a gap of a split-course treatment is exactly the same as after end of treatment to that dose and in that time. This is simply because the second course of irradiation cannot have a retroactive effect on the tumor during the preceding gap. Nevertheless, repopulation during the gap of a split-course treatment is generally used as the major argument in favor of accelerated repopulation during treatment. The most popular examples for this point view are the review article by Fowler & Lindstrom (1992) and the retrospective study by Overgaard et al. (1988) that have already been discussed in the preceding chapter. From a re-analysis of 59 retrospective clinical studies on head and neck cancer, Withers et al. (1988) concluded that the doses required to achieve 50% local tumor control (TCD50) increase with treatment duration by about 0.6 Gy per day. This interpretation is consistent with the idea that clonogenic tumor cells proliferate at an accelerated rate even during continuous fractionated radiation treatment. To overcome the potential hazard from an increase in cell number, Withers et al. recommend shortening of overall treatment time. Even though speculative, this interpretation has been widely accepted and has had and still has a high impact on clinical and experimental radiotherapy. The paper by Withers et al. (1988) is mentioned in nearly every basic radiobiology textbook (e.g.: Steel 1993; Hall 1994; Scherer & Sack 1996; Perez & Brady 1997) and has been quoted 415 times until September 1998 (according to the Science Citation Index). Maciejewski et al. (1991) applied the same kind of analyses to the results of 20 studies on transitional cell carcinoma of the bladder. Here as well, TCD50 was found to increase with treatment duration, which was interpreted by the authors this as evidence for accelerated tumor repopulation during radiotherapy. Shortening of treatment duration in combination with dose reduction, aiming at avoiding severe acute reactions, might result in a diminished local tumor control rate if repopulation is overestimated (Withers 1988; Fowler 1990; Beck-Bornholdt et al. 1991c; Bentzen & Thames 1991). It has also been argued that the relationship between treatment duration and TCD50 might be influenced by the practice of dose-time prescription, i.e. which dose was actually applied in which overall treatment time (Bentzen & Thames 1991; Dubben 1992a). In general, higher doses are associated with longer treatment time and are given to tumor of higher stage and worse prognosis. Longer treatment times are further associated with treatment interruptions which in turn are frequently also related to a worse prognosis. Interruptions are often caused by acute reactions due to higher general morbidity of some patients or due to larger irradiation fields (Lindberg et al. 1988; Royal College of Radiologists 1996). In order to quantify the bias introduced by dose-time prescription habits and to estimate the real impact of treatment time a Monte-Carlo method was used.


TREATMENT DURATION II: TUMOR CONTROL DOSE TCD50 AND DOSE-TIME PRESCRIPTION

3.4.2.

101

Carcinoma of the head and neck

The data of 59 studies on head and neck tumors compiled by Withers et al. (1988) were taken from table 1 in that paper, which specifies the number of patients, dose per fraction, total dose, normalized total dose NTD, treatment duration, local tumor control rate, and the dose required to achieve 50% local tumor control (TCD50). The first five parameters describe the practice of prescription. NTD is the total dose calculated as if it had been given in 2 Gy fractions, assuming α/β = 25 Gy. It differs only slightly from the actually given total dose because of the high α/β-ratio assumed and because in most studies doses per fraction of about 2 Gy were given (Withers et al. 1988). Identical to the procedure used by Withers et al. the tumor control dose TCD50 was calculated from TCD50 = NTD +

1

α eff

× ln( − ln P) − ln( − ln 0.5)

Eq.3.2

where P is the actually achieved tumor control rate. For cell killing by fractionated irradiation, Withers et al. assumed an effective value of D0 = 5 Gy which is equivalent to

α eff = D0−1 = 0.2 Gy −1 . Time factors, measured in Gy/day, are identical with the slope of regression lines in dose-time plots and were obtained from linear regressions. Linear regressions are weighted allowing for the number of patients in the individual studies. TCD50 values, derived from the original tumor control rates, as a function of treatment duration are displayed in Fig.3.11A, which corresponds to Fig.1 in the original publication (Withers et al. 1988). Weighted linear regression reveals a slope of 0.48 Gy per day. Table 3.16 shows the time factors and the corresponding confidence intervals. Fig.3.11A suggests that for every additional treatment day the dose has to be increased by 0.48 Gy to achieve the same effect of 50 % local tumor control. The value derived here is lower than the 0.6 Gy per day calculated by Withers et al. who excluded data below 28 days; the argument was that there is a proliferation lag-phase of about 4 weeks. In Fig.3.11A, all data were used for calculating the time factor with linear regression. In order to apply a rigid test to the data analyzed, tumor control rates were replaced by the corresponding failure rates, i.e. control rate P was replaced by failure rate 1−P. (For example, a control rate of P = 0.2 was replaced by 1−0.2 = 0.8.) By doing so, the worst treatment becomes the best and vice versa. All further data remained unmodified. Subsequently TCD50 values were calculated exactly like before and related to treatment time in Fig.3.11B. Even though treatment outcome was inverted, TCD50 still increases with

3. RESULTS

80

Tumor control dose TCD 50 (Gy)


102

A

70

60

50

40

80

B

70

60

50

40 10

20

30

40

50

60

10

70

20

80

30

40

50

60

70

60

70

Overall treatment time (days)

Normalized total dose NTD (Gy)



C

70

60

50

80

D

70

60

50

40

40 10

20

30

40

50


60

70

10

20

30

40

50


Fig.3.11: Radiation dose versus treatment duration for 59 studies on head and neck cancer. TCD50 and time factors were calculated by means of linear regression using four sets of data: A: the original control rates (Withers et al, 1988); B: failure rates; C: random numbers; D: prescribed dose. The time factors derived for A to D are 0.48 Gy/day, 0.49 Gy/day, 0.47 Gy/day, and 0.48 Gy, respectively. Solid line in all panels: linear regression fit to the data in panel A. (There may be less than 59 symbols in a panel due to coincidences.)

virtually the same increment of 0.49 Gy per day. This value does not differ significantly from the increment derived from the real data (Table 3.16) and suggests that local tumor control rate has little impact in this kind of evaluation. In another rigid test, actual local tumor control rates were replaced by random numbers generated for the range from 0.15 to 0.85, which corresponds to the range of the original data. TCD50 values of these fictive tumor control data were again calculated from Eq.3.2 and related to treatment time (Fig.3.11C). Again weighted linear regression reveals essentially the same increase of TCD50 with treatment time (0.47 Gy per day). The results obtained from three independent sets of random numbers are compiled in Table 3.16. The prescribed dose NTD is plotted versus overall treatment time in Fig.3.11D. Linear regression reveals that prescribed dose increases by 0.48 Gy per day (Tab.3.16). The dose increments per day displayed in Figs.3.11A-C and Table 3.16 do not differ significantly from each other. Thus, TCD50 increases with about 0.48 Gy per day, no matter H.-H. DUBBEN: STUDIES ON RADIOBIOLOGICAL PARAMETERS RELEVANT TO QUANTITATIVE RADIATION ONCOLOGY

103

TREATMENT DURATION II: TUMOR CONTROL DOSE TCD50 AND DOSE-TIME PRESCRIPTION

Table 3.16: Time-factors calculated from different TCD50 data sets

Fig.3.11A Fig.3.11B Fig.3.11C not shown not shown Fig.3.11D

TCD50 (original data)# TCD50 (Inversion)* TCD50 (Random )** TCD50 (Random )** TCD50 (Random )** NTD (original data)

Time-factor (Gy/day) 0.48 0.49 0.47 0.50 0.48 0.48

95% confidence interval 0.38 - 0.58 0.36 - 0.61 0.34 - 0.59 0.37 - 0.62 0.34 - 0.62 0.38 - 0.58

Original data were taken from Withers et al. 1988. TCD50 was calculated from local control rate P of the original data (#), from the failure rate 1 - P (*) or from three independent sets of random numbers (**) replacing the authentic tumor control rates. NTD: normalized total dose (assumed to be given in 2 Gy fractions).

whether it is derived from the actual tumor control rate P, or from the failure rate 1-P, or from meaningless random numbers. In other words, the actual treatment outcome seems to be totally irrelevant for the TCD50-time relationship. Obviously the time-factor does only depend on the prescription habits. Fig.3.12 shows local tumor control rate as a function of normalized total dose NTD. There is no significant impact of dose on tumor control rate (weighted linear regression: p=0.14). Local control rates seem to scatter randomly between 0.15 and 0.85. This leads to the conclusion that control rate P may be regarded as constant on average in Fig.3.12. If it is assumed that control rate P is exactly constant, the second term in Eq.3.2 will be constant as well. In this case Eq.3.2 can be written as TCD50 = NTD + c

Eq.3.3

which is the equation of a straight line (c is a constant positive or negative number, depending on the actually inserted value of P. If P = 0.5 is inserted, then is c = 0 and Eq.3.2 turns into TCD50 = NTD). There is a linear relationship between prescribed dose TCD50 and NTD when local control rate is exactly constant, and there is still a linear relation when P is constant only on average. In that case c has not an exact value but introduces scatter into Eq.3.3. This is demonstrated by Fig.3.13 showing a highly significant linear correlation (p 15 mm (= 1.8 cm3). (b) Haustermans et al., 1996. (c) Raaphorst, 1993. Model: P = exp(-V0×n0×exp(-α×D - β×d×D + γ×T)) with α = -0.5×ln(SF2); γ = (ln(2)/ Tpot (a)

Parameter values used: Tpot = 5 days, n0= 1×109 cm-3, SF2 = 0.4, T= 42 days; V0= 30 cm3

Assuming that the number of clonogenic cells is proportional to tumor volume, i.e. N 0 = n 0 × V0 (n0: cell density; V0: volume at start of treatment) and that there is, for simplicity, no fractionation effect (β=0), Eq.1.7 can be written as

Pcontrol = e −n0V0 ×e

− α × D +γ × T

= e −e

ln ( n0V0 ) −αD +γT

γ is related to the cell doubling time TD by

γ = ln 2 T

D

α is related to SF2, the surviving fraction after 2 Gy, by

α=−

1 × ln( SF2 ) 2

Now Eq.1.7 can be written as

Pcontrol = e or equivalently

(

)

ln 2 ln ( n0V0 ) + ln SF2 D 2 + ×T TD −e

144

4. DISCUSSION

Pcontrol = e − n0V0 × SF2

D2

× 2T

TD

Eq.4.13

The terms n0V0 , SF2 D 2 and 2 T TD are mathematically equivalent. Predictions based on SF2 or estimates of tumor cell doubling times are impossible unless tumor volume is specified. Eq.4.13 allows to derive equations that relate tumor volume either to radiosensitivity or to tumor cell doubling time. This allows to estimate how much predictions based on SF2 or TD are confounded by variations in volume. This will be described in the following.

4.3.3.1.

Tumor volume and prediction using the surviving fraction SF2

If it is assumed that there is no proliferation, i.e. TD = ∞ , it follows 2

T

TD

= 1 . To achieve

isoeffectivity at a level of P = 37% (this level was chosen for simplicity. It is P = e-1 = 0.37 = 37%) the term n 0V0 × SF2 V0 =

D

2

must equal 1. From this follows

1 −D × SF2 2 n0

Eq.4.14

Two tumors, I and II, that differ in radiosensitivity SF2 have the same control probability when V0 ( I )  SF2 ( I )  =  V0 ( II )  SF2 ( II ) 

−D

2

Eq.4.15

This volume ratio is shown in Fig.4.9 assuming a total dose D = 60 Gy. A variation of SF2 by ±10%, e.g. SF2 = 0.5 ± 0.05, is equivalent to deviations in volume by a factor of 410. Such variations in SF2 would override almost any volume effect. In practice, however, even volume variations of less than a factor of 10 are detectable. It is therefore concluded that variation of SF2 between patients is considerably smaller than 10%, apart from rare disorders like ataxia telangiectasia which is associated with extraordinary high radiosensitivity. Quantitatively these estimates only depend on the assumption of a total dose of 60 Gy given in 30 fractions. At higher doses the same variation of SF2 is even more confounding. For illustration, the impact of SF2 on tumor control probability is shown in Fig.4.10. Apparently, if SF2 varies by 10% or more, any other effect is likely to be obscured. To elucidate this point further, the impact of tumor volume on tumor control rate in heterogeneous patient groups was simulated. Patient groups with different dispersion but equal


145

TUMOR VOLUME IN STUDY DESIGN

1000.000

V0(I) / V0(II)

100.000 10.000 1.000 0.100 0.010 0.001 0.8

1.0

1.2

SF2(I) / SF2(II)

Fig.4.9: Comparison of the effect of changes in SF2 and changes in tumor volume. V0(I) and V0(II) or SF2(I) and SF2(II) represent the volume or SF2 values for tumor I and tumor II, respectively. For example, variation of SF2 by 10 % (i.e. SF2(I)/SF2(II)=1 ± 0.1) corresponds to volume variation by a factor of 410.

mean values of SF2 were generated and the theoretical outcome of radiotherapy was calculated as a function of tumor volume. The results in terms of volume-response curves are depicted in Fig.4.11 and compared with the clinical data discussed in section 3.1. Volume response curves are less steep with increasing dispersion. A dispersion of SF2 by more than 0.05 (i.e.10%) seems to be incompatible with clinical observation. Again the maximum conceivable variation of SF2 seems to be less than 10% and, thus, SF2 appears to be relatively homogenous. Since the precision of measured SF2-values is ± 17% (Raaphorst 1993) predictions on the basis of SF2 appear to be impossible with current techniques.

1.0

Local control rate

0.8

0.6

SF2 = 0.5 ± 10%

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

SF2

Fig.4.10: Local tumor control after 60 Gy total dose as a function of surviving fraction SF2.

146

4. DISCUSSION

1.0

Head and neck (Hjelm-Hansen 1979) Head and neck ( van den Bogaert 1995) Head and neck (Johnson 1995a) T3 glottic larynx (Pameijer 1997) Melanoma (Overgaard 1986) Breast cancer (Arriagada 1985) Cervix cancer (Mendenhall 1994)


0.8

0.6

Cervix cancer (Magee 1991)

0.4 SF2 = 0.5 ± 0.15 SF2 = 0.5 ± 0.1

0.2

SF2 = 0.5 ± 0.05 SF2 = 0.5 ± 0

0.0 0.01

0.10

1.00

10.00 100.00

Relative volume

Fig.4.11: Volume response curves obtained from a simulation of radiotherapy. It was assumed that all patient groups had same mean radiosensitivity characterized by SF2 = 0.5 but dispersion of SF2 was different. Calculations were performed for various standard deviations ranging from 0 to 0.15. The clinical data plotted for comparison are taken from Fig.3.3 and Fig.3.4, respectively.

4.3.3.2.

Volume and prediction using potential doubling time Tpot

Clinical trials could not demonstrate that potential doubling time and repopulation in tumors are significant prognostic factors (Hoyer et al. 1988; Begg et al. 1992, 1993). The argument that repopulation is a main cause for treatment failure is based on the idea that more clonogenic tumor cells are left at the end of therapy than expected without repopulation. There are also more cells left at the end when treatment starts at a higher number of tumor cells as compared to a lower number. This is schematically presented in Fig.4.12. According to Poisson statistics, an average of one single clonogenic tumor cell left at end of treatment translates into tumor control probability of 37%. This can be achieved, other factors being equal, with a large but slowly proliferating tumor or with a small but fast growing tumor. A quantitative estimation whether volume dispersion might obscure proliferation effects can be made using Eq.4.13. The equation yields for the constant effect P = 37% (i.e. for one remaining clonogenic tumor cell): n 0V0 × SF2 D 2 × 2 T TD = 1 H.-H. DUBBEN: STUDIES ON RADIOBIOLOGICAL PARAMETERS RELEVANT TO QUANTITATIVE RADIATION ONCOLOGY

147

Number of clonogenic cells

TUMOR VOLUME IN STUDY DESIGN

large and fast large and slow small and fast

1

small and slow start

Time →

end

Dose →

Fig.4.12: Schematic visualization that equal tumor control probability (e.g. of 37% corresponding to one remaining clonogenic tumor cell after treatment; horizontal dotted line) may be achieved for large but slowly proliferating tumors as well as for small but fast proliferating tumors.

From this follows V0 = SF2 − D 2 × 2 − T TD × n 0 −1

Eq.4.16

Variation of tumor size was not reported for the EORTC 22851 trial (Begg et al. 1992) that was designed to measure the impact of doubling time on tumor control rate. In the similar trial EORTC 22811 volume varied by more than a factor of 100. The relationship of volume and doubling time (Eq.4.16) is illustrated in Fig.4.13. For example, a tumor of 0.1

100.00

Volume (cm3)

10.00

1.00

0.10

0.01 2

4

6

8

10 12 14 16 18 20

Doubling time (d)

Fig.4.13: Theoretical equivalent of changes in doubling time TD and changes in tumor volume (Eq.4.16). Parameters: D = 72 Gy in T =32 days (as applied in the EORTC 22851 trial) and n0 = 109 cells per cm3, SF2=0.5. Horizontal lines indicate a variation in tumor volume by a factor of 100 (dotted) or a factor of 3 (dashed). The latter corresponds to a precision in volume measurement of ± 50%.

148

4. DISCUSSION

cm3 and a doubling time TD = 3.5 days and another tumor of 10 cm3 and TD = 11.5 days have equal control probability. The range of doubling times measured by Begg et al. (1992) was 1.4 to 17 days. A persistent significant correlation between doubling time and control rate could not be established by Begg et al. It is conceivable that heterogeneity in tumor volume obscured a potential effect of proliferation. Thus, without estimating the number of tumor cells (or tumor volume as an approximation) proliferation rate alone is not likely to be predictive for treatment outcome.


149

4.4.

General discussion

The linear-quadratic model is not in conflict with many clinical results and in good agreement with some results. Due to an inherent statistical obstacle in demonstrating isoeffects, the linear-quadratic model is not only supported when it is true. Trials with insufficient power, due to low number of patients and/or heterogeneity, are likely to support the model even if it is false. In addition, even with perfectly conducted trials, it is principally impossible to prove the validity of a model. The discussion of the Ellis formula and the linear-quadratic model in context with the hyperfractionation study EORTC 22791 (section 4.2.1.) demonstrates that support by data is not a proof. Other models can describe the same data as well and, of course, suffer from the same problems. In addition, model parameters determined from clinical data cannot always be interpreted unequivocally. Much of the dose-time discussion in radiotherapy of the last 10 years and at present (e.g. Robertson et al. 1998) is about the problem to distinguish cause and consequence. Patients with bad prognosis are more likely to require a break during treatment than patients with better prognosis. As a consequence, treatment breaks and the corresponding prolongation of overall treatment duration are frequently correlated with bad prognosis, thereby pretending a time factor. In that case, however, prolongation is not the cause but the consequence of bad prognosis. Results conflicting with the linear-quadratic model were obtained from several randomized trials. In a randomized hyperfractionation trial on head and neck cancer (Marcial et al. 1987) late reactions increased after lowering both total and fractional dose. This deviation from the prediction of the linear-quadratic model is statistically significant (p=0.029; onesided∗ χ2-test). Hypersensitivity to low dose fractions, which is not predicted by the linearquadratic model, cannot be ruled out on the basis of presently available clinical data and is, though not definite, suggested by the outcome of some trials. Results incompatible with the linear-quadratic model were also obtained from the randomized radiotherapy trials with the highest power and strongest rigor, the CHART trials (Dische 1997, Saunders 1997) on hyperfractionated accelerated radiotherapy. The outcome of a randomized trial on purely accelerated radiotherapy (Jackson et al. 1997) is also conflicting. Assumptions such as long repair half-times of sublethal damage or consequential late damage may explain the outcome. Yet these assumptions are not considered in the linear-quadratic model. A research strategy is to hypothesize that a model is valid, to predict the outcome of an experiment and to perform the experiment. When the experiment had no methodological ∗

A one-sided significance test is justified since only deviations in one direction were foreseen by the linearquadratic model.

150

4. DISCUSSION

flaws and the resulting data are incompatible with the model it may be assumed that the model is incorrect, at least partially. With inclusion of additional mechanisms such as hypoxia, hypersensitivity, and consequential late damage as additional necessary explanations for contradicting results, the LQ model becomes non-refutable and, from the scientific point of view, less credible. In some situations, clinical outcome differs from the prediction of the linear-quadratic model. This does not necessarily mean that the model is wrong in describing cellular response to irradiation but it is conceivable that other mechanisms are prevailing. The transferability of the linear quadratic model into the clinical situation is not self-evident. To establish the linear-quadratic model, to derive its isoeffect relationships, and to develop potential clinical strategies required several assumptions that are not necessarily fulfilled. There are various points to be considered: − The linear-quadratic formula has been derived from in vitro data. The logarithm of the surviving fraction plotted versus dose reveals a linear-quadratic shape. It is assumed that human cells in vivo also follow this relationship in the entire clinically relevant dose range. − It is assumed that there is one population of target cells or TRUs even in complex normal tissues and that the depletion of these cells or units is related to the probability of complications. The outcome of reciprocal dose plots of experimental data is frequently consistent with this idea but this line of evidence is indirect and, thus, does not prove the existence of such target cells. − It is assumed that in fractionated irradiation every single dose fraction has the same effect. Some data indicate that the situation is much more complex and that other phenomena such as cell cycle effects or different oxygen status during radiotherapy may invalidate the assumption. − It is assumed that the model is also valid for tumors even though, in general, tumors contain a subpopulation of hypoxic cells of reduced radiosensitivity in a tumor. It has been shown that the dose response curve of tumor cells in vivo is not linear-quadratic (cf. Powers & Tolmach 1963) but the slope decreases with increasing dose (cf. Hall 1994). − It has been learned from clinical trials that doses per fractions considerably larger than 2 Gy are detrimental (Montague 1968; Singh 1978; Overgaard et al. 1987; Horiot et al. 1992). The inverted conclusion, i.e. that smaller doses per fraction are beneficial, is an extrapolation to low doses which is only sparsely substantiated by data (Fig.1.13, data below 2 Gy). There are some data suggesting an increasing sensitivity to radiation when dose per fraction was lowered beyond 2 Gy (Stewart et al. 1984; Ang 1985; Joiner et al. 1986, 1993; Parkins & Fowler 1986; Joiner & Johns 1987, 1988; Joiner 1989). These observations clearly contradict the linear quadratic model.


151

− Incomplete repair is not regarded for in the LQ-model and there is experimental evidence that repair kinetics in tissues may have more than one component. This concerns strategies like accelerated radiotherapy and hyperfractionation when time intervals between fractions are reduced as compared to standard treatment. − Tumor data on fractionation are not unequivocal. A therapeutic benefit from lowered dose per fractions cannot be expected in general (Fig.1.15). The linear-quadratic model fails to predict radiotherapy outcome reliably, especially when newly designed schedules differ substantially from standard treatment. Discrepancies between prediction and outcome can, in general, be explained by considering additional phenomena that are not included in the linear-quadratic model such as incomplete repair, hypersensitivity, hypoxia, etc. in retrospect. This should be kept in mind when designing new treatment schedules prospectively using the linear-quadratic model. Beyond any doubt, retrospective analysis of clinical data is a time consuming and difficult work. The initiation and conduct of prospective multicentric randomized clinical trials is even more laborious and the few clinical scientists in the field who have initiated such a challenging endeavor and brought it to a fruitful end deserve respect. Notwithstanding, appreciation does not discharge from having a critical second look even on outstanding studies. Standard radiotherapy with 2 Gy fractions and five fractions per week is an important and indispensable clinical modality in the treatment of cancer. It appears difficult to proof further advancement of radiotherapy by exploiting biological differences between tumor and normal tissue. Modification of treatment parameters do not necessarily translate into unequivocally interpretable changes of outcome. There might be two reasons: 1.) current standard dose-time prescription in radiotherapy is already close to an, possibly broad, optimum and 2.) statistical and methodological flaws and inherent problems in radiotherapy trials. Adequate data acquisition in radiotherapy is extremely difficult. Long follow up times up to 10 years or even longer are required to obtain reliable information about treatment outcome in terms of tumor control and especially late side effects. Studies initiated today will yield results only in many years, and their validity will be assessed using the quality standards of tomorrow. This makes it even more important to implement the most valid, stringent and up to date trial design in radiotherapy. In terms of Evidence Based Medicine, which presently is a driving force in development of such standards, no class I evidence concerning hyperfractionation is available. A therapeutic gain for T3-tumor patients is suggested from the EORTC 22791 trial but the evidence is not unequivocal. Class I evidence against the validity of the linear-quadratic

152

4. DISCUSSION

model at doses below 2 Gy may be deduced from the trial by Marcial et al. (1987) because of significantly increased late reactions after reduction of both total and fractional dose. This is, however, no really convincing class I evidence since it was not the primary endpoint of the studies. The CHART trial on non-small-cell-lung cancer (Saunders et al. 1997) would provide class I evidence concerning acceleration in radiotherapy if the caveat is neglected that different patient compliance might have favored the CHART arm. Class I evidence against the combination of hyperfractionation and acceleration with split-course is provided by the randomized trial EORTC 22851 by Horiot et al. 1997. Quantitative clinical radiobiology appears to be only sparsely based on evidence. Clinical research in radiotherapy has been intensified during the last two decades and there is an increasing number of randomized controlled radiotherapy trials. Yet in many of these trials serious methodological problems continue to exist. It is important to recognize these problems in order to improve the situation. Power As outlined in detail, low power, i.e. a high risk for Type II errors, is a major source for false negative results. Freiman et al. (1978) examined 71 "negative" randomized controlled trials published in the Lancet (19), New England Journal of Medicine (11), Journal of the American Medical Association (6), and other journals (35) during 1960 to 1977. A trial was designated "negative" when the authors explicitly stated that a significant difference (p