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Hospital length of stay and probability of acquiring infection Mahmud Hassan Rutgers Business School – Newark and New Brunswick, Newark, New Jersey, USA

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Howard P. Tuckman Fordham University, New York, New York, USA

Robert H. Patrick Rutgers Business School – Newark and New Brunswick, Newark, New Jersey, USA

David S. Kountz Jersey Shore University Medical Center, Neptune, New Jersey, USA, and

Jennifer L. Kohn Drew University, Madison, New Jersey, USA Abstract Purpose – Hospital-acquired infection (HAI) poses important health and financial problems for society. Understanding the causes of infection in hospital care is strategically important for hospital administration for formulating effective infection control programs. The purpose of this paper is to show that hospital length of stay (LOS) and the probability of developing an infection are interdependent. Design/methodology/approach – A two-equation model was specified for hospital LOS and the incidence of infection. Using the patient-level data of hospital discharge in the State of New Jersey merged with other data, the parameters of the two equations were estimated using a simultaneous estimation method. Findings – It was found that extending the LOS by one day increases the probability of catching an infection by 1.37 percent and the onset of infection increases average LOS by 9.32 days. The estimation indicates that HAI elongates LOS increasing the cost of a hospital stay. Research limitations/implications – The findings imply that studies on cost of HAI that do not properly control for the simultaneity of these two variables, will result in a biased estimation of cost. Originality/value – The study produces quantitative estimation of the extent of interdependency of hospital LOS and the probability of catching an infection. Keywords United States of America, Hospitals, Patients, Bacteria, Immunologic diseases Paper type Research paper International Journal of Pharmaceutical and Healthcare Marketing Vol. 4 No. 4, 2010 pp. 324-338 q Emerald Group Publishing Limited 1750-6123 DOI 10.1108/17506121011095182

The authors thank the Department of Health and Senior Services, State of New Jersey, for providing UB 92 data for 2004, also the AHA for providing a set of hospital specific data for the research. The authors have no conflicts of interest and/or any financial interest, relationship, and affiliation with the subject matter or materials of this research.

Introduction Patients acquiring infections while being treated at hospitals pose important health and financial problems for society. For example, nearly 5 percent of admitted patients developed hospital-acquired infections (HAIs) in 2002 and nearly 6 percent of them died (Consumers Union, 2007). Many more were required to stay in the hospital for extended periods and some suffered serious health problems as a result. There has been an increase in HAI over the past few decades despite increasing attention to the issue and the implementation of several infection control measures. While fewer patients have been admitted to US hospitals (36 million in 1995 versus 38 million in 1975) and length of stay (LOS) has shortened (from 7.9 to 5.3 days), the number of nosocomial infections has increased from 7.2 per 1,000 patient-days to 9.8, in part because hospital inpatients are older and sicker now than in the 1970s (Stone et al., 2002; Burke, 2003). Because of numerous identifiable and unidentifiable co-founders including age and underlying illness, it is difficult to conclude that infection control procedures have been unsuccessful and it has not been easy to identify the incremental costs associated with nosocomial infections. This is unfortunate, since this type of information would be valuable to administrators, researchers, and public policy analysts who are concerned with these and related questions. HAI imposes costs on both patients and society in the form of work time lost, increased resources needed to cure HAI patients, and psychological and emotional suffering. In many cases, the onset of HAI extends LOS, requires costly diagnostic tests and additional drugs, and complicates treatment of the original diagnosis that brought the patient to the hospital. It increases the cost to public programs like Medicare and Medicaid, and it requires higher premiums for medical insurance and higher payments from patients. Indeed, HAI has become sufficiently pervasive to warrant many states mandating public reporting of HAI rates and it has caused Medicare to limit coverage of HAI if it occurs due to hospital error. Understanding the causes of infection in hospital care is strategically important for the hospital administration for formulating effective infection control program. Owing to increased public and media scrutiny of hospital care, many states mandate public reporting of infection rates that drive patients away from the high-rate hospitals to low-rate ones because of differences in perceived quality of care (Gooding, 1995; Solaiman, 1992). Moreover, quality of care affects hospitals’ profitability negatively (Hegji et al., 2007). Inpatient stays in hospitals could also affect the incidence of HAI due to cross contamination, patients’ susceptibility to infection, and other clinical and non-clinical reasons. In this paper, we investigate the relationship between LOS and HAI. Specifically, we estimate the marginal probability of HAI for an increase in LOS and the additional days of stay in the hospital of a patient who acquires an infection. The interdependency between LOS and the incidence of hospital-acquired infection (INFECT) is well documented in the literature studying cost of hospital-acquired infections (COST) (Plowman et al., 2001; Graves et al., 2005; Kilgore et al., 2008). The COST equation is typically specified as a function of LOS, INFECT, and a set of control variables some of which are explanatory for both variables. Some studies attempt to capture this interdependency using instrumental variable techniques to adjust for the possible bias in estimating the cost of HAI (Plowman et al., 2001; Graves et al., 2005). Alternatively, some researchers such as Kilgore et al. (2008) adjust

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their cost estimates using a sensitivity analysis of different samples using groups with different LOS. Depending on the method and model used in research, the literature reports the cost estimate to vary from $5 to $29 billion (Wenzel, 1985). In another paper, we estimate the cost to be $16.6 billion in 2004 (Hassan et al., 2010). To date, there has been no study quantifying the extent of interdependency between LOS and INFECT. It is not only of academic interest to quantify the relationship, but also an important piece of information for policymakers and hospital administrators in formulating an optimal infection control program. Our study develops a robust econometric method for exploring the extent of interdependency between these two variables and estimates the marginal probability of acquiring an infection for an additional day of stay at a hospital. This should be of interest to policymakers who seek to provide guidance in HAI control programs. Conceptual framework While patients are admitted into hospitals for the treatment of a variety of health problems, unfortunately in some instances, many of those patients acquire infections while receiving care for the ailments for which they were admitted in hospitals in the first place. The causes of acquiring infections vary by the conditions of the individual patients and the types of procedures performed on those patients. The list of those possible causes include different surgical and therapeutical procedures, patients’ age, co-morbidity (CM), severity of the health condition, hospital characteristics, such as, intensity of nursing care, cross contamination, extent and scope of the hospitals’ infection prevention program, and many other factors. Once an infection is acquired, the patient’s LOS in the hospital gets extended beyond the infection free case. Some patients are more susceptible to acquire infections due to the presence of CM and other health conditions. As the LOSs of these patients increase while they receive the inpatient care for the conditions that brought them in the hospital, the probability of their acquiring infection also increases. Hence, as the HAI increases the LOS of the patient, the probability of acquiring an infection also increases as the LOS of a patient increases. To estimate the extent of interdependency between LOS and INFECT, we need to specify a simultaneous equations system that explains both LOS and INFECT. The determinants of hospital LOS have been studied by many (Burns and Wholey, 1991; Mark and Harless, 2007; Lee and Anderson, 2007; Carey et al., 2009; Lin et al., 1999). Those have also been studied in the context of cost of HAI by Graves et al. (2005) and Kilgore et al. (2008). The most important factors identified in those studies affecting the LOS are patients’ age and severity of illness. The other factors found to be important are patients’ gender, whether the patient had a surgical procedure, and whether the admission was routine or urgent. The literature also identifies several factors affecting the likelihood of acquiring infection in hospitals. The Harvard Medical Practice Study II found the presence of a surgical wound infection is a dominant contributor to adverse events in hospitals (Burke, 2003). Patient’s severity of illness, invasive diagnostic, and therapeutic procedures are also important factors affecting the likelihood of HAI. Costantini et al. (1987) and Swartz (1994) identify patient’s age, the use of extensive surgical and intensive medical therapies, and frequent use of antimicrobial drugs as factors of HAI. A CDC report using the National Nosocomial Infections Surveillance System data finds the HAI rate to be higher at the large teaching hospitals than in small teaching

or non-teaching hospitals (Horan et al., 1986). Hospitals with higher nurse staffing intensity typically provide care at a higher quality, lowering the likelihood of adverse events (Mark and Harless, 2007; Carey et al., 2009). Some of the factors identified above are common to both LOS and INFECT, i.e. age, surgery, and severity of illness. Several factors are unique to each, i.e. patient’s gender and mode of admission for LOS, diagnostic and therapeutic procedures, hospital’s teaching status, and nurse staffing intensity for INFECT. We specifically designate the system as follows: LOS

¼ f (INFECT, age, gender, surgery, severity of illness, and mode of admission).

INFECT ¼ f (LOS, age, surgery, severity of illness, teaching status of the hospital, diagnostic and therapeutic procedures, hospital’s quality indicators, and measure of patient congestion). The two-equations model is more explicit in terms of how the interdependency between LOS and INFECT operate than has previously been available in the literature. We would expect that the findings of our research will create greater interest in exploring HAI in a broader framework. Methods Our approach specifies a continuous/discrete model comprised of the following system of equations: LOS ¼ a0 þ a1 INFECT þ ak Xk þ u1

ð1Þ

INFECT ¼ b0 þ b1 LOS þ bn Xn þ u2

ð2Þ

where Xk and Xn are vectors of exogenous variables, and u1 and u2 are the error terms. LOS is a continuous variable measured in days while INFECT is a binary variable measured as 1 if a patient develops infection while in hospital, and 0 otherwise. We define incidence of infection (INFECT) as a binary value for a patient matching the patient’s ICD-9-CM codes with the relevant infection ICD codes as reported in the literature (Platt et al., 2002; Needleman et al., 2002; Rubin et al., 1999). The list of the infection ICD codes is shown in the Appendix 1, Table AI. The vector Xk consists of patient’s age, gender, having a surgical procedure, severity of illness, and mode of admission into the hospital. The vector Xn consists of patient’s age, gender, having a surgical procedure, severity of illness, having diagnostic and therapeutic procedures, hospital’s teaching status, and quality of care indicators. The variable definitions and measurements are shown in Table I. Severity of illness is denoted by CM; diagnostic and therapeutic procedures are represented by three binary variables “nasogastric tube insertion (NGT)”, “endotracheal suction (ES)”, and “OT”; hospital’s teaching status is represented by “INTERN”; hospital’s quality of care indicators are denoted by two variables “NURSESHR” and “MEDICAID”; finally, patient congestion is measured by two variables – “number of beds” and the “occupancy rate”. Both the equations are over identified using the order condition and identified using the rank condition. To test for endogeneity of INFECT in the LOS equation, using the methodology described in Wooldridge (2009), we used a two-step process: first, estimate


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Table I. Definition of variables and descriptive statistics

Infect LOS Age Surgery Urgent NGT ES OT Female CM Intern Medicaid Nurseshr

Infection Min. Max. SD

Mean

No infection Min. Max. SD

Mean

Combined Min. Max.

SD

Infection binary – – – – – – – – 0.0640 – – – Length of stay 10.0097 0 90 10.1228 3.2441 0 90 4.9497 3.6768 0 90 5.6769 Age in years 65.8932 0 108 21.5893 47.7823 0 124 26.2199 48.9407 0 124 26.3242 Surgery binary 0.0914 – – – 0.1803 – – – 0.1746 – – – Urgent admit binary 0.8663 – – – 0.4780 – – – 0.5029 – – – Nasogastric tube bin 0.0720 – – – 0.0097 – – – 0.0138 – – – Endotrac suc bin 0.0614 – – – 0.0119 – – – 0.0150 – – – Oxygen therapy bin 0.0035 – – – 0.0013 – – – 0.0015 – – – Gender binary 0.6103 – – – 0.5765 – – – 0.5787 – – – Number of diagnosis 7.3617 1.0 9.0 1.9819 3.8056 0 9 2.6501 4.0331 0 9 2.7536 Internee to bed ratio 0.1264 0.0 0.7037 0.1504 0.1282 0.0 0.7037 0.1489 0.1281 0.0 0.7037 0.1490 Mcaid to tot pat days 0.1497 0.0183 0.5152 0.0965 0.1555 0.0183 0.5152 0.1010 0.1552 0.0183 0.5152 0.1008 Nurse to FTE ratio 0.2897 0.1626 0.7716 0.0782 0.2891 0.1626 0.7716 0.0822 0.2892 0.1626 0.7716 0.0819

Mean

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Variables Definition

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the residuals of the reduced form of LOS, then in the second stage we estimate the structural LOS equation as specified in equation (1) with the residual from the reduced form added as one of the explanatory variables and performing a t-test on the parameter estimate of the residual. The estimate is found to be significant at 1 percent level. The results are shown in Appendix 2, Table AII. Partial correlation between LOS and INFECT is 0.2916 which is significant at 1 percent level. We checked for the presence of multicollinearity among the explanatory variables of the model by computing variance inflation factors (VIF) and the condition numbers (CN) in the reduced form regression of LOS. Both the measures confirm that the model is free from multicollinearity problem, see Appendix 3, Table AIII for the results. We estimate equations (1) and (2) in a simultaneous equations system using the LIMDEP econometric software and, because of the skewed distribution of the binary variable INFECT, equation (2) is estimated as a logistic model. Data The analysis presented below uses UB-92 billing data to identify the incidence of HAI and LOS. Unfortunately, nosocomial infections do not have a single ICD-9 code and the CDC defines nosocomial infections based on a complex algorithm using clinical information only accessible through chart review (Horan and Gaynes, 2004). Hence, the database has some loss of precision in diagnosis but this is offset by a significantly larger sample size and much greater scope relative to that offered by studies that rely on chart-based data. Several papers previously explored the accuracy of billing data in identifying patients with HAI and some specifically compared indications of nosocomial infection in chart data and billing data. Ollendorf et al. (2002) compared retrospectively the UB-92 data and clinical charts of 122 patients and found that 75.4 percent of patients with clinically documented sepsis had relevant ICD-9 codes. Platt et al. (2002) analyzed infection post-coronary artery bypass surgery and infection was confirmed in 58 percent of those patients who had an infection indicator in their claims data. This study found significant variability among institutions and speculated that differences between hospitals’ proportions of patients with infection indicator codes might reflect either a real difference in the risk of infection or systematic differences in the way a hospital assigned diagnosis and procedure codes or reported them to payers. Zhan and Miller (2003) and Kilgore et al. (2008) used publicly available administrative datasets for conducting studies on HAI and obtained similar results as in this paper. The State of New Jersey’s Universal Billing (UB-92) database includes all patients admitted into NJ hospitals in 2004. As cost outlier patients are reimbursed at different rates by some payers including Medicare, we followed Sloan et al. (2001) and Taylor et al. (1999) in excluding patients with LOS in excess of 90 days to minimize administrative interventions in LOS management. We also excluded data for the newborns. The UB-92 dataset contains most of the variables used in this study but we added data from the American Hospital Association (AHA)’s annual survey of hospitals in 2004 that include the internee to bed ratio (INTERN), the ratio of Medicaid patient days to total patient days (MEDICAID), and the share of nursing staff in the total full-time equivalent number of employees (NURSESHR). The final count of the number of patients used in the analysis is 1,547,702.


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Table II. Two-step estimation for the system of equations model

Results Descriptive statistics along with the definition of the variables in the study are provided in Table I. The overall rate of infection (INFECT) is estimated to be 6.4 percent of all admitted patients, which is a slight bit on the high side compared to the rate reported elsewhere;, i.e. 5.7 percent by Haley et al. (1985). Given a higher concentration of larger teaching hospitals in New Jersey, this difference is plausible as documented by Horan et al. (1986). LOS for HAI patients is estimated to be 6.76 days longer than for the non-infected patients. This represents a significant increase in LOS compared to the LOS for the population as a whole (3.67). A large majority of infected cases were admitted on an urgent (URGENT) basis, 86.6 percent for infected and 47.8 percent for the non-infected cases. Extent of CM, measured as the number of diagnoses recorded for the infected patient group, is 7.36 as compared to 3.8 for the non-infected group. Several procedures performed on patients who acquired infections are performed more frequently than for non-HAI patients; NGT is over seven times higher, 7.20 percent vs 0.97 percent, and ES is over five times higher, 6.14 percent vs 1.19 percent. Clearly, these additional procedures increase the cost of hospital care. Next, we turn to the results of the model as specified in the methodology section. The estimated coefficients for equations (1) and (2) are shown in Tables II and III and all of the estimated coefficients are significant at 1 percent level. INFECT and LOS affect each other positively, confirming findings reported elsewhere in the literature (Graves et al., 2005; Plowman et al., 2001). Specifically, INFECT increases LOS by 9.3 days and an increase in LOS by one day increases the probability of catching an infection in the hospital by 0.0137. An increase in CM by one additional diagnosis increases LOS by about one day. If a patient is admitted on an urgent basis, he/she is likely to have an additional LOS of 1.5 days. Since our dataset includes children as well as those over 65, we added a non-linear term for age (AGE) and found that this has a U-shaped affect on LOS. The inflection point is computed at 74 years (0.0889/0.0012). If a patient has surgery, this increases the probability of HAI by 0.0096. An increase in CM by one additional diagnosis raises the probability of catching an infection by 0.0001. An increase in nursing staff share (NURSHSHR) measured as the ratio of the number of nurses to total full-time employees increases the probability of HAI by 0.0072. This result is counter intuitive but plausible for the hospitals with more unskilled nurses. Similarly, a higher internee (INTERN) ratio also increases the probability of acquiring an infection. This is consistent with the finding of Horan et al. (1986) that shows that teaching hospitals have higher infection rates than non-teaching hospitals. Variable

Coefficient *

Constant Infect Age Age2 Female Surgery CM Urgent

1.4107 9.3360 20.0889 0.0006 20.0471 20.1907 0.9635 1.4796

Notes: *Significant at 1 percent level; adj R 2 ¼ 0.2526; dependent variable – LOS

SE 0.0123 0.0831 0.0005 0.0000 0.0080 0.0111 0.0019 0.0091

Variable

Coefficient *

SE

Marginal effect

Constant LOS Age Surgery CM Intern Medicaid Nurseshr NGT ES OT Beds OCC

2 5.4642 0.5427 0.0084 0.3501 0.0059 * * 0.3016 2 1.3866 2 0.0031 * * 2 2.4490 2 3.5173 2 0.9748 0.0001 2 0.0053

0.0286 0.0060 0.0002 0.0132 0.0056 0.0305 0.0457 0.0492 0.0398 0.0444 0.0638 0.0000 0.0002

20.1369 0.0137 0.0002 0.0098 0.0001 0.0076 20.0347 20.0008 20.0243 20.0263 20.0159 0.0000 20.0001

Notes: *Significant at 1 percent level except for those shown by * *; x 2 ¼ 167,978; dependent variable – infect logistic regression

An increase in AGE by one year increases the probability of infection by 0.0002. This seems small in magnitude when compared to the Table I probability of HAI for an average patient to be 0.0640. An increase in LOS by one day increases the probability of HAI by 0.0137 which is large compared to the probability of HAI for an average patient, 0.0137 vs 0.0640, and SURGERY increases the probability by 0.0096. Discussion The combination of a very large database (over 1.5 million patients) with rigorous econometric estimation techniques leads to several valuable findings which we hope will trigger further research. Our analysis confirms that LOS and HAI are interdependent as described in Graves et al. (2005). It also offers a better understanding of the process by which costs increase than has been previously available. The longer a patient stays in a hospital, the higher the probability of acquiring an infection; and an increase in probability of an infection increases LOS. Specifically, infection increases LOS by 9.3 days, a result a bit on the high side but consistent with the marginal increase in LOS reported in the literature (Zhan and Miller, 2003). A rise in LOS by one day increases the probability of acquiring an infection by 0.0137. While this seems to be a small increase in probability, it is a significant increase when compared to the base. Since the probability of infection of a patient admitted into a hospital is 0.0640 (Table I), an increase in the probability of infection by 0.0137 for an increase in LOS by one day is over 21 percent (0.0137/0.0640) of the base line probability of 0.0640. The patient congestion variables BEDS and OCC show interesting results. Larger hospitals have higher probability of infection but hospitals with higher occupancy rate have lower probability of infection. This makes intuitive sense because patients crowd out better hospitals. Scope for future studies The above findings suggest that simultaneous equation estimation can both offer greater understanding of the interactions among the cost driving variables than


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Table III. Two-step estimation for the system of equations model

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instrumental variables techniques and bring greater clarity to our understanding of the way different factors interact. This is because these models quantify both the nature of the interaction between LOS and HAI and the impact of the factors that affect the two. The results presented in our paper suggest that more sophisticated models are feasible, that they can bring greater precision to cost estimation, and that they can be estimated effectively using existing statistical techniques and publicly available administrative datasets. Several variables affect the decision to go to the hospital for treatment and, perhaps over time, new behavioral equations for this decision stage will be designed and tested. For example, fear of infection may discourage some people, particularly the elderly from going to a hospital. It would be useful to add to the model an additional stage to predict the probability of visiting a hospital given the fear of infection. Clearly, such an addition would be valuable and it could lead to further inclusion of the opportunity costs incurred because patients do not seek hospital care. Other behavioral additions might analyze the effects of various payer policies on infection, the impact of policies designed to reduce LOS, and the impacts of CM. As computer programs grow increasingly complex and computer power increases, multi-stage models become increasingly feasible. Our analysis demonstrates that several variables are important in explaining infection. As our knowledge of these determinants grows, it should be feasible to build more sophisticated infection equations. These might incorporate such information as which drugs and procedures are used, hospital environment, and treatment differences. Improved specification of the model would strengthen the cost estimation and hopefully allow introduction of variables over which administrators have greater control. Finally, continued public interest in providing a more inclusive health care system, together with concomitant pressures to find funding will likely spillover to ways to reduce HAI. The data in this paper clearly indicate that patients who contract HAI use considerably more resources than those who do not. Combined with an increase in the number of days spent in a hospital, it is clear that HAI is extremely costly. So too, are efforts to reduce HAI. Further, research along the lines suggested in this paper will make it easier for policymakers to make decisions regarding whether providing incremental resources to HAI would be cost effective rather than employing them for other alternatives that bring health care costs down. References Burke, J.P. (2003), “Infection control – a problem for patient safety”, The New England Journal of Medicine, Vol. 348 No. 7, pp. 651-6. Burns, L.R. and Wholey, D.R. (1991), “The effects of patient, hospital, and physician characteristics on length of stay and mortality”, Medical Care, Vol. 29 No. 3, pp. 251-70. Carey, K., Burgess, J.F. Jr and Young, G.J. (2009), “Single specialty hospitals and nurse staffing patterns”, Medical Care Research and Review, Vol. 66 No. 3, pp. 307-19. Consumers Union (2007), “Safe patient project”, available at: www.consumersunion.org/ campaigns/stophospitalinfections/004514indiv.html (accessed 12 September 2010). Costantini, M., Donisi, P.M., Turrin, M.G. and Diana, L. (1987), “Hospital acquired infections surveillance and control in intensive care services – results of an incidence study”, European Journal of Epidemiology, Vol. 3 No. 4, pp. 347-55. Gooding, S.K. (1995), “Quality, sacrifice and value in hospital choice”, Journal of Health Care Marketing, Vol. 15 No. 4, pp. 24-31.

Graves, N., Weinhold, D. and Robberts, J. (2005), “Correcting for bias when estimating the cost of hospital acquired infection: an analysis of lower respiratory tract infections in non-surgical patients”, Journal of Health Economics, Vol. 14, pp. 755-61.


Haley, R., Culver, D., White, J., Morgan, W. and Emori, T. (1985), “The nationwide nosocomial infection rate: a new need for vital statistics”, American Journal of Epidemiology, Vol. 121 No. 2, pp. 159-67. Hassan, M., Tuckman, H., Patrick, R., Kountz, D. and Kohn, J. (2010), “Cost of hospital acquired infection”, Forthcoming, Hospital Topics, Vol. 88 No. 3, pp. 82-9. Hegji, C., Self, D. and Findley, C. (2007), “The link between hospital quality and services profitability”, International Journal of Pharmaceutical and Healthcare Marketing, Vol. 1 No. 4, pp. 290-303. Horan, T.C. and Gaynes, P.R. (2004), “Surveillance of nosocomial infections”, in Mayhall, C.G. (Ed.), Hospital Epidemiology and Infection Control, 3rd ed., Lippincott, Philadelphia, PA. Horan, T.C., White, J.W., Jarvis, W.R., Emory, G., Culver, D.H., Munn, V.P., Thornsberry, C., Olson, D. and Hughes, J.M. (1986), “Nosocomial infection surveillance”, CDC Morbidity and Mortality Weekly Report, Vol. 34, 1 December. Kilgore, M.L., Ghosh, K., Beavers, M., Wong, D.Y., Hymel, P.A. and Brossette, S.E. (2008), “The costs of nosocomial infections”, Medical Care, Vol. 46 No. 1, pp. 101-4. Lee, K.H. and Anderson, Y.M. (2007), “The association between clinical pathways and hospital length of stay: a case study”, Journal of Medical System, Vol. 31, pp. 79-83. Lin, W.C., Kane, R.L., Potthoff, S.J. and Finch, M.D. (1999), “Geographic variation in hospital length of stay of elderly medicare beneficiaries”, Abstract Book of Association of Health services Research Meeting, Vol. 16, pp. 288-9. Mark, B.A. and Harless, D.W. (2007), “Nurse staffing, mortality, and length of stay in for-profit and not-for-profit hospitals”, Inquiry, Vol. 44, pp. 167-86. Needleman, B., Buerhause, P., Mattke, S., Steward, M. and Zelevinsky, K. (2002), “Nurse staffing levels and the quality of care in hospitals”, New England Journal of Medicine, Vol. 346 No. 22, pp. 1715-22. Ollendorf, D.A., Fendrick, A.M., Massey, K., Williams, G.R. and Oster, G. (2002), “Is sepsis accurately coded on hospital bills?”, Value Health, Vol. 2, pp. 79-81. Platt, R., Kleinman, K., Thompson, K., Dokholyan, R., Livingston, J., Bergman, A., Mason, J., Horan, T., Gaynes, R., Solomon, S. and Sands, K. (2002), “Using automated health plan data to assess infection risk from coronary artery bypass surgery”, Emerging Infectious Disease, Vol. 8 No. 12, pp. 1433-41. Plowman, R., Graves, N., Griffin, M., Roberts, J., Swan, A., Cookson, B. and Taylor, L. (2001), “The rate and cost of hospital-acquired in England and the national burden imposed”, Journal of Hospital Infection, Vol. 27, pp. 198-209. Rubin, R.H., Harrington, A.P., Dietrich, K., Greene, J.A. and Moiduddin, A. (1999), “The economic impact of staphylococcus aureus infection in New York City hospitals”, Emerging Infectious Disease, Vol. 5 No. 1, pp. 9-17. Sloan, F.A., Picone, G.A., Taylor, D.H. and Chow, S.Y. (2001), “Hospital ownership and cost and quality of care: is there a dime’s worth of difference?”, Journal of Health Economics, Vol. 20, pp. 1-21. Solaiman, A. (1992), “Assessing the quality of health care: a consumerist approach”, Health Marketing Quaterly, Vol. 10 Nos 1/2, pp. 121-41.

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Stone, P., Larson, E. and Kawar, L. (2002), “A systematic audit of economic evidence linking nosocomial infections and infection control interventions: 1990-2000”, American Journal of Infection Control, Vol. 30 No. 1, pp. 145-52. Swartz, M.N. (1994), “Hospital-acquired infections: diseases with increasingly limited therapies”, Proceedings of National Academy of Sciences of the United States of America, Vol. 91 No. 7, pp. 2420-7. Taylor, D.H., Whellan, D.J. and Sloan, F.A. (1999), “Effects of admission to a teaching hospital on the cost and quality of care for Medicare beneficiaries”, The New England Journal of Medicine, Vol. 340 No. 4, pp. 293-9. Wenzel, R. (1985), “Nosocomial infections, diagonis-related groups, and study on the efficacy of nosocomial infection control: economic implications for hospital under the prospective payment system”, American Journal of Medicine, Vol. 78 No. 6, pp. 23-7. Wooldridge, J. (2009), Introductory Econometrics: A Modern Approach, 4th ed., South-Western Cengage Learning, Mason, OH. Zhan, C. and Miller, M. (2003), “Excess length of stay, charges, and mortality attributable to medical injuries during hospitalization”, Journal of the American Medical Association, Vol. 290 No. 14, pp. 1868-74. Further reading Kohn, L., Corrigan, J. and Donaldson, M. (1999), To Err is Human: Building a Safer Health System, National Academy Press, Washington, DC.


Appendix 1 Source

Code

Description

1,2 2,3 2 2 2 2 2 2 2 3 1 1 1 1,3 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2,3 3 3 3 3 3 3 3 3

38.0 38.1 38.10 38.11 38.19 38.2 38.3 38.4 38.4 421.0 482.0 482.1 482.2 482.4 482.5 482.6 482.7 482.8 482.9 485.0 486.0 507.0 514.0 599.0 611.0 674.3 682.0 682.1 682.2 682.3 682.4 682.5 682.6 682.7 682.8 682.9 686.0 686.1 686.8 686.9 711.00 711.01 711.02 711.03 711.04 711.05 711.06 711.07 711.08

Streptococcal septicemia Staph septicemia Staph septicemia nos Staph aureus septicemia Staph septicemia nec Pneumococcal septicemia Anerobic septicemia Gram-neg septicemia nec Gram-neg septicemia nos Acute and subacute bacterial endocarditis Pneumonia Pneumonia Pneumonia Pneumonia due to Staphylococcus Pneumonia Pneumonia Pneumonia Pneumonia Pneumonia Pneumonia Pneumonia Pneumonia Pneumonia UT Inflam disease of breast Oth comp OB surg wnd Cellulitis of face Cellulitis of neck Cellulitis of trunk Cellulitis of arm Cellulitis of hand Cellulitis of buttock Cellulitis of leg Cellulitis of foot Cellulitis of site nec Cellulitis nos Pyoderma Pyogenic granuloma Local skin infection nec Local skin infection nos Pyogen arthritis-unspec Pyogenic arthritis Pyogenic arthritis Pyogenic arthritis Pyogenic arthritis Pyogenic arthritis Pyogenic arthritis Pyogenic arthritis Pyogenic arthritis (continued)

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Table AI. List of the ICD codes used to define the infection binary

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Table AI.

Source

Code

Description

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 2,3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1,2 2 2 2 2 2,3 2 1 2 2 2,3 2 2

711.09 730.01 730.02 730.03 730.04 730.05 730.06 730.07 730.08 730.09 730.10 730.11 730.12 730.13 730.14 730.15 730.16 730.17 730.18 730.19 780.6 790.70 790.7 875.00 875.10 879.0 879.1 879.2 879.3 879.4 879.5 879.6 879.7 879.8 879.9 891.0 891.1 958.3 958.3 996.6 996.60 996.61 996.62 996.63 996.6 996.64 996.65 996.66 996.67 996.68

Pyogenic arthritis Acute osteomyelitis Acute osteomyelitis Acute osteomyelitis Acute osteomyelitis Acute osteomyelitis Acute osteomyelitis Acute osteomyelitis Acute osteomyelitis Acute osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Chronic osteomyelitis Fever Sepsis Bacteremia Open wnd-chest/S comp Open wnd chest-comp Open wnd of breast Open wnd breast-comp Open wnd anterior abdomen Open wnd ant abdomen-comp Open wnd lateral abdomen Open wnd lateral abdomen-comp Open wnd trunk nec Open wnd trunk nec-comp Open wnd site nos Open wnd site nos-comp Open wnd low leg/s comp Open wnd knee/leg – comp Post-op would disruption Posttram wnd infect nec Infect/inflam-dev/graft Infect D/T device nos Infect D/T hrt device Infect D/T vasc device Infect D/T nerv device UT Infect D/T urethral cath Infect D/T GU device nec Infect D/T joint prosth Infect D/T orth device nec Infect D/T PD cath (continued)

Source

Code

Description

2 2 3 1,2,3 2 2 2 2

996.69 998.0 998.3 998.5 998.51 998.59 998.83 998.90

Infect D/T device nos Postoperative shock Disruption of operation wound Postoperative infection Infected post-op seroma Post-op infection nec Non-healing surg wnd Surgical comp NOS


337

Notes: All codes from source articles cited to International Classification of Diseases, Ninth Revision, Clinical Modification; all descriptions are most specific from source articles Sources: Needleman et al. (2002); Platt et al. (2002); Rubin et al. (1999)

Table AI.

Appendix 2 Variables

Parameter estimate *

SE

Intercept Infect Age Age2 Female Surgery CM Urgent Beds OCC Reslos

0.6246 0.4415 20.0901 0.0007 20.0185 20.1922 0.9609 1.4938 20.0000 0.0095 0.9968

0.0057 0.0042 0.0001 0.0000 0.0020 0.0027 0.0005 0.0022 0.0000 0.0000 0.0002

Note: *All estimates are significant at 1 percent level

Table AII. Test of endogeneity (t-test)

Appendix 3 Variables

VIF

CN

Age Age2 Female Surgery CM Urgent Intern Medicaid Nurseshr Ngt Es Ot Beds OCC

12.7825 12.3771 1.0110 1.1564 1.7933 1.3449 1.6417 1.2895 1.1722 1.0560 1.0638 1.0086 1.4586 1.1884

1.0000 1.2429 1.4628 1.4975 1.5567 1.6503 1.6724 1.7271 1.8415 2.0746 2.1502 2.5028 2.7253 8.1971

Table AIII. VIF and CN

IJPHM 4,4

338

About the authors Mahmud Hassan, PhD, is a Professor of Finance and Economics, Director of the Pharmaceutical Management, and Director of the Blanche and Irwin Lerner Center for the Study of Pharmaceutical Management Issues at the Rutgers Business School – Newark and New Brunswick. His research papers have been published in the Journal of Finance, Journal of Business, Journal of Health Economics, Health Affairs, Inquiry, Journal of American Medical Association, Hospital Topics, and others. His area of specialty is Health Economics/Healthcare Policy. He has a PhD in Economics from Vanderbilt University and an MBA from Indiana University in Bloomington. Mahmud Hassan is the corresponding author and can be contacted at: [email protected] Howard P. Tuckman, PhD, is a Professor of Finance at Fordham University, NY and was previously Dean of the Graduate School of Business at the same university. He works with business and public agencies training in health care and non-profit finance, and served on the Board of Levi Arthritis Hospital in Little Rock, Arkansas, and consulted with several nursing homes, USAID and the World Bank. He is the author of eight books and over 130 journal articles. His work has been cited in the New York Times, Wall Street Journal, and academic, professional, and technical publications. He received his PhD degree in Economics from the University of Wisconsin. Robert H. Patrick, PhD, is an Associate Professor in the Department of Finance and Economics at the Rutgers Business School, Newark and New Brunswick. His areas of expertise are applied microeconomics and applied econometrics, particularly in the fields of natural resource and environmental economics, regulatory economics, and empirical finance. He has published numerous articles on pricing, regulation, natural resource, energy, and environmental economics in professional journals and books; served on the editorial boards of the Journal of Environmental Economics and Management and the Journal of Regulatory Economics. Prior to joining Rutgers’ faculty, he held academic positions at Purdue University, Colorado School of Mines, and Stanford University. He earned his PhD at the University of New Mexico. David S. Kountz, MD, is the Senior Vice President for Academic and Medical Affairs at the Jersey Shore University Medical Center in New Jersey. He is a Board Certified Practicing Physician in Internal Medicine. Earlier, he was an Associate Professor and Chief of Primary Care Division, Department of Medicine, and Associate Dean for Postgraduate Education at the Robert Wood Johnson Medical School in New Jersey. Jennifer L. Kohn, PhD, is the Director of the Business Studies Program and an Assistant Professor at Drew University, New Jersey. She earned a Doctorate in Finance and Economics from Rutgers Business School, an MBA from NYU and a BA in Philosophy from U-Mass-Amherst. Prior to working in academia she held positions in government and hospital administration. Her research focus is on the dynamics of medical care demand and financial risk management.

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