Richard Lampman. Robert J. Novak. Illinois Natural History Survey ... J. S. Mackenzie, and N. W. Beebe. 2002. Isolation of arboviruses from mosquitoes (Diptera: ...
LETTER Problems in Estimating Mosquito Infection Rates Using Minimum Infection Rate TO THE EDITOR: Determining the role of various mosquito species in the transmission of arboviruses relies on an accurate estimate of the proportion of infected individuals in an area. Basically, there are two methods for estimating the proportion of infected individuals from pooled samples. One is the widely used minimum infection rate (MIR), which is calculated as the ratio of the number of positive pools to the total number of mosquitoes tested. The underlying assumption of the MIR is that only one infected individual exists in a positive pool. This assumption is valid for arboviruses that are relatively rare, but it becomes problematic when infection rates are high and/or pool sizes are large. The other method of estimating the proportion of infected individuals in pooled samples is the maximum likelihood estimation (MLE), which is deÞned as the infection rate most likely observed given the testing results and an assumed probabilistic model (i.e., binomial distribution of infected individuals in a positive pool). Obviously, MIR and MLE of infection rates are conceptually different. The former estimates the lower bound of the infection rates, while the latter estimates infection rate itself. The advantages of MLE over MIR are its relaxation of the constraints of MIR and accuracy of its estimates (Walter et al. 1980). Although the values generated by the two methods are not typically different when infection rates are low and pool sizes small, the difference can be signiÞcant when these conditions are violated. Despite considerable technical advances in the sensitive and speciÞc detection of mosquito-borne pathogens, like West Nile virus, there remains considerable confusion in the literature on how to use this data to estimate infection rates. The typical error is to treat MLE of infection rates as MIR (Johansen et al. 2001, van den Hurk et al. 2002), in which the formula by Chiang and Reeves (1962) was cited. In reality, Chiang and Reeves (1962) present an MLE method of estimating infection rate based on constant pool size using the equation. Note there was a misprinting error in the equation cited by Johansen et al. (2001). The correct equation is:
冉 冊
MLE ⫽ 1 ⫺ 1 ⫺
Y X
1/m
[1]
where Y is the number of positive pools; X is the number of pools; and m is the pool size. This equation is only valid for constant pool size. For the situation of unequal pool size, no analytic solution is available and calculation of MLE requires numerical iterations (Walter et al. 1980). To facilitate estimation of infection rates, we wrote a computer program (MLE-IR) using C⫹⫹. The program is executable on PCs and freely available upon request from the authors. There is other software for calculating MLE of infection
rates, such as Poolscreen (Katholi and Barker, for details see, www.math.montana.edu/⬃barker/res. html) and PooledInfRate (Biggerstaff, CDC, www. cdc.gov/ncidod/dvbid/westnile/software.htm). Precision of estimates of infection rates based on pool examination is affected by the true infection rate, number of pools, and pool size. Some researchers adopted a criterion of sample size of ⬎1,000 individual mosquitoes for accurate estimation of MIR or infection rates (Bernard et al. 2001, Nasci et al. 2002). This criterion is arbitrary and unnecessary. To illustrate this, we created a hypothetic mosquito sample that was grouped into pools of 18, 20, 25, 28, 30, 34, 35, 36, 37, 40, 43, 47, 47, and 50 individuals each (14 pools and total individuals of 490). Note variable pool size was used in this example. Assuming laboratory testing results of these pools were 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, and 1, respectively (0 ⫽ negative, 1 ⫽ positive), the estimated infection rate calculated by our MLE-IR was 21.9 per 1,000 (95% c.l. 10.8 Ð39.3), greater than the MIR of 14.3 per 1,000. Clearly, this “small” (comparing to 1,000) sample of mosquitoes could result in a reasonably precise estimate of infection rates. Overall, the MLE of infection rates is more accurate and robust (relaxing the assumption underlying MIR) than the MIR and requires no more data than that for calculation of MIR. Although MLE of infection rates has been in existence since Chiang and Reeves (1962), this method has not been widely appreciated and applied by medical entomologists. Given the importance of estimating infection rates of arbovirus transmission in surveillance programs, we felt obligated to draw attention to this issue. We believe that MLE of infection rates will replace MIR in measuring infection rates with awareness of merits of the method and availability of the software to wide audience of mosquito workers. Weidong Gu Richard Lampman Robert J. Novak Illinois Natural History Survey Champaign, IL 61820 References Cited Bernard, K. A., J. G. Maffei, S. A. Jones, E. B. Kauffman, G. D. Ebel, A. P. Dupuis II, et al. 2001. West Nile virus infection in birds and mosquitoes, New York State, 2000. Emerg. Infect. Dis. 7: 679 Ð 85. Chiang, C. L., and W. C. Reeves. 1962. Statistical estimation of virus infection rates in mosquito vector populations. Am. J. Hyg. 75: 377Ð91. Johansen, C. A., A. F. van den Hurk, A. T. Pyke, P. Zborowski, D. A. Phillips, J. S. Mackenzie, and S. A. Ritchie. 2001. Entomological investigations of an outbreak of Japanese encephalitis virus in the Torres Strait, Australia, in 1998. J. Med. Entomol. 38: 581Ð 8. van den Hurk, A. F., D. J. Nisbet, P. N. Foley, S. A. Ritchie, J. S. Mackenzie, and N. W. Beebe. 2002. Isolation of arboviruses from mosquitoes (Diptera: Culicidae) collected from the Gulf Plains region of northwest Queensland, Australia. J. Med. Entomol. 39: 786 Ð92.
0022-2585/03/0595Ð0596$04.00/0 䉷 2003 Entomological Society of America
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Nasci, R. S., K. L. Gottfried, K. L. Burkhalter, V. L. Kulasekera, A. J. Lambert, R. S. Lanciotti, et al. 2002. Comparison of Vero cell plaque assay, TaqMan reverse transcriptase polymerase chain reaction RNA assay, and VecTest antigen assay for detection of West Nile virus in
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Þeld-collected mosquitoes. J. Am. Mosq. Cont. Assoc. 18: 294 Ð300. Walter, S. D., S. W. Hildreth, and B. J. Beaty. 1980. Estimation of infection rates in populations of organisms using pools of variable size. Am. J. Epidemiol. 112: 124 Ð 8.
