Estimation of fish and wildlife disease prevalence from imperfect diagnostic tests on pooled samples with varying pool sizes

Methods of estimating disease or parasite prevalence in free-ranging and some captive fish and wildlife populations are frequently lacking in precision due to limited numbers of observations and different assay procedures. Recently statistical methods and software programs have been developed to use Bayesian and other methods to obtain estimates of disease prevalence from diagnostic tests in which sensitivity and/or specificity is not perfect (imperfect) and with sampling schemes using pooled samples. However, these published methods and software programs that consider pooled data sampling have generally considered the case of one uniform pool size for all samples. We present a method for estimating disease prevalence from imperfect diagnostic tests with pooled data collected from a variety of pool sizes. We use a Bayesian approach and obtain a sample from the posterior distribution of prevalence, sensitivity, and specificity, using an MCMC sampling algorithm implemented in the WINBUGS statistical package. We illustrate the use of these methods with three examples and perform efficiency calculations to investigate the performance of these estimators relative to maximum likelihood estimators that assume perfect diagnostic tests. Our results illustrate that the estimates produced from these methods adjust for imperfect tests, and are often more efficient than estimates assuming perfect tests, except in some situations when there is not much prior information on diagnostic test sensitivity and specificity.