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Estimation of disease prevalence in many animal populations is challenging due to limited sample size and use of different sampling procedures.
Our interest in this problem is motivated by estimation of disease prevalence in fish populations, using grouped (pooled) data of different sizes,
with imperfect diagnostic tests. Recently Bayesian methods and software have been developed for estimation of disease prevalence from diagnostic
tests in which sensitivity and/or specificity is not perfect and with sampling schemes using pooled samples. However, these methods that consider
pooled data sampling have generally considered the case of one uniform pool size for all samples. We present a method for estimation of 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 some 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. However, in some
situations when there is not much prior information on diagnostic test sensitivity and specificity the Bayesian method can be less efficient.
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