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

Abstract

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.

Introduction

Estimation of disease or parasite prevalence in wild, free-ranging or captive animal populations is crucial for effective risk analysis, prediction and management. Exotic or endemic diseases or parasites can be transferred among populations and considerable uncertainty often exists regarding findings and interpretations (Daszak and Cunningham, 2000, Krkošek et al., 2004, Bruno, 2004, Moffitt et al., 2004, Murray et al., 2009, O'Brien et al., 2009a). Managers of animal health must consider the disease dynamics and risks to target animal populations in the context of commerce and other human activities, and spatial analysis tools and assessment of uncertainty are needed in disease prediction models (Clough et al., 2003, Haine et al., 2004, Murray and Peeler, 2005, Jennelle et al., 2007). The data needed for management of these risks often come from a variety of sources and may be collected using different sampling protocols, tools, and methods for assessment. Additionally, the data typically come from diagnostic tests in which sensitivity and/or specificity are not perfect (Cannon, 2001, Williams and Moffitt, 2003, Kalis et al., 2004, Branscum et al., 2005, O'Brien et al., 2009b). Studies of free-ranging fish and wildlife populations pose additional challenges for regulatory and management entities, as the science of pathogen identification and methods for screening are relatively new, and difficulties exist in opportunities for consistent sampling. To improve both the sensitivity and specificity of testing procedures, new tools are used as they are developed (USFWS and AFS-FHS, 2003, Diggles et al., 2003, Hogge et al., 2004, López-Vázquez et al., 2006). Many animal disease prevalence monitoring processes use pooled samples for efficient and economical detection of disease (Wells et al., 2003, Bruno, 2004, Jordan, 2005, Muñoz-Zanzi et al., 2006). For all these reasons, the data used to monitor disease status in wild or free-ranging fish or other wildlife populations can be heterogeneous, and samples can be unpooled or pooled with varying pool sizes.

Statistical methods have been reported and software developed to consider imperfect tests for prevalence estimation from a wide variety of sampling plans (Mendoza-Blanco et al., 1996, Cowling et al., 1999, Hanson et al., 2003, Humphry et al., 2004), but these methods consider only a common pool size. Estimation of disease prevalence from pooled samples with common pool sizes has been evaluated both by maximum likelihood-based approaches that assume perfect sensitivity and specificity (Williams and Moffitt, 2001), and with Bayesian approaches that reflect imperfect sensitivity and specificity (Williams and Moffitt, 2003).

Recent studies and evaluations of salmon and other animal populations have utilized a variety of statistical tools, especially Bayesian methods, to consider the outcome of diagnostic tests for pathogens for which there is no true gold standard (Branscum et al., 2005, Gari et al., 2008, Nérette et al., 2008). It is important in all these exercises to provide guidance for understanding disease prevalence under the wide variety of circumstances that observations are made on both captive and free-ranging populations.

The objectives of this paper are to: 1) provide statistical methods to estimate and examine disease prevalence in fish and wildlife populations with data from imperfect diagnostic tests and varying pool sizes; 2) using three data sets, compare prevalence estimates obtained with Bayesian methods and imperfect sensitivity and specificity with estimates calculated with maximum likelihood methods that assume perfect sensitivity and specificity of diagnostic tests, and 3) conduct two efficiency studies to compare the mean-squared error of the Bayesian and maximum likelihood methods for a range of prevalence, sensitivity, and specificity values as well as for different pooled sample structures.