Estimating Disease Prevalence Using Inverse Binomial Pooled Testing

Abstract

Monitoring populations of hosts as well as insect vectors is an important part of agricultural and public health risk assessment. In applications where pathogen prevalence is likely low, it is common to test pools of subjects for the presence of infection, rather than to test subjects individually. This technique is known as pooled (group) testing. In this paper, we revisit the problem of estimating the population prevalence p from pooled testing, but we consider applications where inverse binomial sampling is used. Our work is unlike previous research in pooled testing, which has largely assumed a binomial model. Inverse sampling is natural to implement when there is a need to report estimates early on in the data collection process and has been used in individual testing applications when disease incidence is low. We consider point and interval estimation procedures for p in this new pooled testing setting, and we use example data sets from the literature to describe and to illustrate our methods.

Bayesian inference for disease prevalence using negative binomial group testing

“…As in Pritchard and Tebbs (2010), we assume that individual (e.g. mosquito) statuses are independent and identically distributed Bernoulli random variables with mean p and that tests are performed on pools of individuals until the n th positive pool is found.…”

“…Pritchard and Tebbs (2010) have suggested that inverse (negative) binomial pooled sampling may be preferred when the prevalence p is known to be small, when sampling and testing occurs sequentially, and when positive pool results instigate the need for immediate analysis, such as in WNV screening. Under this model, unlike the binomial, the number of positive pools to be observed is fixed a priori, and testing stops when this number is reached.…”

“…Under this model, unlike the binomial, the number of positive pools to be observed is fixed a priori, and testing stops when this number is reached. Pritchard and Tebbs (2010) use maximum likelihood as a basis to develop classical point and interval estimators for p under inverse pooled sampling. In this paper, we have the same goals, but we instead take a Bayesian approach.…”

“…This is sensible, and possibly preferred, as in the context of WNV screening; for example, known information about p can be incorporated seamlessly into a prior model. In addition, the classical methods presented in Pritchard and Tebbs (2010) have serious shortcomings in small samples when p is small. In particular, the maximum likelihood estimator (MLE) of p can be severely biased, and interval estimates can extend outside the parameter space.…”

“…In Section 2, we state assumptions and briefly review the classical methodology in Pritchard and Tebbs (2010). In Section 3, we present Bayesian and empirical Bayesian estimators obtained from a variety of prior models.…”