A maximum likelihood estimator for the prevalence rate using pooled sample tests

Abstract

Since Dorfman’s seminal work, research on methodologies involving pooled sample tests has increased significantly.Moreover, the use of pooled samples refers not only to the classification problem (identifying all the infected individuals in a population), but also refers to the problem of estimating the prevalence rate p, as Sobel and Elashoff stated. The use of compound tests is not restricted to hierarchical algorithms where the most common example is Dorfman’s two-stage procedure. Matrix schemes such as the square array algorithm or multidimensional matrices schemes in certain cases outperform Dorfman’s procedure. Maximum likelihood estimates are quite difficult to compute when a procedure does not classify all individuals. This paper presents two innovative methods to compute maximum likelihood estimates in both type of procedures.