Group testing is frequently used to reduce the costs of screening a large number of individuals for infectious diseases or other binary characteristics in small prevalence situations. In many applications, the goals include both identifying individuals as positive or negative and estimating the probability of positivity. The identification aspect leads to additional tests being performed, known as “retests,” beyond those performed for initial groups of individuals. In this paper, we investigate how regression models can be fit to estimate the probability of positivity while also incorporating the extra information from these retests. We present simulation evidence showing that significant gains in efficiency occur by incorporating retesting information, and we further examine which testing protocols are the most efficient to use. Our investigations also demonstrate that some group testing protocols can actually lead to more efficient estimates than individual testing when diagnostic tests are imperfect. The proposed methods are applied retrospectively to chlamydia screening data from the Infertility Prevention Project. We demonstrate that significant cost savings could occur through the use of particular group testing protocols.

When the prevalence of a disease or of some other binary characteristic is small, group testing (also known as pooled testing) is frequently used to estimate the prevalence and/or to identify individuals as positive or negative. We have developed the binGroup package as the first package designed to address the estimation problem in group testing. We present functions to estimate an overall prevalence for a homogeneous population. Also, for this setting, we have functions to aid in the very important choice of the group size. When individuals come from a heterogeneous population, our group testing regression functions can be used to estimate an individual probability of disease positivity by using the group observations only. We illustrate our functions with data from a multiple vector transfer design experiment and a human infectious disease prevalence study.

Group testing, where individual specimens are composited into groups to test for the presence of a disease (or other binary characteristic), is a procedure commonly used to reduce the costs of screening a large number of individuals. Group testing data are unique in that only group responses may be available, but inferences are needed at the individual level. A further methodological challenge arises when individuals are tested in groups for multiple diseases simultaneously, because unobserved individual disease statuses are likely correlated. In this paper, we propose new regression techniques for multiple-disease group testing data. We develop an expectation-solution based algorithm that provides consistent parameter estimates and natural large-sample inference procedures. Our proposed methodology is applied to chlamydia and gonorrhea screening data collected in Nebraska as part of the Infertility Prevention Project and to prenatal infectious disease screening data from Kenya.

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