Regression models for group testing data with pool dilution effects

Group testing is widely used to reduce the cost of screening individuals for infectious diseases. There is an extensive literature on group testing, most of which traditionally has focused on estimating the probability of infection in a homogeneous population. More recently, this research area has shifted towards estimating individual-specific probabilities in a regression context. However, existing regression approaches have assumed that the sensitivity and specificity of pooled biospecimens are constant and do not depend on the pool sizes. For those applications, where this assumption may not be realistic, these existing approaches can lead to inaccurate inference, especially when pool sizes are large. Our new approach, which exploits the information readily available from underlying continuous biomarker distributions, provides reliable inference in settings where pooling would be most beneficial and does so even for larger pool sizes. We illustrate our methodology using hepatitis B data from a study involving Irish prisoners.