Global goodness-of-fit tests for group testing regression models

In a variety of biomedical applications, particularly those involving screening for infectious diseases, testing individuals (e.g. blood/urine samples, etc.) in pools has become a standard method of data collection. This experimental design, known as group testing (or pooled testing), can provide a large reduction in testing costs and can offer nearly the same precision as individual testing. To account for covariate information on individual subjects, regression models for group testing data have been proposed recently. However, there are currently no tools available to check the adequacy of these models. In this paper, we present various global goodness-of-fit tests for regression models with group testing data. We use simulation to examine the small-sample size and power properties of the tests for different pool composition strategies. We illustrate our methods using two infectious disease data sets, one from an HIV study in Kenya and one from the Infertility Prevention Project.