Group testing regression analysis with covariates and specimens subject to missingness

We develop parametric estimators of a conditional prevalence in the group testing context. Group testing is applied when a binary outcome variable, often a disease indicator, is assessed by testing a specimen for the presence of the disease. Instead of testing all individual specimens separately, these are pooled in groups and the grouped specimens are tested for the disease, which permits to significantly reduce the number of tests to be performed. Various techniques have been developed in the literature for estimating a conditional prevalence from group testing data, but most of them are not valid when the data are subject to missingness. We consider this problem in the case where the specimen and the covariates are subject to nonmonotone missingness. We propose parametric estimators of the conditional prevalence, establish identifiability conditions for a logistic missing not at random model, and introduce an ignorable missing at random model. In theory, our estimators could be applied with multiple covariates missing, but in practice, they face numerical challenges when more than one covariate is missing for given individuals. We illustrate the method on simulated data and on a dataset from the Demographics and Health Survey.