Estimation of conditional prevalence from group testing data with missing covariates

We consider estimating the conditional prevalence of a disease from data pooled according to the group testing mechanism. Consistent estimators have been proposed in the literature, but they rely on the data being available for all individuals. In infectious disease studies where group testing is frequently applied, the covariate is often missing for some individuals. There, unless the missing mechanism occurs completely at random, applying the existing techniques to the complete cases without adjusting for missingness does not generally provide consistent estimators, and finding appropriate modifications is challenging. We develop a consistent spline estimator, derive its theoretical properties, and show how to adapt local polynomial and likelihood estimators to the missing data problem. We illustrate the numerical performance of our methods on simulated and real examples.