Misclassified group-tested current status data

Group testing, introduced by Dorfman (1943), has been used to reduce costs when estimating the prevalence of a binary characteristic based on a screening test of $k$ groups that include $n$ independent individuals in total. If the unknown prevalence is low and the screening test suffers from misclassification, it is also possible to obtain more precise prevalence estimates than those obtained from testing all $n$ samples separately (Tu et al., 1994). In some applications, the individual binary response corresponds to whether an underlying time-to-event variable $T$ is less than an observed screening time $C$, a data structure known as current status data. Given sufficient variation in the observed $C$ values, it is possible to estimate the distribution function $F$ of $T$ nonparametrically, at least at some points in its support, using the pool-adjacent-violators algorithm (Ayer et al., 1955). Here, we consider nonparametric estimation of $F$ based on group-tested current status data for groups of size $k$ where the group tests positive if and only if any individual's unobserved $T$ is less than the corresponding observed $C$. We investigate the performance of the group-based estimator as compared to the individual test nonparametric maximum likelihood estimator, and show that the former can be more precise in the presence of misclassification for low values of $F(t)$. Potential applications include testing for the presence of various diseases in pooled samples where interest focuses on the age-at-incidence distribution rather than overall prevalence. We apply this estimator to the age-at-incidence curve for hepatitis C infection in a sample of U.S. women who gave birth to a child in 2014, where group assignment is done at random and based on maternal age. We discuss connections to other work in the literature, as well as potential extensions.