Semiparametric isotonic regression modelling and estimation for group testing data

In the group testing procedure, several individual samples are grouped and the pooled samples, instead of each individual sample, are tested for outcome status (e.g., infectious disease status). Although this cost‐effectiveness strategy in data collection is both labour and time‐efficient, it poses statistical challenges to derive statistically and computationally efficient estimators under semiparametric models. We consider semiparametric isotonic regression models for the simultaneous estimation of the conditional probability curve and covariate effects, in which a parametric form for combining the covariate information is assumed and the monotonic link function is left unspecified. We develop an expectation–maximization algorithm to overcome the computational challenge and embed the pool‐adjacent violators algorithm in the M‐step to facilitate the computation. We establish the large sample behaviour of the proposed estimators and examine their finite sample performance in simulation studies. We apply the proposed method to data from the National Health and Nutrition Examination Survey for illustration.