Likelihood‐based methods for regression analysis with binary exposure status assessed by pooling

The need for resource-intensive laboratory assays to assess exposures in many epidemiologic studies provides ample motivation to consider study designs that incorporate pooled samples. In this paper, we consider the case in which specimens are combined for the purpose of determining the presence or absence of a pool-wise exposure, in lieu of assessing the actual binary exposure status for each member of the pool. We presume a primary logistic regression model for an observed binary outcome, together with a secondary regression model for exposure. We facilitate maximum likelihood analysis by complete enumeration of the possible implications of a positive pool, and we discuss the applicability of this approach under both cross-sectional and case-control sampling. We also provide a maximum likelihood approach for longitudinal or repeated measures studies where the binary outcome and exposure are assessed on multiple occasions and within-subject pooling is conducted for exposure assessment. Simulation studies illustrate the performance of the proposed approaches along with their computational feasibility using widely available software. We apply the methods to investigate gene-disease association in a population-based case-control study of colorectal cancer.