Generalized case-control sampling under generalized linear models

Abstract

A generalized case-control (GCC) study, like the standard case-control study, leverages outcome-dependent sampling (ODS) to extend to nonbinary responses. We develop a novel, unifying approach for analyzing GCC study data using the recently developed semiparametric extension of the generalized linear model (GLM), which is substantially more robust to model misspecification than existing approaches based on parametric GLMs. For valid estimation and inference, we use a conditional likelihood to account for the biased sampling design. We describe analysis procedures for estimation and inference for the semiparametric GLM under a conditional likelihood, and we discuss problems with estimation and inference under a conditional likelihood when the response distribution is misspecified. We demonstrate the flexibility of our approach over existing ones through extensive simulation studies, and we apply the methodology to an analysis of the Asset and Health Dynamics Among the Oldest Old study, which motives our research. The proposed approach yields a simple yet versatile solution for handling ODS in a wide variety of possible response distributions and sampling schemes encountered in practice.

Keywords: conditional likelihood; efficiency; generalized case-control studies; generalized linear models; outcome-dependent sampling.

FIGURE 1

Example of resulting response distribution for varying amount of overdispersion (25%, 50%, and 100%) compared to generating binomial responses with probability equal to μ_i. This figure appears in color in the electronic version of this article, and any mention of color refers to that version