Inference for case‐control studies with incident and prevalent cases

We propose and study a fully efficient method to estimate associations of an exposure with disease incidence when both, incident cases and prevalent cases, i.e., individuals who were diagnosed with the disease at some prior time point and are alive at the time of sampling, are included in a case‐control study. We extend the exponential tilting model for the relationship between exposure and case status to accommodate two case groups, and correct for the survival bias in the prevalent cases through a tilting term that depends on the parametric distribution of the backward time, i.e., the time from disease diagnosis to study enrollment. We construct an empirical likelihood that also incorporates the observed backward times for prevalent cases, obtain efficient estimates of odds ratio parameters that relate exposure to disease incidence and propose a likelihood ratio test for model parameters that has a standard chi‐squared distribution. We quantify the changes in efficiency of association parameters when incident cases are supplemented with, or replaced by, prevalent cases in simulations. We illustrate our methods by estimating associations of single nucleotide polymorphisms (SNPs) with breast cancer incidence in a sample of controls, incident and prevalent cases from the U.S. Radiologic Technologists Health Study.