Non‐hierarchical logistic models and case‐only designs for assessing susceptibility in population‐based case‐control studies

This article describes how genetic components of disease susceptibility can be evaluated in case‐control studies, where cases and controls are sampled independently from the population at large. Subjects are assumed unrelated, in contrast to studies of familial aggregation and linkage. The logistic model can be used to test collapsibility over phenotypes or genotypes, and to estimate interactions between environmental and genetic factors. Such interactions provide an example of a context where non‐hierarchical models make sense biologically. Also, if the exposure and genetic categories occur independently and the disease is rare, then analyses based only on cases are valid, and offer better precision for estimating gene‐environment interactions than those based on the full data.