Retrospective Association Analysis of Binary Traits: Overcoming Some Limitations of the Additive Polygenic Model

Case-control genetic association analysis is an extremely common tool in human complex trait mapping. From a statistical point of view, the analysis of binary traits poses somewhat different challenges from the analysis of quantitative traits. Desirable features of a binary trait mapping approach would include (1) phenotype modeled as binary, with appropriate dependence between the mean and variance; (2) appropriate correction for relevant covariates; (3) appropriate correction for sample structure of various types, including related individuals, admixture and other types of population structure; (4) both fast and accurate computations; (5) robustness to ascertainment and other types of phenotype model misspecification, and (6) ability to leverage partially missing data to increase power. We review these challenges and argue, both theoretically and in simulations, for the value of retrospective association analysis as a way to overcome some of the limitations of the phenotype model, including model misspecification due to ascertainment. We give an overview of two recent retrospective methods, CARAT and CERAMIC, that are designed to meet criteria 1-6.