Regression analysis is commonly used in genome-wide association studies (GWAS) to assess genotype-phenotype associations when a single trait value is observed for each individual. In some genetic epidemiologic studies, longitudinally collected phenotype data are available. Methodologic developments for longitudinal GWAS have proliferated to make full use of the available data. In epidemiologic studies, as many of the disease conditions are rare, efficient designs are commonly applied to recruit study subjects. Prospective analysis in which a population-based model is used ignoring ascertainment bias can result in compromised statistical inference. To generalize case-control sampling, outcome-dependent sampling designs have become popular for binary data in longitudinal cohort studies. However, association tests for longitudinally measured binary data are less well developed in GWAS. Here, we propose L-BRAT, a retrospective, GEE-based method for genetic association analysis of longitudinal binary outcomes. It requires specification of the mean of the outcome distribution and a working correlation matrix of repeated measurements. It allows both static and time-varying covariates to be included in the analysis. L-BRAT is a retrospective score approach in which genotypes are treated as random conditional on the phenotype and covariates. We perform simulation studies to evaluate the performance of L-BRAT, and compare it to the existing prospective methods. The results demonstrate that the retrospective association tests have better control of type I error when the phenotype model is misspecified, and are robust to various ascertainment schemes. Moreover, they are more powerful than the prospective tests. Finally, we apply L-BRAT to a genome-wide association analysis of repeated measurements of cocaine use in a longitudinal cohort.
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