Integrative omics, the joint analysis of outcome and multiple types of omics data, such as genomics, epigenomics, and transcriptomics data, constitute a promising approach for powerful and biologically relevant association studies. These studies often employ a
case-control design, and often include nonomics covariates, such as age and gender, that may modify the underlying omics risk factors. An open question is how to best integrate multiple omics and nonomics information to maximize statistical power in case-control studies that ascertain individuals based on the phenotype. Recent work on integrative omics have used prospective approaches, modeling
case-control status conditional on omics, and nonomics risk factors. Compared to univariate approaches, jointly analyzing multiple risk factors with a prospective approach increases power in nonascertained cohorts. However, these prospective approaches often lose power in
case-control studies. In this article, we propose a novel statistical method for integrating multiple omics and nonomics factors in
case-control association studies. Our method is based on a retrospective likelihood function that models the joint distribution of omics and nonomics factors conditional on
case-control status. The new method provides accurate control of Type I error rate and has increased efficiency over prospective approaches in both simulated and real data.