Quantile Regression in the Secondary Analysis of Case–Control Data

Case–control design is widely used in epidemiology and other fields to identify factors associated with a disease. Data collected from existing case–control studies can also provide a cost-effective way to investigate the association of risk factors with secondary outcomes. When the secondary outcome is a continuous random variable, most of the existing methods focus on the statistical inference on the mean of the secondary outcome. In this article, we propose a quantile-based approach to facilitating a comprehensive investigation of covariates’ effects on multiple quantiles of the secondary outcome. We construct a new family of estimating equations combining observed and pseudo outcomes, which lead to consistent estimation of conditional quantiles using case–control data. Simulations are conducted to evaluate the performance of our proposed approach, and a case–control study on genetic association with asthma is used to demonstrate the method. Supplementary materials for this article are available online.