Robust estimation for secondary trait association in case-control genetic studies.

Secondary trait genetic association provides insight into the genetic architecture of disease etiology but requires caution in estimation. Ignoring case-control sampling may introduce bias into secondary trait association. In this paper, we compare the efficiency and robustness of various inverse probability weighted (IPW) estimators and maximum likelihood (ML) estimators. ML methods have been proposed but require correct modeling of both the secondary and the primary trait associations for valid inference. We show that ML methods using a misspecified primary trait model can severely inflate the type I error. IPW estimators are typically less efficient than ML estimators but are robust against model misspecification. When the secondary trait is available for the entire cohort, the IPW estimator with selection probabilities estimated nonparametrically and the augmented IPW estimator improve efficiency over the simple IPW estimator. We conclude that in large genetic association studies with complex sampling schemes, IPW-based estimators offer flexibility and robustness, and therefore are a viable option for analysis.