Estimation of odds ratios of genetic variants for the secondary phenotypes associated with primary diseases

Genetic association studies for binary diseases are designed as case-control studies: the cases are those affected with the primary disease and the controls are free of the disease. At the time of case-control collection, information about secondary phenotypes is also collected. Association studies of secondary phenotype and genetic variants have received a great deal of interest recently. To study the secondary phenotypes, investigators use standard regression approaches, where individuals with secondary phenotypes are coded as cases and those without secondary phenotypes are coded as controls. However, using the secondary phenotype as an outcome variable in a case-control study might lead to a biased estimate of odds ratios (ORs) for genetic variants. The secondary phenotype is associated with the primary disease; therefore, individuals with and without the secondary phenotype are not sampled following the principles of a case-control study. In this article, we demonstrate that such analyses will lead to a biased estimate of OR and propose new approaches to provide more accurate OR estimates of genetic variants associated with the secondary phenotype for both unmatched and frequency-matched (with respect to the secondary phenotype) case-control studies. We also propose a bootstrapping method to estimate the empirical confidence intervals for the corrected ORs. Using simulation studies and analysis of lung cancer data for single-nucleotide polymorphism associated with smoking quantity, we compared our new approaches to standard logistic regression and to an extended version of the inverse-probability-of-sampling-weighted regression. The proposed approaches provide more accurate estimation of the true OR.