Gene‐based association analysis for bivariate time‐to‐event data through functional regression with copula models

Several gene‐based association tests for time‐to‐event traits have been proposed recently to detect whether a gene region (containing multiple variants), as a set, is associated with the survival outcome. However, for bivariate survival outcomes, to the best of our knowledge, there is no statistical method that can be directly applied for gene‐based association analysis. Motivated by a genetic study to discover the gene regions associated with the progression of a bilateral eye disease, age‐related macular degeneration (AMD), we implement a novel functional regression (FR) method under the copula framework. Specifically, the effects of variants within a gene region are modeled through a functional linear model, which then contributes to the marginal survival functions within the copula. Generalized score test statistics are derived to test for the association between bivariate survival traits and the genetic region. Extensive simulation studies are conducted to evaluate the type I error control and power performance of the proposed approach, with comparisons to several existing methods for a single survival trait, as well as the marginal Cox FR model using the robust sandwich estimator for bivariate survival traits. Finally, we apply our method to a large AMD study, the Age‐related Eye Disease Study, and to identify the gene regions that are associated with AMD progression.