Copula-based score test for bivariate time-to-event data, with application to a genetic study of AMD progression

Motivated by a genome-wide association study to discover risk variants for the progression of Age-related Macular Degeneration (AMD), we develop a computationally efficient copula-based score test, in which the dependence between bivariate progression times is taken into account. Specifically, a two-step estimation approach with numerical derivatives to approximate the score function and observed information matrix is proposed. Both parametric and weakly parametric marginal distributions under the proportional hazards assumption are considered. Extensive simulation studies are conducted to evaluate the Type I error control and power performance of the proposed method. Finally, we apply our method to a large randomized trial data, the Age-related Eye Disease Study, to identify susceptible risk variants for AMD progression. The top variants identified on Chromosome 10 show significantly differential progression profiles for different genetic groups, which are critical in characterizing and predicting the risk of progression-to-late-AMD for patients with mild to moderate AMD.