With advancements in high-throughput technologies, studies have been conducted to investigate the role of massive genetic variants in human diseases. While multi-marker tests have been developed for binary and continuous disease outcomes, there are few such tests available for time-to-event outcomes. The existing tests have various drawbacks, including slow computation speed, being conservative in small samples, incapability of dealing with confounding, etc. To facilitate the genetic association and interaction analyses of time-to-event outcomes, we develop four suites of novel multi-marker survival tests for genetic association and interaction. The new tests address all the drawbacks of the existing tests. Furthermore, they can account for potential genetic heterogeneity to enhance power and deal with left truncation of survival data. Some of the new tests can handle competing risks, and some apply to interval-censored data. Simulation studies show that the new tests perform very well in finite samples of various sizes. When the genetic effect is heterogeneous across individuals/subpopulations, the new association tests considering genetic heterogeneity are more powerful than the existing tests, which do not account for genetic heterogeneity. Using the new methods, we performed genome-wide association analyses of 1) age to Alzheimer's disease data from the Religious Orders Study and the Rush Memory and Aging Project (ROSMAP) and 2) age to early childhood caries data from a dbGaP study, Dental Caries: Whole Genome Association and Gene x Environment Studies.
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