  Kernel-based multi-marker tests for survival outcomes use primarily the Cox
model to adjust for covariates. The proportional hazards assumption made by the
Cox model could be unrealistic, especially in the long-term follow-up. We
develop a suite of novel multi-marker survival tests for genetic association
based on the accelerated failure time model, which is a popular alternative to
the Cox model due to its direct physical interpretation. The tests are based on
the asymptotic distributions of their test statistics and are thus
computationally efficient. The association tests can account for the
heterogeneity of genetic effects across sub-populations/individuals to increase
the power. All the new tests can deal with competing risks and left truncation.
Moreover, we develop small-sample corrections to the tests to improve their
accuracy under small samples. Extensive numerical experiments show that the new
tests perform very well in various scenarios. An application to a genetic
dataset of Alzheimer's disease illustrates the tests' practical utility.
