Family-based association test for time-to-onset data with time-dependent differences between the hazard functions

In genetic association studies, the differences between the hazard functions for the individual genotypes are often time-dependent. We address the non-proportional hazards data by using the weighted logrank approach by Fleming and Harrington [1981]:Commun Stat-Theor M 10:763-794. We introduce a weighted FBAT-Logrank whose weights are based on a non-parametric estimator for the genetic marker distribution function under the alternative hypothesis. We show that the computation of the marker distribution under the alternative does not bias the significance level of any subsequently computed FBAT-statistic. Hence, we use the estimated marker distribution to select the Fleming-Harrington weights so that the power of the weighted FBAT-Logrank test is maximized. In simulation studies and applications to an asthma study, we illustrate the practical relevance of the new methodology. In addition to power increases of 100% over the original FBAT-Logrank test, we also gain insight into the age at which a genotype exerts the greatest influence on disease risk.