Random-effects Cox proportional hazards model: general variance components methods for time-to-event data

Proportional hazards regression models are commonly used to study factors associated with time-to-event data. Because many complex genetic diseases exhibit variation in age at onset, it is important to have the capability to perform survival analyses on data collected from individuals whose observations are correlated due to shared genes or environment. While there are widely accepted methods for variance components analysis for simple quantitative traits, a parallel methodology for survival data has not been available. This manuscript outlines a method to perform variance component analyses under general random effects proportional hazards models. This method is based on a Laplace approximation, and makes computation for correlated time-to-event data feasible. The correlated frailty models described here can be used to perform genetic analyses, and other analyses with structured random effects, on age-at-onset data in a manner analogous to standard variance components methods for quantitative traits. We illustrate the use of the method by examining the heritability of breast cancer in a large familial cohort study. We also perform variance components linkage analyses on data simulated for the Twelfth Genetic Analysis Workshop (GAW12), and further examine the performance of this method for linkage analysis in a simulation study. The breast cancer analyses support significant heritability of disease age-at-onset that is of moderate size. The variance component linkage analyses successfully identify the location of the disease genes that were simulated to have a direct impact on age-at-onset. The methods outlined here make it possible to perform general variance components analyses on time-to-event endpoints, even on large data sets, in a computationally efficient manner.