On proportional hazards assumption under the random effects models

The proportional hazards mixed-effects model (PHMM) was proposed to handle dependent survival data. Motivated by its application in genetic epidemiology, we study the interpretation of its parameter estimates under violations of the proportional hazards assumption. The estimated fixed effect turns out to be an averaged regression effect over time, while the estimated variance component could be unaffected, inflated or attenuated depending on whether the random effect is on the baseline hazard, and whether the non-proportional regression effect decreases or increases over time. Using the conditional distribution of the covariates we define the standardized covariate residuals, which can be used to check the proportional hazards assumption. The model checking technique is illustrated on a multi-center lung cancer trial.