On the random effects cox model with time-varying regression parameter

In a recent paper, Xu and Gamst (Lifetime Data Anal., 13, 2007) investigate the effect of misspec14 ifying a time-varying regression effect in the random effects Cox model. The authors show that the non-parametric maximum likelihood estimator of the regression coefficient, derived from a misspeci16 fied random effects proportional hazards Cox model, is consistent for a quantity that can be interpreted as an averaged regression effect over time. Such an average effect may be of interest as a summary measure, even if it is derived from a misspecified model. In this work, we formally prove the existence of the estimator proposed by Xu and Gamst (Lifetime Data Anal., 13, 2007), and we show its asymp20 totic normality. A simulation study is provided, that explores this normal approximation for various finite sample sizes. © 2009 Taylor & Francis Group, LLC. All rights reserved.