Abstract
In a recent paper, Xu and Gamst (Lifetime Data Anal., 13, 2007) investigate the effect of misspecifying 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 misspecified 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 asymptotic normality. A simulation study is provided, that explores this normal approximation for various finite sample sizes.
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Dupuy, JF. On the Random Effects Cox Model with Time-varying Regression Parameter. J Stat Theory Pract 3, 763–776 (2009). https://doi.org/10.1080/15598608.2009.10411958
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DOI: https://doi.org/10.1080/15598608.2009.10411958