Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 1, 25--42

MISSPECIFICATION OF MARGINAL HAZARDS MODELS IN MULTIVARIATE FAILURE TIME DATA

By

LIMIN X. CLEGG, * National Cancer Institute, Bethesda*

JIANWEN CAI,

PRANAB KUMAR SEN

and

LAWRENCE L. KUPPER,
* University of
North Carolina, Chapel Hill*

SUMMARY. Hazard functions for correlated censored data are usually formulated through the Cox regression model in a marginal regression framework. We investigate properties of the maximum pseudo partial likelihood estimator vector under a possibly misspecified marginal Cox regression model. The estimator vector is shown to be consistent for an implicitly defined parameter vector and is asymptotically Gaussian as well, with a covariance matrix that can be consistently estimated. The general results are applied to some special cases, including the case of misspecifying the type of baseline hazards function for the Cox model when the regression functional form is correctly specified. Simulation results confirm that the asymptotic results are applicable for sample sizes seen in practice.

*AMS (1991) subject classification.* 62H99, 62P10.

*Key words and phrases. *Censoring, Cox regression, correlated failure
times, marginal hazard rate, martingale, model misspecification,
multivariate failure times, partial likelihood, semiparametric
model, survival data.