Sankhya: The Indian Journal of Statistics

2003, Volume 65, Pt. 2, 422-439

On The Asymptotic Relative Efficiency Of Estimates From Cox's Model

By

JONG-HYEON JEONG, University of Pittsburgh, Pittsburgh, USA and DAVID OAKES, University of Rochester Medical Center, Rochester, USA

SUMMARY: Some new explicit results are derived for the asymptotic relative efficiency of the semiparametric (partial likelihood) estimates of the regression coefficient and cumulative baseline hazard in Cox's model, relative to those from a correctly specified exponential or Weibull parametric model. It is assumed that the hazard ratio corresponding to the single scalar covariate follows a gamma distribution. Our results generalize those of Miller (1983) for the single sample setting, i.e. without covariates, and of Dabrowska and Doksum (1987), who assumed independence of the survival time from the covariate under the true distribution. It is shown that, in contrast to the results for estimation from partial likelihood, use of the semiparametric estimation model for prediction will usually lead to substantial loss of efficiency.

AMS (1991) subject classification. 62N99.

Key words and phrases. Baseline hazard, censoring, counting process, frailty model, proportional hazards model, survival analysis.

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