Estimates and confidence intervals for median and mean life in the proportional hazard model

Abstract

Estimation procedures and confidence intervals are given for the median and mean survival time in the proportional hazard regression model. For median survival, the methods apply to censored data. The procedures are based on Cox's partial likelihood estimates of the linear model parameters in the log linear proportional hazard model and on Breslow's estimate of the baseline hazard function. The asymptotic properties of these semiparametric estimates are developed and they are compared with the optimal parametric estimates for the Weibull regression model. For the parameter values considered, the more generally valid semiparametric estimate of mean survival loses little efficiency relative to the optimal parametric estimates in this model unless the Weibull shape parameter is close to zero. The efficiency loss for the semiparametric estimate of median survival is greater but not severe unless censoring is heavy. We also compare the optimal parametric estimates of mean and median survival with the Weibull shape parameter known and unknown and find that the efficiency loss for the unknown shape estimate is small.