Confidence Intervals for the Survival Function Using Cox's Proportional- Hazard Model with Covariates

An estimate of the survival function is presented which combines the parameter estimates derived by Cox and the estimate of the underlying hazard function derived by Breslow. Using a heuristic argument, an asymptotic variance is derived for this estimate of the survival function, and the results are extended to the log and logit survival functions. From the derived asymptotic variance, confidence intervals can be formed for the survival function for any values of the time and the covariates. Simulation results indicate that these confidence intervals give accurate coverage probabilities even for small sample sizes.