CONFIDENCE-INTERVALS FOR MEDIAN SURVIVAL TIMES UNDER A PIECEWISE EXPONENTIAL MODEL WITH PROPORTIONAL HAZARDS COVARIATE EFFECTS

Brookmeyer and Crowley derived a non-parametric confidence interval fo r the median survival time of a homogeneous population by inverting a generalization of the sign test for censored data. The 1-alpha confide nce interval for the median is essentially the set of all values t suc h that the Kaplan-Meier estimate of the survival function at time t do es not differ significantly from one-half at significance level alpha. Here I extend the method to incorporate covariates into the analysis by assuming an underlying piecewise exponential model with proportiona l hazards covariate effects. Maximum likelihood estimates of the model parameters are obtained via iterative techniques, from which the esti mated (log) survival curve is easily constructed. The delta method pro vides asymptotic standard errors. Following Brookmeyer and Crowley, I find the confidence interval for the median survival time at a specifi ed value of the covariate vector by inverting the sign test. I illustr ate the methods using data from a clinical trial conducted by the Radi ation Therapy Oncology Group in cancer of the mouth and throat. It is seen that the piecewise exponential model provides considerable flexib ility in accommodating to the shape of the underlying survival curve a nd thus offers advantages to other, more restrictive, parametric model s. Simulation studies indicate that the method provides reasonably acc urate coverage probabilities.