Confidence Intervals and Confidence Bands for the Difference of Two Median Survival Times

Abstract

We are concerned with the estimation of the discrepancy between two treatments when right-censored survival data are accompany with covariates. Conditional confidence intervals given the available covariates and confidence bands over a certain region of covariates are constructed for the difference of two median survival times under the unstratified and stratified Cox proportional hazards models, respectively. The proposed confidence intervals and confidence bands provide the information about the difference in survivorship for patients with common covariates but in different treatments. The results of the simulation study investigation of the coverage probability and expected length of the confidence intervals and bands suggest the one designed for the stratified Cox model when data fit reasonably with the model. When the stratified Cox model is not feasible, however, the one designed for the unstratified Cox model is recommended. The use of the confidence intervals and confidence bands is finally illustrated with a HIV+ data set.