STATISTICS IN MEDICINE Statist. Med. 2007; 26:2203–2213 Published online 22 August 2006 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/sim.2669 Covariates-dependent confidence intervals for the difference or ratio of two median survival times Yuh-Ing Chen ∗, † and Yu-Mei Chang ‡ Institute of Statistics, National Central University, Jhongli 320, Taiwan, R.O.C. SUMMARY In this paper, we are concerned with the estimation of the discrepancy between two treatments when right-censored survival data are accompanied with covariates. Conditional confidence intervals given the available covariates are constructed for the difference between or ratio of two median survival times under the unstratified and stratified Cox proportional hazards models, respectively. The proposed confidence intervals provide the information about the difference in survivorship for patients with common covariates but in different treatments. The results of a simulation study investigation of the coverage probability and expected length of the confidence intervals 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 is finally illustrated with a HIV+ data set. Copyright 2006 John Wiley & Sons, Ltd. KEY WORDS: confidence interval; median survival time; right-censored data; stratified Cox model 1. INTRODUCTION The median survival time is usually of interest when one investigates the survival distribution of patients in a clinical trial. In fact, confidence-interval estimation of a median survival time with right-censored data has been extensively studied by Reid [1], Brookmeyer and Crowley [2], Emerson [3], Slud et al. [4], and among others. For comparing two treatment groups with right- censored survival data, Wang and Hettmansperger [5] proposed a non-parametric confidence interval for the difference of two median survival times based on one-sample confidence intervals for individual median survival times. To avoid the estimation of the related density functions ∗ Correspondence to: Yuh-Ing Chen, Institute of Statistics, National Central University, Jhongli 320, Taiwan, R.O.C. † E-mail: ychen@stat.ncu.edu.tw ‡ E-mail: zhangym@mx.stat.ncu.edu.tw Contract/grant sponsor: National Science Council of Taiwan; contract/grant number: NSC95-2118-M-008-007-MY2 Received 17 January 2006 Copyright 2006 John Wiley & Sons, Ltd. Accepted 28 June 2006