Seminars

In survival analysis interest is often focused on the median time to event. This is particularly true in cancer clinical trials where the median survival time or median time to disease progression is frequently used to summarize the outcome from a particular therapy. One-sample procedures for generating confidence intervals for the median failure time have received considerable attention in the statistical literature (Reid, 1981; Brookmeyer and Crowley, 1982; Slud, Byar, and Green, 1984). Surprisingly less attention has been given to interval estimation for the difference in medians between two groups. We propose a nonparametric method based on a multiple imputation approach. Complete survival times for censored observations are first imputed by drawing survival times from the conditional distribution given survival up to the time of censoring, using the Kaplan-Meier curve for each group. Due to the censoring, it will often be necessary to restrict the observation period to maximum time T. The difference in medians and the variance of the difference for the "complete" dataset are estimated as described in Price and Bonett (2002), where the variance estimate is computed from the order statistics for each group. Rubin's (1987) multiple imputation procedure is then used to obtain the total variance of the estimated difference by combining the within and between-imputation variances, from which confidence intervals are derived. Preliminary simulation results indicate that the method provides reasonably accurate coverage probabilities for sample sizes ranging from 30 to 100 per group with censoring proportions of 10% - 40%.

This is joint work with Theodore Karrison, PhD.