Confidence Intervals for the Median Survival Time: A Monte Carlo Evaluation and a Software-Issue Application

Abstract

The median survival time is widely reported because it is robust and easily interpretable. Under right censoring, however, obtaining a confidence interval with two finite endpoints can be difficult. We present a Monte Carlo comparison of four confidence-interval procedures: the linear-scale Brookmeyer–Crowley interval, the log-minus-log Brookmeyer–Crowley interval, the bootstrap percentile interval and the direct asymptotic interval. Performance is evaluated under different censoring and follow-up conditions using finite-interval coverage, finite-interval length and the probability that a finite two-sided interval is unavailable. The main design uses exponential, lognormal and Weibull lifetimes, while targeted extensions compare equal censoring percentages with different follow-up support, larger samples and additional bootstrap resamples. We also relate this behaviour to a simple theoretical result and illustrate it using software-issue resolution times. The first three procedures perform similarly when follow-up is sufficient, whereas the direct asymptotic interval is more sensitive due to the need for density estimation. An application to 619 issues from the scikit-learn GitHub repository illustrates these findings—the median time to closure cannot be estimated with 14 days of follow-up, but Zis estimated as 14.17 days when follow-up is extended to 30 days. Although the specific procedure affects finite-sample performance, sufficient follow-up beyond the median remains the key requirement for reliable inference.