Meta-analysis of median survival times with inverse-variance weighting

We consider the problem of meta-analyzing outcome measures based on median survival times. Primary studies with time-to-event outcomes often report estimates of median survival times and confidence intervals based on the Kaplan-Meier estimator. However, outcome measures based on median survival are rarely meta-analyzed, as standard inverse-variance weighted methods require within-study standard errors that are typically not reported. In this article, we consider an inverse-variance weighted approach to meta-analyze median survival times that estimates the within-study standard errors from the reported confidence intervals. We show that this method consistently estimates the standard error of median survival when applied to confidence intervals constructed by the Brookmeyer-Crowley method. We conduct a series of simulation studies evaluating the performance of this approach at the study level (i.e., for estimating the standard error of median survival) and the meta-analytic level (i.e., for estimating the pooled median, difference of medians, and ratio of medians) for commonly used confidence intervals for median survival, including the Brookmeyer-Crowley method and nonparametric bootstrap. We find that this approach often performs comparably to a benchmark approach that uses the true within-study standard errors for meta-analyzing median-based outcome measures when within-study sample sizes are moderately large (e.g., above 50). However, when the effective sample sizes are small, the method can yield biased estimates of within-study standard errors. We illustrate an application of this approach in a meta-analysis evaluating survival benefits of being assigned to experimental arms versus comparator arms in randomized trials for non-small cell lung cancer therapies.

💡 Research Summary

This paper addresses a practical gap in meta‑analysis of time‑to‑event outcomes: while many primary studies report median survival times (MST) together with confidence intervals (CIs) derived from Kaplan‑Meier curves, standard inverse‑variance weighted meta‑analysis requires the within‑study standard error (SE) of the effect estimate, which is rarely provided for medians. The authors propose a simple yet theoretically justified method to recover the SE from the reported CI, enabling the use of conventional inverse‑variance weighting for pooling medians, differences of medians, or ratios of medians across studies.

Methodological core
The key insight is that, under the Brookmeyer‑Crowley (BC) construction of CIs for the median, the width of the interval converges to (2z_{1-\alpha/2}\times SE) as the sample size grows. Consequently, the SE can be back‑calculated by the Wald‑type approximation
\