Meta-analysis of median survival times with inverse-variance weighting
Pith reviewed 2026-05-23 01:49 UTC · model grok-4.3
The pith
Estimating standard errors from reported confidence intervals enables inverse-variance meta-analysis of median survival times.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
When confidence intervals for median survival are constructed by the Brookmeyer-Crowley method, the standard error of the median can be recovered from the interval width in a way that is consistent for the true sampling variability of the Kaplan-Meier median; this recovered standard error then supports unbiased inverse-variance weighted meta-analysis of single medians, differences, and ratios.
What carries the argument
Inverse-variance weighting that derives each study's standard error by scaling the width of its reported confidence interval for the median survival time.
If this is right
- Median survival times that come with Brookmeyer-Crowley intervals can be combined using ordinary inverse-variance meta-analysis.
- The resulting pooled estimates of the median, difference of medians, and ratio of medians match the performance of an oracle that knows the true within-study standard errors once sample sizes are moderately large.
- The approach applies directly to both single-arm and comparative (difference or ratio) median-based summaries.
- Bias appears when effective sample sizes fall below moderate levels, limiting use in very small studies.
Where Pith is reading between the lines
- The same interval-to-standard-error recovery could be examined for other quantiles or for parametric survival models that also produce interval estimates whose width scales with variance.
- Meta-analysts working with time-to-event data might compare this median-focused method against hazard-ratio or restricted-mean approaches that avoid the need to recover standard errors.
- Validation across disease areas with different censoring patterns would show how far the moderate-sample-size performance carries over.
Load-bearing premise
The reported confidence interval widths must be a consistent multiple of the true standard error of the median estimator.
What would settle it
A Monte Carlo experiment that generates repeated Kaplan-Meier medians under the Brookmeyer-Crowley interval construction and checks whether the standard errors recovered from the intervals match the empirical standard deviation of those medians.
read the original abstract
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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript proposes an inverse-variance weighted meta-analysis for median survival times by estimating within-study standard errors directly from reported confidence intervals. It establishes consistency of the resulting SE estimator when the intervals are constructed by the Brookmeyer-Crowley method, evaluates finite-sample performance via simulations at both the study level and the meta-analytic level (pooled median, difference of medians, ratio of medians) against a benchmark that uses the true SEs, and illustrates the approach on a meta-analysis of randomized trials in non-small cell lung cancer.
Significance. If the consistency result holds, the work supplies a theoretically grounded and practically usable route to meta-analyze a commonly reported but previously difficult-to-pool outcome measure. Credit is due for the direct analytic argument under the Brookmeyer-Crowley construction together with simulation evidence across study sizes and meta-analytic targets.
minor comments (2)
- [Abstract] Abstract: the description of the simulation studies omits the exact parameter values (sample sizes, number of replications, censoring rates) and does not indicate whether variability measures or error bars accompany the reported performance metrics.
- [Simulation studies] Simulation studies section: the text notes degradation for small effective sample sizes but does not quantify the threshold at which bias in the estimated SE becomes practically consequential for the meta-analytic estimators.
Simulated Author's Rebuttal
We thank the referee for the positive assessment of the manuscript, the recognition of the consistency result under the Brookmeyer-Crowley construction, and the recommendation of minor revision. No specific major comments were listed in the report, so we have no points requiring direct rebuttal or revision at this stage.
Circularity Check
No significant circularity; direct estimation with external consistency check
full rationale
The paper defines an estimator for within-study SEs by inverting reported CIs and proves its consistency specifically when those CIs come from the Brookmeyer-Crowley procedure (whose width is asymptotically a known multiple of the true median SE). This is an external property of the BC method, not a self-definition or fitted parameter renamed as a prediction. Performance is validated in simulations against known true SEs rather than by construction. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling appears in the derivation chain. A score of 2 reflects only the possibility of routine self-citation that is not central to the consistency result.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Brookmeyer-Crowley confidence intervals for the median have widths that are consistent for the true standard error of the Kaplan-Meier median estimator.
discussion (0)
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