Meta-analytic Cox Proportional Hazards — Pooling Survival Estimates Across Studies

A fixed-effects model assumes all studies estimate the same underlying true hazard ratio and differences between study results are due solely to sampling error. A random-effects model (e.g., DerSimonian-Laird) treats the true HR as varying across studies and estimates the between-study variance tau^2. The random-effects pooled HR is more conservative (wider CI) and more appropriate when studies differ in population, follow-up, or covariate adjustment. When heterogeneity is low (I^2 < 25%), both models give similar results.

The Parmar method uses reported statistics such as log-rank p-values, observed event counts, or total follow-up person-time to back-calculate ln HR and SE. The Guyot algorithm (2012) reconstructs the full individual-patient dataset from digitised Kaplan-Meier curves and at-risk numbers, then re-fits a Cox model. Both approaches introduce approximation error — clearly document the reconstruction method and treat reconstructed estimates as secondary in sensitivity analyses.

Strictly speaking, pooling adjusted and unadjusted HRs conflates different estimands. In practice, systematic review teams often do so pragmatically while presenting unadjusted and adjusted subgroups separately in sensitivity analyses. If the adjustment sets differ widely across studies, consider restricting the primary analysis to studies reporting a consistent adjustment strategy or use meta-regression to examine whether adjustment level moderates the pooled HR.

There is no strict minimum, but with fewer than four or five studies the random-effects estimate of tau^2 is highly imprecise and confidence intervals are unreliable. With only two studies, heterogeneity statistics are essentially uninformative. For small collections, use a fixed-effects model with extreme caution, report the prediction interval from a random-effects model even if tau^2 is poorly estimated, and interpret the pooled HR as a weighted average of the available evidence rather than a precise population parameter.

IPD meta-analysis is the gold standard: it allows consistent covariate adjustment, direct verification of the proportional hazards assumption, and flexible subgroup analysis within each study. It also avoids reconstruction error. However, IPD sharing requires data-sharing agreements and substantial resource investment. Aggregate-data pooling using published HRs or reconstructed estimates is far more feasible and gives similar point estimates when study-level summaries are adequately reported.