How do I meta-analyse hazard ratios?
Pool the natural logarithm of each hazard ratio, weighted by the inverse of its variance, then exponentiate the result back. When a paper reports only a hazard ratio and its confidence interval, you can recover the standard error from the interval — that is usually all you need.
Recovering the standard error
Time-to-event papers almost never publish a standard error. They publish a hazard ratio and a 95% confidence interval, and that is sufficient: on the log scale the interval is symmetric around the log hazard ratio, so the standard error is the width of the log interval divided by twice 1.96.
Concretely: take the natural log of the upper and lower limits, subtract, and divide by 3.92. If the interval is reported at a level other than 95%, use the matching multiplier instead of 1.96 — this is an easy and invisible mistake.
When the paper gives you almost nothing
Some trials report only a survival curve, a log-rank p-value, and numbers at risk. Established indirect methods can reconstruct an estimate and its variance from these ingredients, and they are legitimate when applied transparently.
Any reconstructed estimate should be flagged as such in your extraction and tested in a sensitivity analysis that excludes them. If your conclusion depends on the reconstructed studies, that is a finding about your evidence base, and it belongs in the results.
What not to mix
A hazard ratio is a ratio of event rates over time. A risk ratio is a ratio of cumulative probabilities at a point in time. They answer different questions and are not interchangeable, even though both are ratios that sit near 1 and both get called "the effect on survival" in discussion sections.
Do not pool them together. If some trials report a hazard ratio and others report survival at a fixed timepoint, either restrict to one measure and report the other narratively, or analyse them as separate outcomes with separate certainty ratings.
Checking the assumption before you rely on it
Proportional hazards is an assumption, not a property of the data. Look at the published Kaplan–Meier curves. Crossing curves, or a treatment effect that only appears after a delay, both violate it — and both are common in immunotherapy and in prevention trials.
When it is violated, a pooled hazard ratio is still computable and still meaningless as a single summary. Say so, and consider reporting effects at clinically relevant timepoints instead of, or alongside, the ratio.
Where this answer stops
A hazard ratio assumes the ratio of hazards is roughly constant over follow-up. When survival curves cross or separate late, a single hazard ratio summarises a quantity that changed during the trial, and pooling several such numbers compounds the problem rather than averaging it away.