Pooling of HR from univariate or multivariable Cox PH for meta-analysis?

Hi all,

I would like to perform meta-analysis of survival outcomes, specifically hazard ratio (HR) obtained from Cox PH model. I understand that some things have to be made similar across different studies. i.e.

  • The calculation of time-to-event. Start date - whether it is at the time of diagnosis or time of surgery and end date - whether it is death from any causes or death due to disease; this has to be pre-specified and only the ones with the same definition can be pooled together.

They are plenty of papers that did the univariate Cox PH models and only enter the significant ones in the multivariable analysis (I understand that this practice should not be done). Hence, the set of factors included in multivariable models may be different across different studies.

I heard HR should be obtained from univariate Cox PH model so that the HR is “pure”; “before any adjustments”. But I am not too if this how it should be done.

Seeking your knowledge and expertise. Thanks!

Univariate unadjusted HRs are improper and are shown to depend on the covariate distribution for the covariates UNadjusted for. See Statistical Thinking - Unadjusted Odds Ratios are Conditional

Meta-analysis using only summary data is in general less valuable that it appears. I’d take a single large prospective study with patient-level data almost any day.


I will second that. Also HRs are noncollapsible therefore the unconditional estimates will be tilted towards the null. Finally, because covariate distribution varies between trials, heterogeneity will increase (sometimes markedly) simply for this reason


Thank you!

We have identified a list of studies in our meta-analyses. A particular variable is part of the multivariable model for some studies but a univariate model for others. Can I pool them in the meta-analysis, or should I do a subgroup of meta-analysis to separate these two? If I can pool them without the split, should I include the information (whether uni or multivariable) in the supplementary?

This is an interesting topic. Has any study assessed it in the context of meta-analysis?

A thesis supervised by the late Doug Altman attempted this but was not conclusive - see here. We are also working on this at the moment. The main issue is that this can only work with noncollapsible effect measures as these are the only ones that will have different effect magnitudes for two groups (say male and female) as well as the group of all of them together. All three must be different (if gender is prognostic for the outcome) because males and females are different groups of people and are also different from the group of both together. This distinction fails with collapsible measures and was what first brought our attention to this issue that resulted in that massive thread you started.

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I just found this paper written by Frank on this topic

A newer version is here.

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