Meta-analysis of time-to-event data for single group design

Hi everyone,

I would like to perform a meta-analysis of time-to-event data for a single group (i.e. there is no comparison group). How do I do so, what are the statistics required?

I understand that for 2-group studies, the effect sizes are hazard ratio and its variance.


Ignoring for the moment the likely heterogeneity across studies that makes the use of random effects a good idea, after getting the individual subject level data combined across studies you can compute the Kaplan-Meier estimate and its 0.95 confidence interval.

We do this type of analysis at work relatively commonly the purpose of creating a baseline natural history model for cost-effectiveness analyses. The usual questions up front are whether you need a meta-analysis at all since usually one of the component studies will provide the most useful estimate of time-to-event in your given geographical region/health system/time. A pooled average will probably be pooling across these things and thus not really be applicable to anywhere in particular. Less commonly, if you are desperate to reduce variance in the study most relevant to your particular question you can fit an RE model and then use the shrunken estimate from the study of interest. This will be an estimate of time to event in that study accounting for some borrowing of strength from the other studies. As usual you’ll have to determine whether bias/variance trade-off makes sense.

In any event I would recommend digitizing curves and using the guyot algorithm to recreate pseudo-ipd. From there you can do as @f2harrell suggests above or do the usual exercise of fitting a variety of parametric models. There’s lots of code out there to do this in a Bayesian way (Jeroen Janssen is the key author there) but with pseudo-ipd from every study you have a lot of flexibility using existing software like flexsurvreg in R. I think survHE has an implementation of the guyot algo.

Some good methods advice from a health ec perspective here: Technical Support Documents – NICE Decision Support Unit


Thank you for the great insights. Can clarify if it it’s okay to combine the individual studies IPD into a single dataset and run the usual survival analysis, without taking into a consideration any heterogeneity between studies?

I think there are many ways to consider heterogeneity in your analysis. I described a few different approaches above (choose a single study, fit an RE model and use a shrunken estimate of the same, use an RE model and take the average if it is meaningful). Another option if there is lots of heterogeneity and you still think a meta-analysis is reasonable would be to use the predictive distribution from an RE model. The TSDs linked above discuss all of this (particularly TSD 3 and TSD 5) and are well worth the read.

Stephen Senn in his 2000 article on meta-analysis shows that there is a clear map from methods to analyze a multi-center RCT to a meta-analysis. I don’t see how ignoring the study level in the hierarchy could be valid.

The meta-analysis of a group of simple clinical trials can, from one point of view, be regarded as isomorphic to a multi-center clinical trial, with ‘group’, ‘trial’, ‘patient’ in the former being replaced by ‘trial’, ‘center’, ‘patient’ in the latter. Both are examples of hierarchical data sets.

The best way to deal with this is to use some of the regression methods mentioned above, that do not ignore the hierarchical structure of the data.

Senn S. The Many Modes of Meta. Drug Information Journal. 2000;34(2):535-549. (link)