# Meta-analysis random effects model for survival estimates

I want to perform a meta-analysis of survival estimates, and I want to fit a random effects model. I am working in R, and my data.frame looks something along the lines of:

Study  Age10  Age20  Age30 ...
A      0.90   0.83   0.70
B      0.99   0.93   0.78
.      .      .      .
.      .      .      .
.      .      .      .


I've been looking into the DerSimonian-Laird model and the function I came across in R only handles meta-analysis of odds ratios? What's an R function for handling survival estimates?

library("rmeta")
data("smoking", package = "HSAUR")
smokingDSL <- meta.DSL(smoking[["tt"]], smoking[["tc"]], smoking[["qt"]], smoking[["qc"]],
names = rownames(smoking))
summary(smokingDSL)


Does it make sense to apply the DSL model to meta-analyze survival estimates? Or should I look into another random effects model? Also, is there a package in R that lets me fit the model?

• Try reading the documentation for meta.summaries. There are plenty of other options, see the CRAN TaskView on MetaAnalysis for some suggestions. Apr 5 '17 at 13:17
• Thank you, I will take a look. Do you know if the DerSimonian-Laird random effects model can be directly used to combine survival estimates like the ones in my data? Apr 5 '17 at 14:28
• From your description, it is not clear what your data is. In principle, if you have a log-hazard ratio with SEs (you can usually get them from confidence intervals, p-values or numbers of events), then you can usually use just about any method that takes effect estimate & SE as an input (inverse variance, DSL, Hartung-Knapp, various Bayesian variants etc.). This is a generic approach that applies for many outcomes (with certain limitations, e.g. if events are somewhat rare or est+-SE is not a good summary for other reasons, if the number of studies is low etc. these methods run into trouble). Apr 12 '17 at 15:44
• I have added an extra paragraph to my answer which includes some of @Björn material to make the answer more comprehensive. Apr 12 '17 at 16:31

There are a number of methods for estimating the $\tau^2$ parameter in meta-analysis. Perhaps because DerSimonian and Laird were first on the scene their method is sometimes erroneously identified with random effects meta-analysis. For a review of some of the methods for estimating $\tau^2$ one might refer to this article by Wolfgang Viechtbauer entitled "Bias and Efficiency of Meta-Analytic Variance Estimators in the Random-Effects Model" which compares five methods with extensive discussion. There is also a recent article with more simulations here. The short conclusion is that no method is demonstrably superior but the restricted maximum likelihood estimator and Paule and Mandel method have good overall properties.
As far as what statistics can be extracted from the primary studies and used then note that all that is needed is an estimate $y_i$ with its standard error $s_i$ and optionally the value of $\tau^2$ mentioned above.