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A comparison of methods for fixed effects meta-analysis of individual patient data with time to event outcomes

Centre for Medical Statistics and Health Evaluation, University of Liverpool, Liverpool, L69 3GS and Cancer Research UK Liverpool Cancer Trials Unit, cat1{at}liv.ac.uk

Paula Ruth Williamson

Centre for Medical Statistics and Health Evaluation, University of Liverpool, Liverpool, L69 3GS and Cancer Research UK Liverpool Cancer Trials Unit

Background Alternative methods for individual patient data (IPD) meta-analysis of time-to-event outcomes have been established and utilized in practice. The most common approach is a stratified log-rank analysis. The IPD approach is considered to be the gold standard approach for meta-analysis and is becoming increasingly more popular but the performance of different methods has not been studied previously.

Purpose To compare commonly used methods for fixed effects meta-analysis of individual patient time-to-event data.

Methods The stratified log-rank analysis, an inverse variance weighted average of Cox model estimates, and the stratified Cox regression model are compared. First, a theoretical comparison of approaches is undertaken. Second, the bias and coverage are assessed for the pooled hazard ratio using simulated data under commonly encountered meta-analysis conditions. Finally, a comparison is presented using empirical data from four separate systematic reviews of anti-epileptic drug trials where IPD are available for two time-to-event outcomes.

Results For hazard ratio close to 1 with minimal heterogeneity between trials, theoretical results suggest similar results should be expected from all the three methods. Results for empirical and simulated data are in keeping with the theoretical results and show all the three methods perform well under these conditions. When there is no heterogeneity and the proportional hazards assumption holds, the stratified Cox model and inverse variance weighted average produce similar estimates of the pooled treatment effect and are to be preferred to the stratified log-rank analysis when the underlying treatment effect is large. Coverage values diminish for all the three methods and are below 95% for low or moderate heterogeneity. The low coverage values highlight the need for models that appropriately account for or explore the between trial variation.

Limitations Until larger simulations can be undertaken, conclusions based on the simulated and empirical data should only be applied to small meta-analyses of four or five trials.

Conclusions These investigations suggest that under normal conditions all three methods provide similar results. For moderate heterogeneity coverage for all the three fixed effects models depreciates. Clinical Trials 2007; 4: 621—630. http://ctj.sagepub.com

Clinical Trials, Vol. 4, No. 6, 621-630 (2007)
DOI: 10.1177/1740774507085276


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