A Note on Estimating Treatment Effect for Time-to-event Data in a Literature-based Meta-analysis

Objectives: In a literature-based meta-analysis for time-to-event data, the hazard ratio in each trial is often estimated from the summary statistics described in the article. Several methods have been proposed: the direct method (Peto method); the indirect method using a p-value by the log-rank test and the number of total events; and the survival curve method using the Kaplan-Meier estimate. However, there has been no published report on a detailed investigation of these methods. We evaluated the performance of these methods by simulation. Methods: In a set of simulation experiments, performance of five methods was evaluated by the bias of estimated log hazard ratio and coverage probability of the confidence interval. The methods evaluated were: 1) Cox regression analysis, 2) direct method, 3) indirect method, 4) survival curve method, and 5) modified survival curve method with an alternative weighting scheme. Results: The direct method was confirmed to have a high degree of accuracy. Although the indirect method was also highly accurate, it tended to underestimate effect size when there was a strong effect. The survival curve method tended to underestimate effect size when event numbers were small and effect size was large. The modified survival curve method could alleviate this tendency toward underestimation of effect size found with the original survival curve method. Conclusions: When the Kaplan-Meier curve is used to estimate hazard ratios in trials with small sample size in the literature-based meta-analysis, we should check critically whether those trials’ hazard ratios and overall hazard ratio are underestimated or not.