Synthesis of Median Survival Time in Meta-analysis

Abstract

To the Editor: Individual patient data meta-analysis, the gold standard of systematic review, could provide both pooled median survival time and combined hazard ratio (HR) for survival outcomes.1 However, individual patient data are not usually available; only aggregate data can be obtained from most studies.2 The combined HRs and associated 95% confidence intervals (CIs) were usually calculated from aggregate data meta-analysis without pooled median survival times, which is sometimes problematic. First, combined HRs convey only the relative hazard risk of an event between different treatment groups. Second, HRs are not generally familiar to doctors or the patients who want to evaluate the efficacy of treatment. They are often more concerned about the direct effect of a treatment rather than the relative risk. Third, median survival times might be different in each group when the same HRs and 95% CIs are obtained from different aggregate data meta-analysis. Because of the inadequacy of pooled HRs, a method is needed to combine median survival times in aggregate data meta-analysis. We explore and test alternative methods of combining median survival times when conducting meta-analysis using aggregate data of survival outcomes. The study-level aggregate data and individual patient data were generated from simulated data to fit and evaluate the model we built. The effect size is the logarithm of median survival times, and the standard error is calculated from the sample size of each group and the 95% CIs of HRs, which represent the precision of the effect size. (SAS code for synthesis of median survival time in meta-analysis is provided in the eAppendix https://links.lww.com/EDE/A654.) Both fixed and random effect models were considered. We evaluated the model-fitting effect using Bland-Altman methods and relative change from gold standard. Feasibility was illustrated with an actual meta-analysis that evaluated the efficacy of various maintenance treatments in patients with non−small-cell lung cancer.3 Eight kinds of simulated datasets of meta-analysis were generated. The number of included studies varied from 5 to 20 and the sample size of each dataset varied from 1,000 to 15,000. Each kind of dataset was simulated 500 times. Statistical models for the synthesis of median survival time in aggregate data meta-analysis of survival data were built and tested using simulated data. For the fixed and random models of all simulated datasets, the mean of the difference between pooled value and gold standard are no more than −0.418 and −0.334, and the widest 95% CIs of the difference are −4.102 to 3.266 and −5.510 to 5.079, respectively. At least 92.4% of the difference in fixed models and 91.0% of the difference in random models are <5% of the gold standard (Table). The results showed good agreement between pooled median survival times from both fixed and random effect models and individual patient data meta-analysis.TABLE: Results of Comparing the Agreement Between Pooled Median Survival Times Derived from the Model and the Gold Standard from Individual Patient DataIn the actual meta-analysis, the original results found that switch maintenance therapy was associated with an improvement in progression-free survival compared with controls (HR = 0.67 [95% CI = 0.57–0.78]). It is not helpful for doctors or patients to evaluate the direct effect of different treatment based only on the combined HR. The combined median survival times are 3.6 and 2.5 months for these two groups, using our method, which is a more intuitive index to demonstrate the effect of the treatment. The combined median survival time can provide useful information in addition to combined HRs, for traditional meta-analysis. Jiajie Zang Department of Health Statistics Second Military Medical University Shanghai, China Department of Nutrition Hygiene Shanghai Municipal Center for Disease Control and Prevention Shanghai, China Chun Xiang Department of Health Statistics Second Military Medical University Shanghai, China Jia He Department of Health Statistics Second Military Medical University Shanghai, China [email protected]