Meta-analysis of rare adverse events in randomized clinical trials: Bayesian and frequentist methods

Regulatory approval of a drug or device involves an assessment of not only the benefits but also the risks of adverse events associated with the therapeutic agent. Although randomized controlled trials (RCTs) are the gold standard for evaluating effectiveness, the number of treated patients in a single RCT may not be enough to detect a rare but serious side effect of the treatment. Meta-analysis plays an important role in the evaluation of the safety of medical products and has advantage over analyzing a single RCT when estimating the rate of adverse events.

In this article, we compare 15 widely used meta-analysis models under both Bayesian and frequentist frameworks when outcomes are extremely infrequent or rare. We present extensive simulation study results and then apply these methods to a real meta-analysis that considers RCTs investigating the effect of rosiglitazone on the risks of myocardial infarction and of death from cardiovascular causes.

Our simulation studies suggest that the beta hyperprior method modeling treatment group-specific parameters and accounting for heterogeneity performs the best. Most models ignoring between-study heterogeneity give poor coverage probability when such heterogeneity exists. In the data analysis, different methods provide a wide range of log odds ratio estimates between rosiglitazone and control treatments with a mixed conclusion on their statistical significance based on 95% confidence (or credible) intervals.

In the rare event setting, treatment effect estimates obtained from traditional meta-analytic methods may be biased and provide poor coverage probability. This trend worsens when the data have large between-study heterogeneity. In general, we recommend methods that first estimate the summaries of treatment-specific risks across studies and then relative treatment effects based on the summaries when appropriate. Furthermore, we recommend fitting various methods, comparing the results and model performance, and investigating any significant discrepancies among them.