Frequentist and Bayesian multiple-treatments meta­analyses of rare events: risk of malignancies following anti-TNF therapy in rheumatoid arthritis patients

Article type
Authors
Thorlund K, A Wells G, Bliddal H, Gluud C, Christensen R
Abstract
Background: Multiple-treatments meta-analyses (MTM) are predominantly carried out in the Bayesian framework. Bayesian methods have some shortcomings and frequentist methods need to be developed. Further, there is no consensus on how to meta-analyse so-called rare event data. Objectives: To compare Bayesian and frequentist MTM models for rare event data. Methods: We used data from two published systematic reviews on the risk of malignancy after anti-TNF therapy in rheumatoid arthritis (Bongartz et al. JAMA 2006; Bongartz et al. Ann Rheum Dis 2008), that included 16 trials comparing placebo to three anti-TNF therapies: adalimumab, etanercept and infliximab. We employed the conventional logistic MTM model using WinBUGS (i.e. Bayesian) and the empirical Bayesian method GLIMMIX procedure in SAS (i.e. frequentist). We calculated the odds ratio (OR) for each therapy compared to placebo via the Bayesian and frequentist models; including indirect comparisons. We also calculated the presumed equivalent estimates using the Peto’s, Mantel-Haenszel and Inverse-Variance-OR options available in RevMan. Results: Independent of the model used, there was an increased risk of malignancies following use of these products compared to placebo (p < 0.02); however, there was no evidence of differences between the therapies (Figure 1). The Bayesian MTM yielded an indirect OR 2.64 (95% CI 0.30 to 24.4) favouring etanercept over adalimumab or infliximab. The frequentist MTM did not reveal any significant difference between the three therapies. The Bayesian models yielded much lower precision than the frequentist models. The GLIMMIX model estimated an overall OR 2.65 (95% CI 1.34 to 5.24) for any anti-TNF therapy versus placebo. Conclusion: There is evidence of an increased risk of serious malignancies in patients with rheumatoid arthritis treated with all major anti-TNF therapies compared to placebo; no differences between the therapies were evident. From a multitude of statistical models, the frequentist approach using an empirical Bayesian model in GLIMMIX seems reasonable for future use in meta-analysis development.