Purpose: Bayesian random-effects meta-analyses combine existing knowledge and prior belief distributions with new knowledge. While much research has examined the effect of prior distributions for treatment effects, we conducted a study to assess the effect of prior distributions for between-study variance.
Methods: We re-analyzed individual trials that were included in 7 published systematic reviews with rare (event rates: < 5%), moderate (15-50%) and frequent binary outcomes (> 50%). The reviews varied by the number of pooled studies (5-14) and the degree of heterogeneity (I2 =21- 84%). We used 8 non-informative priors for between-study variance: inverse gamma, uniform distributions on the between-study standard deviation (τ) and variance (τ2), the uniform shrinkage and DuMouchel priors, and the half-normal priors on τ2 and on τ with variances of 100 and 1. For each analysis, we calculated the posterior distributions for the mean treatment effect in current studies, predicted treatment effect in future studies, and the between-study standard deviation (τ). We assessed goodness of fit using the deviance information criterion (DIC) and total residual deviance.
Results: Using residual deviance, the best fitting prior distributions in studies with frequent and moderate binary outcomes were the DuMouchel and half-normal on τ2, while the best fitting priors in studies with rare binary outcomes were the half-normal on τ and the DuMouchel. The differences in residual deviance between the best and the worst fitting priors were large in moderate (-19.2 vs. 28.6; 5.9 vs. 10.3) and frequent outcomes (-28.3 vs. -21.2; -174.7 vs. -120.8) but not in rare outcomes (2.03 vs. 2.08; 0.77 vs. 1.94; -2.93 vs. 1.82). Using DIC, the best fitting prior distributions in moderate and frequent outcomes were the DuMouchel, the uniform and half-normal on τ2, while the best fitting priors in rare outcomes were the inverse gamma and half-normal on τ2. We found no large differences in DICs between the priors. Changing assumptions about the distribution of between-study variance did not change posterior estimates of the treatment effect for current studies but substantially changed such estimates for future studies.
Conclusions: In a sample of Bayesian meta-analyses with binary outcomes, the choice of non-informative priors for between-study variance affected model fit and the predictions of future treatment effects. Sensitivity analysis using multiple prior distributions for between-study variance is suggested.
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