A Bayesian bias‐adjusted random‐effects model for synthesizing evidence from randomized controlled trials and nonrandomized studies of interventions

Objective An important consideration when combining RCTs and NRSIs is how to address their potential biases in the pooled estimates. This study aimed to propose a Bayesian bias‐adjusted random effects model for the synthesis of evidence from RCTs and NRSIs. Methods We present a Bayesian bias‐adjusted random effects model based on power prior method, which combines the likelihood contribution of the NRSIs, raised to the power parameter of alpha, with the likelihood of the RCT data, modeled with an additive bias. The method was illustrated using a meta‐analysis on the association between low‐dose methotrexate exposure and melanoma. We also combined RCTs and NRSIs using the naïve data synthesis. Results The results including only RCTs has a posterior median and 95% credible interval (CrI) of 1.18 (0.31–4.04), the posterior probability of any harm (> 1.0) and a meaningful association (> 1.15) were 0.61 and 0.52, respectively. The posterior median and 95% CrI based on the naïve data synthesis resulted in 1.17 (0.96–1.47), and the posterior probability of any harm and a meaningful association were 0.96 and 0.60, respectively. For the Bayesian bias‐adjusted analysis, the median OR was 1.16 (95% CrI: 0.83–1.71), and the posterior probabilities of any and a meaningful clinical association were 0.88 and 0.53, respectively. Conclusions The results indicated that integrating NRSIs into meta‐analysis could increase the certainty of the body of evidence. However, directly combining RCTs and NRSIs in the same meta‐analysis without distinction may lead to misleading conclusions.