Fig. 2: Bayesian meta-analysis of incident diabetes.

Hazard ratios based on a Cox proportional-hazards model and adjusted for the confounding variables listed in Supplementary Tables 5, 7, 9, 11, and 13 were estimated separately for each database and are shown in black along with their 95% confidence intervals. A Bayesian meta-analysis was performed using a random-effects model and a weakly informative hierarchical half-Cauchy prior distribution^85,86 for between-study variance with the assumption that it was unlikely for the between-study hazard ratios to vary by more than 3-fold (scale = 0.280). A sensitivity analysis to the choice of the prior by assuming that it was unlikely for the between-study hazard ratios to vary by more than 10-fold was also performed (scale = 0.587). The Bayesian shrinkage estimates and the summary estimates of the adjusted hazard ratio of incident diabetes for NRTI exposure (ever versus never), along with the 95% credible intervals, are shown in red (scale = 0.280) and blue (scale = 0.587). The dashed vertical line denotes a hazard ratio of 1.0, which represents no difference in risk between nucleoside reverse-transcriptase inhibitor (NRTI) exposure and non-exposure. The estimates of heterogeneity (τ²) and the posterior probabilities of a non-beneficial effect for each model are shown below the plot.