OBJECTIVES: Standard formulations of bivariate network meta-analysis (bvNMA) for measuring the study-level correlation of treatment effect on a pair of outcomes typically employ the within-study correlation parameter as a fixed input. This feature may be problematic if this quantity is unknown, for instance, if there is no relevant patient-level data available, or if there is expected uncertainty due to its heterogeneity across studies. Here, we investigate the impact of employing alternative prior distributions for the within-study correlation.

METHODS: We analyzed a network of 15 trials in relapsed/refractory multiple myeloma (RRMM) using Bayesian bivariate random effects meta-analysis to estimate the study-level correlation between complete response rate (CRR) odds ratios and progression-free survival (PFS) hazard ratios. The included studies were those that were the subject of previous NMAs (Botta 2017) for which both outcomes were reported. We considered three alternative prior distributions for the within-study correlation parameter, which was assumed to be homogeneous across treatments: first, a weakly informative prior centred at zero correlation (mean 0.00 [90% credible interval (CrI): -0.62,0.62]), second, a weakly informative uniform prior enforcing negative correlation, and third, a strongly informative prior indicating moderately negative correlation (mean -0.55 [90% CrI: -0.65,-0.45]). We implemented the bvNMA model in the Stan language.

RESULTS: Posterior mean estimates for the between-study correlation parameter in the three respective scenarios were -0.67 [90% CrI: -0.94,-0.21], -0.66 [90% CrI: -0.96,-0.19], and -0.65 [90% CrI: -0.94,-0.19]. In all cases, the posterior distribution for the within-study correlation parameter was highly similar to the corresponding prior distribution.

CONCLUSIONS: Estimates for between-study CRR-PFS correlation in RRMM obtained from bvNMA are strongly robust to the specified prior distribution for the within-study correlation. While it is feasible to allow the within-study correlation to be a free parameter in bvNMA, the corresponding prior is liable to dominate the posterior density when the network is relatively small.