USE OF BAYESIAN BIVARIATE RANDOM-EFFECTS META-ANALYSIS TO EXPLORE UNCERTAINTY IN THE TREATMENT EFFECT OF VITAMIN K ON BONE MINERAL DENSITY AND FRACTURES

Purpose: Systematic reviews that do not account for correlated outcomes may lead to biased estimates of treatment effects. We examined uncertainty in the estimate of treatment effects on two correlated outcomes in a Bayesian meta-analysis and explored how these results would alter a published cost-effectiveness analysis.

Method: We used data from a systematic review of 14 vitamin K trials that reported either bone mineral density (BMD) or fractures or both endpoints. We identified 3 trials, reporting both outcomes. We used Bayesian hierarchical random-effects meta-analysis and linear regression to sample incomplete data and model simultaneously 3 pairs of outcomes: lumbar spine BMD and all fractures; lumbar spine BMD and vertebral fractures; and, femoral neck BMD and non-vertebral fractures. We specified non-informative priors on the mean treatment effects and a Wishart prior on the inverse variance-covariance matrix. For each outcome, we estimated the population treatment effect in current trials and the predictive treatment effect in future trials. The between-study correlations and the probability that treatments jointly benefited both BMD and fractures were also calculated. We compared univariate with bivariate random-effects meta-analysis and used the population and predictive odds ratios as input parameters into a model examining the cost-effectiveness of the K vitamins for preventing fractures in women initially without osteoporosis.

Result:    While the bivariate and univariate random-effects meta-analysis pooled estimates were similar, the bivariate 95% credible intervals (CrIs) were narrower and excluded implausible values. The predictive distributions shrank the most. For example, the population and predictive odds ratios for the effect of vitamin K2 on vertebral fractures and lumbar spine BMD using bivariate methods were 0.81(95% CrI: 0.5-1.1) and 0.84(95% CrI: 0.4-1.5); the corresponding univariate estimates were 0.67(95% CrI: 0.2-1.5) and 1.20(95% CrI: 0.1-5.2). The probabilities of joint benefit were 89% (vitamin K2) and 12% (vitamin K1) for vertebral fractures and lumbar spine BMD and 49% (vitamin K2) and 75% (vitamin K1) for non-vertebral fractures and femoral neck BMD. Using the results from the univariate analysis, both vitamin K2 and K1 strategies cost less than $50,000/QALY; using predictive odds ratios from the bivariate analysis, vitamin K2 strategy cost more than $100,000/QALY and vitamin K1 was cost-saving.

Conclusion:   Bivariate random-effects meta-analysis can yield more plausible estimates of treatment effects that can meaningfully change the results of an economic analysis.