Vitamin K has a negligible effect on bone mineral density (BMD) and a large but uncertain effect on fractures. The three studies in the thesis explored uncertainty about the effect of vitamin K on fractures using the methods of economic evaluation and Bayesian meta-analysis.

In study 1, a Markov probabilistic microsimulation model was developed for a hypothetical cohort of 50-year-old postmenopausal women without osteoporosis. This was a fracture incidence-based model, populated with data from the literature. It was used to examine the costeffectiveness of two supplementation strategies over a lifetime horizon. We compared vitamin K2 (or vitamin K1) concurrent with vitamin D3 and calcium versus vitamin D3 and calcium alone. Study 2 included a systematic review, and classical and Bayesian univariate meta-analyses to determine the efficacies of the K vitamins on BMD or fractures in current and future trials. Study 3 used Bayesian bivariate random-effects meta-analysis to jointly model the treatment effects on two correlated bone outcomes. We compared the estimates from the univariate and bivariate meta-analyses and explored how these results would change the conclusions of the cost-effectiveness analysis.

The strategies including vitamin K were highly cost-effective at willingness-to-pay of $50,000/QALY (quality-adjusted life year);​ however, the results were most sensitive to changes in the efficacy of vitamin K. The univariate meta-analyses showed large uncertainties in the anti-fracture effects of vitamin K2 in current and future trials. The bivariate 95% credible intervals were considerably narrower than those from the univariate meta-analyses. Using future odds ratios from the bivariate meta-analyses, vitamin K2 cost more than $100,000/QALY while vitamin K1 was cost-saving.

Our analyses found substantial uncertainty around the estimates of the vitamin K effect on fractures. We recommend against routine use of vitamin K for fracture prevention. Bayesian bivariate meta-analysis accounts for all available information and should be considered when the treatment effects are measured on two correlated outcomes.