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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 cost-effectiveness 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.

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 cost-effectiveness 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.

Statistical heterogeneity refers to differences among results of studies combined in a meta-analysis beyond that expected by chance. On the one hand, excessive heterogeneity can diminish power to discover genetic signals; on the other, moderate heterogeneity can reveal important biological differences among studies. Given its double-edged nature, this thesis dissects heterogeneity in genetic association meta-analyses from three vantage points. First, a novel multi-variant statistic, M is proposed to detect genome-wide (systematic) heterogeneity patterns in genetic association meta-analyses. This was motivated by the limited availability of appropriate methodology to measure the impact of heterogeneity across genetic signals, since traditional metrics (Q, I² and T²) measure heterogeneity at individual variants. Second, given that meta-analyses comprising small numbers of studies typically report imprecise summary effect estimates; GWAS-derived empirical heterogeneity priors are used to improve precision in estimation of average genetic effects and heterogeneity in smaller meta-analyses (e.g. ≤ 10 studies). Third, a critical evaluation of the Han-Eskin random-effects model shows how it can identify small effect heterogeneous loci overlooked by traditional fixed and random-effects methods. This work draws attention to the existence of genome-wide heterogeneity patterns, to reveal systematic differences among the ascertainment criteria of participating studies in a meta-analysis of coronary disease (CAD) risk. Furthermore, simulation studies with the Han-Eskin random-effects model revealed inflated genetic signals at small effect loci when heterogeneity levels were high. However, it did reveal an additional CAD risk variant overlooked by traditional meta-analysis methods. We therefore recommend a holistic approach to exploring heterogeneity in meta-analyses which assesses heterogeneity of genetic effects both at individual variants with traditional statistics and across multiple genetic signals with the M statistic. Furthermore, it is critically important to review forest plots for small effect loci identified using the Han-Eskin random-effects model amidst moderate-to-high heterogeneity (I² ≥ 40%).