Bayesian numerical analysis : global optimization and other applications

We present a unifying framework for the global optimization of functions which are expensive to evaluate. The framework is based on a Bayesian interpretation of radial basis function interpolation which incorporates existing methods such as Kriging, Gaussian process regression and neural networks. This viewpoint enables the application of Bayesian decision theory to derive a sequential global optimization algorithm which can be extended to include existing algorithms of this type in the literature. By posing the optimization problem as a sequence of sampling decisions, we optimize a general cost function at each stage of the algorithm. An extension to multi-stage decision processes is also discussed. The key idea of the framework is to replace the underlying expensive function by a cheap surrogate approximation. This enables the use of existing branch and bound techniques to globally optimize the cost function. We present a rigorous analysis of the canonical branch and bound algorithm in this setting as well as newly developed algorithms for other domains including convex sets. In particular, by making use of Lipschitz continuity of the surrogate approximation, we develop an entirely new algorithm based on overlapping balls. An application of the framework to the integration of expensive functions over rectangular domains and spherical surfaces in low dimensions is also considered. To assess performance of the framework, we apply it to canonical examples from the literature as well as an industrial model problem from oil reservoir simulation.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Effect modification by population dietary folate on the association between MTHFR genotype, homocysteine, and stroke risk: a meta-analysis of genetic studies and randomised trials

BACKGROUND: The MTHFR 677C→T polymorphism has been associated with raised homocysteine concentration and increased risk of stroke. A previous overview showed that the effects were greatest in regions with low dietary folate consumption, but differentiation between the effect of folate and small-study bias was difficult. A meta-analysis of randomised trials of homocysteine-lowering interventions showed no reduction in coronary heart disease events or stroke, but the trials were generally set in populations with high folate consumption. We aimed to reduce the effect of small-study bias and investigate whether folate status modifies the association between MTHFR 677C→T and stroke in a genetic analysis and meta-analysis of randomised controlled trials. METHODS: We established a collaboration of genetic studies consisting of 237 datasets including 59,995 individuals with data for homocysteine and 20,885 stroke events. We compared the genetic findings with a meta-analysis of 13 randomised trials of homocysteine-lowering treatments and stroke risk (45,549 individuals, 2314 stroke events, 269 transient ischaemic attacks). FINDINGS: The effect of the MTHFR 677C→T variant on homocysteine concentration was larger in low folate regions (Asia; difference between individuals with TT versus CC genotype, 3·12 μmol/L, 95% CI 2·23 to 4·01) than in areas with folate fortification (America, Australia, and New Zealand, high; 0·13 μmol/L, -0·85 to 1·11). The odds ratio (OR) for stroke was also higher in Asia (1·68, 95% CI 1·44 to 1·97) than in America, Australia, and New Zealand, high (1·03, 0·84 to 1·25). Most randomised trials took place in regions with high or increasing population folate concentrations. The summary relative risk (RR) of stroke in trials of homocysteine-lowering interventions (0·94, 95% CI 0·85 to 1·04) was similar to that predicted for the same extent of homocysteine reduction in large genetic studies in populations with similar folate status (predicted RR 1·00, 95% CI 0·90 to 1·11). Although the predicted effect of homocysteine reduction from large genetic studies in low folate regions (Asia) was larger (RR 0·78, 95% CI 0·68 to 0·90), no trial has evaluated the effect of lowering of homocysteine on stroke risk exclusively in a low folate region. INTERPRETATION: In regions with increasing levels or established policies of population folate supplementation, evidence from genetic studies and randomised trials is concordant in suggesting an absence of benefit from lowering of homocysteine for prevention of stroke. Further large-scale genetic studies of the association between MTHFR 677C→T and stroke in low folate settings are needed to distinguish effect modification by folate from small-study bias. If future randomised trials of homocysteine-lowering interventions for stroke prevention are undertaken, they should take place in regions with low folate consumption

The interleukin-6 receptor as a target for prevention of coronary heart disease: a mendelian randomisation analysis

Background: A high circulating concentration of interleukin 6 is associated with increased risk of coronary heart disease. Blockade of the interleukin-6 receptor (IL6R) with a monoclonal antibody (tocilizumab) licensed for treatment of rheumatoid arthritis reduces systemic and articular inflammation. However, whether IL6R blockade also reduces risk of coronary heart disease is unknown. Methods: Applying the mendelian randomisation principle, we used single nucleotide polymorphisms (SNPs) in the gene IL6R to evaluate the likely efficacy and safety of IL6R inhibition for primary prevention of coronary heart disease. We compared genetic findings with the effects of tocilizumab reported in randomised trials in patients with rheumatoid arthritis. Findings: In 40 studies including up to 133 449 individuals, an IL6R SNP (rs7529229) marking a non-synonymous IL6R variant (rs8192284; p.Asp358Ala) was associated with increased circulating log interleukin-6 concentration (increase per allele 9.45%, 95% CI 8.34-10.57) as well as reduced C-reactive protein (decrease per allele 8.35%, 95% CI 7.31-9.38) and fibrinogen concentrations (decrease per allele 0.85%, 95% CI 0.60-1.10). This pattern of effects was consistent with IL6R blockade from infusions of tocilizumab (4-8 mg/kg every 4 weeks) in patients with rheumatoid arthritis studied in randomised trials. In 25 458 coronary heart disease cases and 100 740 controls, the IL6R rs7529229 SNP was associated with a decreased odds of coronary heart disease events (per allele odds ratio 0.95, 95% CI 0.93-0.97, p=1.53x10(-5)). Interpretation: On the basis of genetic evidence in human beings, IL6R signalling seems to have a causal role in development of coronary heart disease. IL6R blockade could provide a novel therapeutic approach to prevention of coronary heart disease that warrants testing in suitably powered randomised trials. Genetic studies in populations could be used more widely to help to validate and prioritise novel drug targets or to repurpose existing agents and targets for new therapeutic uses