Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure

The accumulation of deficits approach to describe frailty

The advancing age of the participants of the European Prospective Investigation into Cancer and Nutrition (EPIC)-Potsdam study was the incentive to investigate frailty as a major parameter of ageing. The aim of this study was to develop a multidimensional tool to measure frailty in an ageing, free-living study population. The "accumulation of deficits approach" was used to develop a frailty index (FI) to characterize a sub-sample (N = 815) of the EPIC-Potsdam (EPIC-P) study population regarding the aging phenomenon. The EPIC-P frailty index (EPIC-P-FI) included 32 variables from the following domains: health, physical ability, psychosocial and physiological aspects. P-values were calculated for the linear trend between sociodemographic and life style variables and the EPIC-P-FI was calculated using regression analysis adjusted for age. The relationship between the EPIC-P-FI and age was investigated using fractional polynomials. Some characteristics such as age, education, time spent watching TV, cycling and a biomarker of inflammation (C-reactive protein) were associated with frailty in men and women. Interestingly, living alone, having no partner and smoking status were only associated with frailty in men, and alcohol use and physical fitness (VO2max) only in women. The generated, multidimensional FI, adapted to the EPIC-P study, showed that this cohort is a valuable source for further exploration of factors that promote healthy ageing

Metabolic syndrome and risk of incident diabetes: findings from the European Prospective Investigation into Cancer and Nutrition-Potsdam Study

<p>Abstract</p> <p>Background</p> <p>Several aspects concerning the relationship between the metabolic syndrome and incident diabetes are incompletely understood including the magnitude of the risk estimate, potential gender differences in the associations between the metabolic syndrome and incident diabetes, the associations between the components of the metabolic syndrome and incident diabetes, and whether the metabolic syndrome provides additional prediction beyond its components. To shed light on these issues, we examined the prospective association between the metabolic syndrome defined by the National Cholesterol Education Program (NCEP) and International Diabetes Federation (IDF) and diabetes.</p> <p>Methods</p> <p>We used data for 2796 men and women aged 35–65 years from the European Prospective Investigation into Cancer and Nutrition-Potsdam Study followed for an average of 6.9 years. This analysis employed a case-cohort design that included 697 participants who developed diabetes and 2099 participants who did not. Incident diabetes was identified on the basis of self-reports and verified by contacting the patient's attending physician.</p> <p>Results</p> <p>The adjusted hazard ratio for the NCEP definition was 4.62 (95% confidence interval [CI]: 3.90–5.48) and that for the IDF definition was 4.59 (95% CI: 3.84–5.50). The adjusted hazard ratios for the NCEP but not IDF definition were higher for women than men. When participants who had no cardiometabolic abnormalities were used as the reference group for the NCEP definition, the adjusted hazard ratio for having 3 or more abnormalities increased to 22.50 (95% CI: 11.21–45.19). Of the five components, abdominal obesity and hyperglycemia were most strongly associated with incident diabetes.</p> <p>Conclusion</p> <p>In this study population, both definitions of the metabolic syndrome provided similar estimates of relative risk for incident diabetes. The increase in risk for participants with the metabolic syndrome according to the NCEP definition was very large when contrasted with the risk among those who had no cardiometabolic abnormalities.</p

Comparative effects of different dietary approaches on blood pressure in hypertensive and pre-hypertensive patients: A systematic review and network meta-analysis

Pairwise meta-analyses have shown beneficial effects of individual dietary approaches on blood pressure but their comparative effects have not been established. Objective: Therefore we performed a systematic review of different dietary intervention trials and estimated the aggregate blood pressure effects through network meta-analysis including hypertensive and pre-hypertensive patients. Design: PubMed, Cochrane CENTRAL, and Google Scholar were searched until June 2017. The inclusion criteria were defined as follows: i) Randomized trial with a dietary approach; ii) hypertensive and pre-hypertensive adult patients; and iii) minimum intervention period of 12 weeks. In order to determine the pooled effect of each intervention relative to each of the other intervention for both diastolic and systolic blood pressure (SBP and DBP), random effects network meta-analysis was performed. Results: A total of 67 trials comparing 13 dietary approaches (DASH, lowfat, moderate-carbohydrate, high-protein, low-carbohydrate, Mediterranean, Palaeolithic, vegetarian, low-GI/GL, low-sodium, Nordic, Tibetan, and control) enrolling 17,230 participants were included. In the network metaanalysis, the DASH, Mediterranean, low-carbohydrate, Palaeolithic, high-protein, low-glycaemic index, lowsodium, and low-fat dietary approaches were significantly more effective in reducing SBP (¡8.73 to ¡2.32 mmHg) and DBP (¡4.85 to ¡1.27 mmHg) compared to a control diet. According to the SUCRAs, the DASH diet was ranked the most effective dietary approach in reducing SBP (90%) and DBP (91%), followed by the Palaeolithic, and the low-carbohydrate diet (ranked 3rd for SBP) or the Mediterranean diet (ranked 3rd for DBP). For most comparisons, the credibility of evidence was rated very low to moderate, with the exception for the DASH vs. the low-fat dietary approach for which the quality of evidence was rated high. Conclusion: The present network meta-analysis suggests that the DASH dietary approach might be the most effective dietary measure toreduce blood pressure among hypertensive and pre-hypertensive patients based on high quality evidence