Bayesian inverse problems for recovering coefficients of two scale elliptic equations

We consider the Bayesian inverse homogenization problem of recovering the locally periodic two scale coefficient of a two scale elliptic equation, given limited noisy information on the solution. We consider both the uniform and the Gaussian prior probability measures. We use the two scale homogenized equation whose solution contains the solution of the homogenized equation which describes the macroscopic behaviour, and the corrector which encodes the microscopic behaviour. We approximate the posterior probability by a probability measure determined by the solution of the two scale homogenized equation. We show that the Hellinger distance of these measures converges to zero when the microscale converges to zero, and establish an explicit convergence rate when the solution of the two scale homogenized equation is sufficiently regular. Sampling the posterior measure by Markov Chain Monte Carlo (MCMC) method, instead of solving the two scale equation using fine mesh for each proposal with extremely high cost, we can solve the macroscopic two scale homogenized equation. Although this equation is posed in a high dimensional tensorized domain, it can be solved with essentially optimal complexity by the sparse tensor product finite element method, which reduces the computational complexity of the MCMC sampling method substantially. We show numerically that observations on the macrosopic behaviour alone are not sufficient to infer the microstructure. We need also observations on the corrector. Solving the two scale homogenized equation, we get both the solution to the homogenized equation and the corrector. Thus our method is particularly suitable for sampling the posterior measure of two scale coefficients

Antimicrobial resistance among migrants in Europe: a systematic review and meta-analysis

BACKGROUND: Rates of antimicrobial resistance (AMR) are rising globally and there is concern that increased migration is contributing to the burden of antibiotic resistance in Europe. However, the effect of migration on the burden of AMR in Europe has not yet been comprehensively examined. Therefore, we did a systematic review and meta-analysis to identify and synthesise data for AMR carriage or infection in migrants to Europe to examine differences in patterns of AMR across migrant groups and in different settings. METHODS: For this systematic review and meta-analysis, we searched MEDLINE, Embase, PubMed, and Scopus with no language restrictions from Jan 1, 2000, to Jan 18, 2017, for primary data from observational studies reporting antibacterial resistance in common bacterial pathogens among migrants to 21 European Union-15 and European Economic Area countries. To be eligible for inclusion, studies had to report data on carriage or infection with laboratory-confirmed antibiotic-resistant organisms in migrant populations. We extracted data from eligible studies and assessed quality using piloted, standardised forms. We did not examine drug resistance in tuberculosis and excluded articles solely reporting on this parameter. We also excluded articles in which migrant status was determined by ethnicity, country of birth of participants' parents, or was not defined, and articles in which data were not disaggregated by migrant status. Outcomes were carriage of or infection with antibiotic-resistant organisms. We used random-effects models to calculate the pooled prevalence of each outcome. The study protocol is registered with PROSPERO, number CRD42016043681. FINDINGS: We identified 2274 articles, of which 23 observational studies reporting on antibiotic resistance in 2319 migrants were included. The pooled prevalence of any AMR carriage or AMR infection in migrants was 25·4% (95% CI 19·1-31·8; I2 =98%), including meticillin-resistant Staphylococcus aureus (7·8%, 4·8-10·7; I2 =92%) and antibiotic-resistant Gram-negative bacteria (27·2%, 17·6-36·8; I2 =94%). The pooled prevalence of any AMR carriage or infection was higher in refugees and asylum seekers (33·0%, 18·3-47·6; I2 =98%) than in other migrant groups (6·6%, 1·8-11·3; I2 =92%). The pooled prevalence of antibiotic-resistant organisms was slightly higher in high-migrant community settings (33·1%, 11·1-55·1; I2 =96%) than in migrants in hospitals (24·3%, 16·1-32·6; I2 =98%). We did not find evidence of high rates of transmission of AMR from migrant to host populations. INTERPRETATION: Migrants are exposed to conditions favouring the emergence of drug resistance during transit and in host countries in Europe. Increased antibiotic resistance among refugees and asylum seekers and in high-migrant community settings (such as refugee camps and detention facilities) highlights the need for improved living conditions, access to health care, and initiatives to facilitate detection of and appropriate high-quality treatment for antibiotic-resistant infections during transit and in host countries. Protocols for the prevention and control of infection and for antibiotic surveillance need to be integrated in all aspects of health care, which should be accessible for all migrant groups, and should target determinants of AMR before, during, and after migration. FUNDING: UK National Institute for Health Research Imperial Biomedical Research Centre, Imperial College Healthcare Charity, the Wellcome Trust, and UK National Institute for Health Research Health Protection Research Unit in Healthcare-associated Infections and Antimictobial Resistance at Imperial College London

Impact of cardiac arrest centers on the survival of patients with nontraumatic out‐of‐hospital cardiac arrest : a systematic review and meta‐analysis

Background The role of cardiac arrest centers (CACs) in out‐of‐hospital cardiac arrest care systems is continuously evolving. Interpretation of existing literature is limited by heterogeneity in CAC characteristics and types of patients transported to CACs. This study assesses the impact of CACs on survival in out‐of‐hospital cardiac arrest according to varying definitions of CAC and prespecified subgroups. Methods and Results Electronic databases were searched from inception to March 9, 2021 for relevant studies. Centers were considered CACs if self‐declared by study authors and capable of relevant interventions. Main outcomes were survival and neurologically favorable survival at hospital discharge or 30 days. Meta‐analyses were performed for adjusted odds ratio (aOR) and crude odds ratios. Thirty‐six studies were analyzed. Survival with favorable neurological outcome significantly improved with treatment at CACs (aOR, 1.85 [95% CI, 1.52–2.26]), even when including high‐volume centers (aOR, 1.50 [95% CI, 1.18–1.91]) or including improved‐care centers (aOR, 2.13 [95% CI, 1.75–2.59]) as CACs. Survival significantly increased with treatment at CACs (aOR, 1.92 [95% CI, 1.59–2.32]), even when including high‐volume centers (aOR, 1.74 [95% CI, 1.38–2.18]) or when including improved‐care centers (aOR, 1.97 [95% CI, 1.71–2.26]) as CACs. The treatment effect was more pronounced among patients with shockable rhythm ( P =0.006) and without prehospital return of spontaneous circulation ( P =0.005). Conclusions were robust to sensitivity analyses, with no publication bias detected. Conclusions Care at CACs was associated with improved survival and neurological outcomes for patients with nontraumatic out‐of‐hospital cardiac arrest regardless of varying CAC definitions. Patients with shockable rhythms and those without prehospital return of spontaneous circulation benefited more from CACs. Evidence for bypassing hospitals or interhospital transfer remains inconclusive

Surgical site infection after gastrointestinal surgery in high-income, middle-income, and low-income countries: a prospective, international, multicentre cohort study

Background: Surgical site infection (SSI) is one of the most common infections associated with health care, but its importance as a global health priority is not fully understood. We quantified the burden of SSI after gastrointestinal surgery in countries in all parts of the world. Methods: This international, prospective, multicentre cohort study included consecutive patients undergoing elective or emergency gastrointestinal resection within 2-week time periods at any health-care facility in any country. Countries with participating centres were stratified into high-income, middle-income, and low-income groups according to the UN's Human Development Index (HDI). Data variables from the GlobalSurg 1 study and other studies that have been found to affect the likelihood of SSI were entered into risk adjustment models. The primary outcome measure was the 30-day SSI incidence (defined by US Centers for Disease Control and Prevention criteria for superficial and deep incisional SSI). Relationships with explanatory variables were examined using Bayesian multilevel logistic regression models. This trial is registered with ClinicalTrials.gov, number NCT02662231. Findings: Between Jan 4, 2016, and July 31, 2016, 13 265 records were submitted for analysis. 12 539 patients from 343 hospitals in 66 countries were included. 7339 (58·5%) patient were from high-HDI countries (193 hospitals in 30 countries), 3918 (31·2%) patients were from middle-HDI countries (82 hospitals in 18 countries), and 1282 (10·2%) patients were from low-HDI countries (68 hospitals in 18 countries). In total, 1538 (12·3%) patients had SSI within 30 days of surgery. The incidence of SSI varied between countries with high (691 [9·4%] of 7339 patients), middle (549 [14·0%] of 3918 patients), and low (298 [23·2%] of 1282) HDI (p < 0·001). The highest SSI incidence in each HDI group was after dirty surgery (102 [17·8%] of 574 patients in high-HDI countries; 74 [31·4%] of 236 patients in middle-HDI countries; 72 [39·8%] of 181 patients in low-HDI countries). Following risk factor adjustment, patients in low-HDI countries were at greatest risk of SSI (adjusted odds ratio 1·60, 95% credible interval 1·05–2·37; p=0·030). 132 (21·6%) of 610 patients with an SSI and a microbiology culture result had an infection that was resistant to the prophylactic antibiotic used. Resistant infections were detected in 49 (16·6%) of 295 patients in high-HDI countries, in 37 (19·8%) of 187 patients in middle-HDI countries, and in 46 (35·9%) of 128 patients in low-HDI countries (p < 0·001). Interpretation: Countries with a low HDI carry a disproportionately greater burden of SSI than countries with a middle or high HDI and might have higher rates of antibiotic resistance. In view of WHO recommendations on SSI prevention that highlight the absence of high-quality interventional research, urgent, pragmatic, randomised trials based in LMICs are needed to assess measures aiming to reduce this preventable complication

Numerical analysis of some Bayesian inverse problems

Bayesian inverse problems for partial differential equations arise from many important real world applications. We find the physical properties of a medium in the form of an unknown coefficient of a partial differential equation, given limited noisy observations on the solution. The noise follows a known probability distribution. The unknown coefficient, or the parameters on which it depends, belong to a prior probability space. We aim to find the posterior probability which is the conditional probability of the unknown given the observations. The first part of the thesis is devoted to Bayesian inverse problems to find the unknown locally periodic coefficient of a two scale elliptic equation. In the remaining part, we develop the Multilevel Markov Chain Monte Carlo method for approximating posterior expectation of a quantity of interest for Bayesian inverse problems for partial differential equations. The method achieves an approximation within a prescribed accuracy but uses only an optimal number of total degrees of freedom. We develop the method for elliptic forward equations with the Gaussian prior distribution for the log-normal coefficients, and for parabolic equations with both uniform and Gaussian prior distributions for the coefficients. In Chapter 2, we consider the problem of finding coefficients of locally periodic two scale elliptic problems. We consider both the uniform prior and the Gaussian prior in the space of locally periodic coefficients. In the first case, the coefficient is uniformly coercive and bounded for all the realizations. In the second case, the coefficient is positive but can get arbitrarily large and arbitrarily close to $0$. We approximate the posterior by the probability measure obtained from solution of the two scale homogenized equation. We show an explicit error for this approximation with respect to the Hellinger distance of the two measures, in terms of the microscopic scale. This error estimate holds when the solution of the two scale homogenized equation is sufficiently regular. The two scale homogenized equation provides all the information we need: the solution to the homogenized equation which approximates the solution to the two scale forward equation macroscopically, and the corrector term which encodes the microscopic behavior. Although this equation is posed in a high dimensional tensorized domain, the sparse tensor product finite element method developed in V. H. Hoang and Ch. Schwab, Multiscale Model. Simul. Vol 3, pp 168-194 (2005), solves this equation with essentially optimal complexity. We then approximate the posterior measure by the measure obtained from the sparse tensor product finite element solution of the two scale homogenized equation, with an explicit error in terms of the finite element mesh and the microscopic scale. We show numerically that observations on the macroscopic behavior alone are not sufficient to infer the microstructure. We need also observations on the corrector. Solving the two scale homogenized equation, we get both the solution to the homogenized equation and the corrector. Thus our method is particularly suitable for sampling the posterior measure of two scale coefficients. Chapter 3 reviews the Multilevel Markov Chain Monte Carlo method for approximating posterior expectation of a quantity of interest in Bayesian inverse problems for forward elliptic equations with uniform prior probability. This chapter serves as a basis for the development in the subsequent chapters. We define the uniform prior probability space. We then outline the Multilevel Markov Chain Monte Carlo method developed in V. H. Hoang, Ch. Schwab, A. M. Stuart, Inverse Problems, Vol. 29, 085010, 37pp (2013). The method achieves an approximation for the posterior expectation of a quantity of interest within a prescribed accuracy, using only an optimal level of degrees of freedom (with a possible logarithmic factor). We show that the logarithmic factor in the error can be reduced by slightly increasing the Markov Chain Monte Carlo sample size. The paper by Hoang et al. does not include numerical examples. We perform new numerical examples to illustrate the theory. The Multilevel Markov Chain Monte Carlo method by Hoang et al. is only valid for the uniform prior probability. Their proof of convergence is not valid for the Gaussian prior probability of the coefficient of a forward elliptic equation as it relies essentially on the uniform boundedness of the solution. In Chapter 4, we develop a new Multilevel Markov Chain Monte Carlo method for elliptic equation with Gaussian prior probability. We show theoretically the convergence of the method together with the explicit optimal convergence rate. We provide numerical examples using both independence sampler and preconditioned Crank-Nicolson (pCN) sampler to verify the rigorously justified theoretical convergence rate. In Chapter 5, we consider Bayesian inverse problems for finding coefficient of forward parabolic equations with the uniform prior probability. We consider the coefficient of the parabolic equation to be an expansion of random variables each uniformly distributed in a compact interval. We assume that the coefficient is uniformly coercive and bounded for all the realizations. We approximate the posterior measure by the approximated solution of the forward parabolic equation which is solved by backward Euler and finite element method with coefficient taking only a finite number of terms in the expansion. We then develop the Multilevel Markov Chain Monte Carlo method to estimate the posterior expectation of a quantity of interest. As in the paper by Hoang, Schwab and Stuart, the key point to achieve optimal convergence is to judiciously balance the level of resolution and the sample size of each run of the Markov Chain Monte Carlo algorithm. We establish rigorously the convergence rate. We present numerical examples that support the theory. We consider Gaussian prior probability where the coefficient of the parabolic equation takes the log-normal form in Chapter 6. We use the backward Euler finite element method to approximate the truncated forward parabolic equation taking only a finite number of terms in the coefficient. This approximation leads to an approximation for the posterior measure where the forward functional is determined from the approximated solution of the forward equation. We then approximate the posterior expectation of a quantity of interest by this approximated posterior measure. We develop the Multilevel Markov Chain Monte Carlo to estimate the posterior expectation in this case of forward parabolic equations with log-normal coefficients. We show theoretically the convergence of the method together with the explicit optimal convergence rate. We present numerical examples for both the independent sampler and the preconditioned Crank-Nicolson sampler. The results for both cases verify the theoretical prediction.Doctor of Philosoph

Surgical site infection after gastrointestinal surgery in children : an international, multicentre, prospective cohort study

Introduction Surgical site infection (SSI) is one of the most common healthcare-associated infections (HAIs). However, there is a lack of data available about SSI in children worldwide, especially from low-income and middle-income countries. This study aimed to estimate the incidence of SSI in children and associations between SSI and morbidity across human development settings. Methods A multicentre, international, prospective, validated cohort study of children aged under 16 years undergoing clean-contaminated, contaminated or dirty gastrointestinal surgery. Any hospital in the world providing paediatric surgery was eligible to contribute data between January and July 2016. The primary outcome was the incidence of SSI by 30 days. Relationships between explanatory variables and SSI were examined using multilevel logistic regression. Countries were stratified into high development, middle development and low development groups using the United Nations Human Development Index (HDI). Results Of 1159 children across 181 hospitals in 51 countries, 523 (45 center dot 1%) children were from high HDI, 397 (34 center dot 2%) from middle HDI and 239 (20 center dot 6%) from low HDI countries. The 30-day SSI rate was 6.3% (33/523) in high HDI, 12 center dot 8% (51/397) in middle HDI and 24 center dot 7% (59/239) in low HDI countries. SSI was associated with higher incidence of 30-day mortality, intervention, organ-space infection and other HAIs, with the highest rates seen in low HDI countries. Median length of stay in patients who had an SSI was longer (7.0 days), compared with 3.0 days in patients who did not have an SSI. Use of laparoscopy was associated with significantly lower SSI rates, even after accounting for HDI. Conclusion The odds of SSI in children is nearly four times greater in low HDI compared with high HDI countries. Policies to reduce SSI should be prioritised as part of the wider global agenda.Peer reviewe