On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

Pooled analysis of WHO Surgical Safety Checklist use and mortality after emergency laparotomy

Background The World Health Organization (WHO) Surgical Safety Checklist has fostered safe practice for 10 years, yet its place in emergency surgery has not been assessed on a global scale. The aim of this study was to evaluate reported checklist use in emergency settings and examine the relationship with perioperative mortality in patients who had emergency laparotomy. Methods In two multinational cohort studies, adults undergoing emergency laparotomy were compared with those having elective gastrointestinal surgery. Relationships between reported checklist use and mortality were determined using multivariable logistic regression and bootstrapped simulation. Results Of 12 296 patients included from 76 countries, 4843 underwent emergency laparotomy. After adjusting for patient and disease factors, checklist use before emergency laparotomy was more common in countries with a high Human Development Index (HDI) (2455 of 2741, 89.6 per cent) compared with that in countries with a middle (753 of 1242, 60.6 per cent; odds ratio (OR) 0.17, 95 per cent c.i. 0.14 to 0.21, P <0001) or low (363 of 860, 422 per cent; OR 008, 007 to 010, P <0.001) HDI. Checklist use was less common in elective surgery than for emergency laparotomy in high-HDI countries (risk difference -94 (95 per cent c.i. -11.9 to -6.9) per cent; P <0001), but the relationship was reversed in low-HDI countries (+121 (+7.0 to +173) per cent; P <0001). In multivariable models, checklist use was associated with a lower 30-day perioperative mortality (OR 0.60, 0.50 to 073; P <0.001). The greatest absolute benefit was seen for emergency surgery in low- and middle-HDI countries. Conclusion Checklist use in emergency laparotomy was associated with a significantly lower perioperative mortality rate. Checklist use in low-HDI countries was half that in high-HDI countries.Peer reviewe

Global variation in anastomosis and end colostomy formation following left-sided colorectal resection

Background End colostomy rates following colorectal resection vary across institutions in high-income settings, being influenced by patient, disease, surgeon and system factors. This study aimed to assess global variation in end colostomy rates after left-sided colorectal resection. Methods This study comprised an analysis of GlobalSurg-1 and -2 international, prospective, observational cohort studies (2014, 2016), including consecutive adult patients undergoing elective or emergency left-sided colorectal resection within discrete 2-week windows. Countries were grouped into high-, middle- and low-income tertiles according to the United Nations Human Development Index (HDI). Factors associated with colostomy formation versus primary anastomosis were explored using a multilevel, multivariable logistic regression model. Results In total, 1635 patients from 242 hospitals in 57 countries undergoing left-sided colorectal resection were included: 113 (6·9 per cent) from low-HDI, 254 (15·5 per cent) from middle-HDI and 1268 (77·6 per cent) from high-HDI countries. There was a higher proportion of patients with perforated disease (57·5, 40·9 and 35·4 per cent; P < 0·001) and subsequent use of end colostomy (52·2, 24·8 and 18·9 per cent; P < 0·001) in low- compared with middle- and high-HDI settings. The association with colostomy use in low-HDI settings persisted (odds ratio (OR) 3·20, 95 per cent c.i. 1·35 to 7·57; P = 0·008) after risk adjustment for malignant disease (OR 2·34, 1·65 to 3·32; P < 0·001), emergency surgery (OR 4·08, 2·73 to 6·10; P < 0·001), time to operation at least 48 h (OR 1·99, 1·28 to 3·09; P = 0·002) and disease perforation (OR 4·00, 2·81 to 5·69; P < 0·001). Conclusion Global differences existed in the proportion of patients receiving end stomas after left-sided colorectal resection based on income, which went beyond case mix alone

Cardiovascular Efficacy and Safety of Bococizumab in High-Risk Patients

Bococizumab is a humanized monoclonal antibody that inhibits proprotein convertase subtilisin- kexin type 9 (PCSK9) and reduces levels of low-density lipoprotein (LDL) cholesterol. We sought to evaluate the efficacy of bococizumab in patients at high cardiovascular risk. METHODS In two parallel, multinational trials with different entry criteria for LDL cholesterol levels, we randomly assigned the 27,438 patients in the combined trials to receive bococizumab (at a dose of 150 mg) subcutaneously every 2 weeks or placebo. The primary end point was nonfatal myocardial infarction, nonfatal stroke, hospitalization for unstable angina requiring urgent revascularization, or cardiovascular death; 93% of the patients were receiving statin therapy at baseline. The trials were stopped early after the sponsor elected to discontinue the development of bococizumab owing in part to the development of high rates of antidrug antibodies, as seen in data from other studies in the program. The median follow-up was 10 months. RESULTS At 14 weeks, patients in the combined trials had a mean change from baseline in LDL cholesterol levels of -56.0% in the bococizumab group and +2.9% in the placebo group, for a between-group difference of -59.0 percentage points (P<0.001) and a median reduction from baseline of 64.2% (P<0.001). In the lower-risk, shorter-duration trial (in which the patients had a baseline LDL cholesterol level of ≥70 mg per deciliter [1.8 mmol per liter] and the median follow-up was 7 months), major cardiovascular events occurred in 173 patients each in the bococizumab group and the placebo group (hazard ratio, 0.99; 95% confidence interval [CI], 0.80 to 1.22; P = 0.94). In the higher-risk, longer-duration trial (in which the patients had a baseline LDL cholesterol level of ≥100 mg per deciliter [2.6 mmol per liter] and the median follow-up was 12 months), major cardiovascular events occurred in 179 and 224 patients, respectively (hazard ratio, 0.79; 95% CI, 0.65 to 0.97; P = 0.02). The hazard ratio for the primary end point in the combined trials was 0.88 (95% CI, 0.76 to 1.02; P = 0.08). Injection-site reactions were more common in the bococizumab group than in the placebo group (10.4% vs. 1.3%, P<0.001). CONCLUSIONS In two randomized trials comparing the PCSK9 inhibitor bococizumab with placebo, bococizumab had no benefit with respect to major adverse cardiovascular events in the trial involving lower-risk patients but did have a significant benefit in the trial involving higher-risk patients

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\ub75%) patient were from high-HDI countries (193 hospitals in 30 countries), 3918 (31\ub72%) patients were from middle-HDI countries (82 hospitals in 18 countries), and 1282 (10\ub72%) patients were from low-HDI countries (68 hospitals in 18 countries). In total, 1538 (12\ub73%) patients had SSI within 30 days of surgery. The incidence of SSI varied between countries with high (691 [9\ub74%] of 7339 patients), middle (549 [14\ub70%] of 3918 patients), and low (298 [23\ub72%] of 1282) HDI (p&lt;0\ub7001). The highest SSI incidence in each HDI group was after dirty surgery (102 [17\ub78%] of 574 patients in high-HDI countries; 74 [31\ub74%] of 236 patients in middle-HDI countries; 72 [39\ub78%] 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\ub760, 95% credible interval 1\ub705\u20132\ub737; p=0\ub7030). 132 (21\ub76%) 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\ub76%) of 295 patients in high-HDI countries, in 37 (19\ub78%) of 187 patients in middle-HDI countries, and in 46 (35\ub79%) of 128 patients in low-HDI countries (p&lt;0\ub7001). 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. Funding: DFID-MRC-Wellcome Trust Joint Global Health Trial Development Grant, National Institute of Health Research Global Health Research Unit Grant

Precision Electroweak Measurements on the Z resonance.

We report on the final electroweak measurements performed with data taken at the Z resonance by the experiments operating at the electron–positron colliders SLC and LEP. The data consist of 17 million Z decays accumulated by the ALEPH, DELPHI, L3 and OPAL experiments at LEP, and 600 thousand Z decays by the SLD experiment using a polarised beam at SLC. The measurements include cross-sections, forward–backward asymmetries and polarised asymmetries. The mass and width of the Z boson, mZ and ΓZ, and its couplings to fermions, for example the ρ parameter and the effective electroweak mixing angle for leptons, are precisely measured: The number of light neutrino species is determined to be 2.9840±0.0082, in agreement with the three observed generations of fundamental fermions. The results are compared to the predictions of the Standard Model (SM). At the Z-pole, electroweak radiative corrections beyond the running of the QED and QCD coupling constants are observed with a significance of five standard deviations, and in agreement with the Standard Model. Of the many Z-pole measurements, the forward–backward asymmetry in b-quark production shows the largest difference with respect to its SM expectation, at the level of 2.8 standard deviations. Through radiative corrections evaluated in the framework of the Standard Model, the Z-pole data are also used to predict the mass of the top quark, , and the mass of the W boson, . These indirect constraints are compared to the direct measurements, providing a stringent test of the SM. Using in addition the direct measurements of mt and mW, the mass of the as yet unobserved SM Higgs boson is predicted with a relative uncertainty of about 50% and found to be less than at 95% confidence level