On an extremal problem for poset dimension

Let $f(n)$ be the largest integer such that every poset on $n$ elements has a $2$-dimensional subposet on $f(n)$ elements. What is the asymptotics of $f(n)$? It is easy to see that $f(n)\geqslant n^{1/2}$. We improve the best known upper bound and show $f(n)=\mathcal{O}(n^{2/3})$. For higher dimensions, we show $f_d(n)=\mathcal{O}\left(n^\frac{d}{d+1}\right)$, where $f_d(n)$ is the largest integer such that every poset on $n$ elements has a $d$-dimensional subposet on $f_d(n)$ elements.Comment: removed proof of Theorem 3 duplicating previous work; fixed typos and reference

Treedepth vs circumference

The circumference of a graph $G$ is the length of a longest cycle in $G$, or$+\infty$ if $G$ has no cycle. Birmel\'e (2003) showed that the treewidth of agraph $G$ is at most its circumference minus one. We strengthen this result for$2$-connected graphs as follows: If $G$ is $2$-connected, then its treedepth isat most its circumference. The bound is best possible and improves on anearlier quadratic upper bound due to Marshall and Wood (2015).<br

Dietary polyphenol intake and risk of type 2 diabetes in the Polish arm of the Health, Alcohol and Psychosocial factors in Eastern Europe (HAPIEE) study

This study aimed to test the association between dietary content of total and individual classes of polyphenols and incident cases of type 2 diabetes in Polish adults participating to the Health, Alcohol and Psychosocial factors In Eastern Europe study. At baseline, diet by 148-item FFQ and health information were collected from 5806 participants free of diabetes. Self-reported incident type 2 diabetes was ascertained at 2-4-year follow-up visit. OR and 95 % CI of type 2 diabetes comparing the various categories of polyphenol intake to the lowest one (reference category) and as 1 sd increase modelled as continuous variable were calculated by performing age-, energy-, and multivariate-adjusted logistic regression models. During the follow-up, 456 incident cases of type 2 diabetes occurred. When comparing extreme quartiles, intake of total polyphenol was inversely associated with the risk of type 2 diabetes (OR 0·43; 95 % CI 0·30, 0·61); 1 sd increase was associated with a reduced risk of diabetes (OR 0·68; 95 % CI 0·59, 0·79). Among the main classes of polyphenols, flavonoids, phenolic acids, and stilbenes were independent contributors to this association. Both subclasses of phenolic acids were associated with decreased risk of type 2 diabetes, whereas among subclasses of flavonoids, high intake of flavanols, flavanones, flavones and anthocyanins was significantly associated with decreased risk of type 2 diabetes. Total dietary polyphenols and some classes of dietary polyphenols were associated with lower risk of type 2 diabetes

Coffee consumption and mortality in three Eastern European countries: results from the HAPIEE (Health, Alcohol and Psychosocial factors In Eastern Europe) study

OBJECTIVE: To test the association between coffee consumption and risk of all-cause, CVD and cancer death in a European cohort. DESIGN: Prospective cohort study. Cox proportional hazards models with adjustment for potential confounders to estimate multivariable hazard ratios (HR) and 95 % CI were used. SETTING: Czech Republic, Russia and Poland. SUBJECTS: A total of 28561 individuals followed for 6·1 years. RESULTS: A total of 2121 deaths (43·1 % CVD and 35·7 % cancer mortality) occurred during the follow-up. Consumption of 3-4 cups coffee/d was associated with lower mortality risk in men (HR=0·83; 95 % CI 0·71, 0·99) and women (HR=0·63; 95 % CI 0·47, 0·84), while further intake showed non-significant reduced risk estimates (HR=0·71; 95 % CI 0·49, 1·04 and HR=0·51; 95 % CI 0·24, 1·10 in men and women, respectively). Decreased risk of CVD mortality was also found in men (HR=0·71; 95 % CI 0·54, 0·93) for consumption of 3-4 cups coffee/d. Stratified analysis revealed that consumption of a similar amount of coffee was associated with decreased risk of all-cause (HR=0·61; 95 % CI 0·43, 0·87) and cancer mortality (HR=0·59; 95 % CI 0·35, 0·99) in non-smoking women and decreased risk of all-cause mortality for >4 cups coffee/d in men with no/moderate alcohol intake. CONCLUSIONS: Coffee consumption was associated with decreased risk of mortality. The protective effect was even stronger when stratification by smoking status and alcohol intake was performed

Dietary polyphenol intake and risk of hypertension in the Polish arm of the HAPIEE study

PURPOSE: Dietary polyphenols have been studied for their potential effects on metabolic disorders, but studies on risk of hypertension are scarce. This study aimed to test the association between total and individual classes of dietary polyphenols and incidence of hypertension in the Polish arm of the Health, Alcohol and Psychosocial factors In Eastern Europe (HAPIEE) study. METHODS: A total of 2725 participants free of hypertension at baseline were tested for blood pressure or taking hypertensive medication within the last 2 weeks at 2-4-year follow-up visit. A 148-item food frequency questionnaire and the Phenol-Explorer database were used to estimate dietary polyphenol intake. Odds ratios (ORs) and 95% confidence intervals (CIs) of hypertension comparing the various categories of exposure (total and individual classes of polyphenol intake) with the lowest one (reference category) were calculated by performing age- and energy-adjusted and multivariate-adjusted logistic regression models. RESULTS: During follow-up, 1735 incident cases of hypertension occurred. The highest quartile of total polyphenol intake was associated with 31% decreased risk of hypertension compared with the lowest intake (OR 0.69, 95% CI 0.48, 0.98) in women. There was no significant association in men. Among main classes of polyphenols, flavonoids and phenolic acids were independent contributors to this association. The analysis of individual subclasses of polyphenol revealed that, among phenolic acids, hydroxycynnamic acids were independently associated to lower odds of hypertension (OR 0.66, 95% CI 0.47, 0.93), while among flavonoids, most of the association was driven by flavanols (OR 0.56, 95% CI 0.36, 0.87). CONCLUSION: Certain classes of dietary polyphenols were associated with lower risk of hypertension, but potential differences between men and women should be further investigated

Impact of gram-negative bacilli resistance rates on risk of death in septic shock and pneumonia

BACKGROUND: Sepsis is a major cause of morbidity and mortality worldwide. When selecting empiric antibiotics for sepsis, clinicians are encouraged to use local resistance rates, but their impact on individual outcomes is unknown. Improved methods to predict outcomes are needed to optimize treatment selection and improve antibiotic stewardship. METHODS: We expanded on a previously developed theoretical model to estimate the excess risk of death in gram-negative bacilli (GNB) sepsis due to discordant antibiotics using 3 factors: the prevalence of GNB in sepsis, the rate of antibiotic resistance in GNB, and the mortality difference between discordant and concordant antibiotic treatments. We focused on ceftriaxone, cefepime, and meropenem as the anti-GNB treatment backbone in sepsis, pneumonia, and urinary tract infections. We analyzed both publicly available data and data from a large urban hospital. RESULTS: Publicly available data were weighted toward culture-positive cases. Excess risk of death with discordant antibiotics was highest in septic shock and pneumonia. In septic shock, excess risk of death was 4.53% (95% confidence interval [CI], 4.04%-5.01%), 0.6% (95% CI, .55%-.66%), and 0.19% (95% CI, .16%-.21%) when considering resistance to ceftriaxone, cefepime, and meropenem, respectively. Results were similar in pneumonia. Local data, which included culture-negative cases, showed an excess risk of death in septic shock of 0.75% (95% CI, .57%-.93%) for treatment with discordant antibiotics in ceftriaxone-resistant infections and 0.18% (95% CI, .16%-.21%) for cefepime-resistant infections. CONCLUSIONS: Estimating the excess risk of death for specific sepsis phenotypes in the context of local resistance rates, rather than relying on population resistance data, may be more informative in deciding empiric antibiotics in GNB infections

Clinical implications for patients treated inappropriately for community-acquired pneumonia in the emergency department

BACKGROUND: Community-acquired pneumonia (CAP) is one of the most common infections presenting to the emergency department (ED). Increasingly, antibiotic resistant bacteria have been identified as causative pathogens in patients treated for CAP, especially in patients with healthcare exposure risk factors. METHODS: We retrospectively identified adult subjects treated for CAP in the ED requiring hospital admission (January 2003-December 2011). Inappropriate antibiotic treatment, defined as an antibiotic regimen that lacked in vitro activity against the isolated pathogen, served as the primary end point. Information regarding demographics, severity of illness, comorbidities, and antibiotic treatment was recorded. Logistic regression was used to determine factors independently associated with inappropriate treatment. RESULTS: The initial cohort included 259 patients, 72 (27.8%) receiving inappropriate antibiotic treatment. There was no difference in hospital mortality between patients receiving inappropriate and appropriate treatment (8.3% vs. 7.0%; p = 0.702). Hospital length of stay (10.3 ± 12.0 days vs. 7.0 ± 8.9 days; p = 0.017) and 30-day readmission (23.6% vs. 12.3%; p = 0.024) were greater among patients receiving inappropriate treatment. Three variables were independently associated with inappropriate treatment: admission from long-term care (AOR, 9.05; 95% CI, 3.93-20.84), antibiotic exposure in the previous 30 days (AOR, 1.85; 95% CI, 1.35-2.52), and chronic obstructive pulmonary disease (AOR, 2.05; 95% CI, 1.52-2.78). CONCLUSION: Inappropriate antibiotic treatment of presumed CAP in the ED negatively impacts patient outcome and readmission rate. Knowledge of risk factors associated with inappropriate antibiotic treatment of presumed CAP could advance the management of patients with pneumonia presenting to the ED and potentially improve patient outcomes

A Mediterranean-type diet is associated with better metabolic profile in urban Polish adults: Results from the HAPIEE study

The aim of this study was to evaluate the relationship between adherence to a Mediterranean-type diet and metabolic syndrome (MetS) in the Polish arm of the Health, Alcohol and Psychosocial factors In Eastern Europe (HAPIEE) cohort study