Optimal single threshold stopping rules and sharp prophet inequalities

This paper considers a finite horizon optimal stopping problem for a sequence of independent and identically distributed random variables. The objective is to design stopping rules that attempt to select the random variable with the highest value in the sequence. The performance of any stopping rule may be benchmarked relative to the selection of a "prophet" that has perfect foreknowledge of the largest value. Such comparisons are typically stated in the form of "prophet inequalities." In this paper we characterize sharp prophet inequalities for single threshold stopping rules as solutions to infinite two person zero sum games on the unit square with special payoff kernels. The proposed game theoretic characterization allows one to derive sharp non-asymptotic prophet inequalities for different classes of distributions. This, in turn, gives rise to a simple and computationally tractable algorithmic paradigm for deriving optimal single threshold stopping rules

Renal Function Following Three Distinct Weight Loss Dietary Strategies During 2 Years of a Randomized Controlled Trial

OBJECTIVE This study addressed the long-term effect of various diets, particularly low-carbohydrate high-protein, on renal function on participants with or without type 2 diabetes. RESEARCH DESIGN AND METHODS In the 2-year Dietary Intervention Randomized Controlled Trial (DIRECT), 318 participants (age, 51 years; 86% men; BMI, 31 kg/m2; mean estimated glomerular filtration rate [eGFR], 70.5 mL/min/1.73 m2; mean urine microalbumin-to-creatinine ratio, 12:12) with serum creatinine 0.05) across diet groups. The increased eGFR was at least as prominent in participants with (+6.7%) or without (+4.5%) type 2 diabetes or those with lower baseline renal function of eGFR <60 mL/min/1.73 m2 (+7.1%) versus eGFR ≥60 mL/min/1.73 m2 (+3.7%). In a multivariable model adjusted for age, sex, diet group, type 2 diabetes, use of ACE inhibitors, 2-year weight loss, and change in protein intake (confounders and univariate predictors), only a decrease in fasting insulin (β = −0.211; P = 0.004) and systolic blood pressure (β = −0.25; P < 0.001) were independently associated with increased eGFR. The urine microalbumin-to-creatinine ratio improved similarly across the diets, particularly among participants with baseline sex-adjusted microalbuminuria, with a mean change of −24.8 (P < 0.05). CONCLUSIONS A low-carbohydrate diet is as safe as Mediterranean or low-fat diets in preserving/improving renal function among moderately obese participants with or without type 2 diabetes, with baseline serum creatinine <176 μmol/L. Potential improvement is likely to be mediated by weight loss–induced improvements in insulin sensitivity and blood pressure

Two Patterns of Adipokine and Other Biomarker Dynamics in a Long-Term Weight Loss Intervention

Objective: Long-term dietary intervention frequently induces a rapid weight decline followed by weight stabilization/regain. Here, we sought to identify adipokine biomarkers that may reflect continued beneficial effects of dieting despite partial weight regain. Research design and methods: We analyzed the dynamics of fasting serum levels of 12 traditional metabolic biomarkers and novel adipokines among 322 participants in the 2-year Dietary Intervention Randomized Controlled Trial (DIRECT) of low-fat, Mediterranean, or low-carbohydrate diets for weight loss. Results: We identified two distinct patterns: Pattern A includes biomarkers (insulin, triglycerides, leptin, chemerin, monocyte chemoattractant protein 1, and retinol-binding protein 4) whose dynamics tightly correspond to changes in body weight, with the trend during the weight loss phase (months 0–6) going in the opposite direction to that in the weight maintenance/regain phase (months 7–24) (P < 0.05 between phases, all biomarkers). Pattern B includes biomarkers (high molecular weight adiponectin, HDL cholesterol [HDL-C], high-sensitivity C-reactive protein [hsCRP], fetuin-A, progranulin, and vaspin) that displayed a continued, cumulative improvement (P < 0.05 compared with baseline, all biomarkers) throughout the intervention. These patterns were consistent across sex, diabetic groups, and diet groups, although the magnitude of change varied. Hierarchical analysis suggested similar clusters, revealing that the dynamic of leptin (pattern A) was most closely linked to weight change and that the dynamic of hsCRP best typified pattern B. Conclusions: hsCRP, HDL-C, adiponectin, fetuin-A, progranulin, and vaspin levels display a continued long-term improvement despite partial weight regain. This may likely reflect either a delayed effect of the initial weight loss or a continuous beneficial response to switching to healthier dietary patterns

Abdominal Superficial Subcutaneous Fat

OBJECTIVE: Unlike visceral adipose tissue (VAT), the association between subcutaneous adipose tissue (SAT) and obesity-related morbidity is controversial. In patients with type 2 diabetes, we assessed whether this variability can be explained by a putative favorable, distinct association between abdominal superficial SAT (SSAT) (absolute amount or its proportion) and cardiometabolic parameters. RESEARCH DESIGN AND METHODS: We performed abdominal magnetic resonance imaging (MRI) in 73 patients with diabetes (mean age 58 years, 83% were men) and cross-sectionally analyzed fat distribution at S1-L5, L5-L4, and L3-L2 levels. Patients completed food frequency questionnaires, and subgroups had 24-h ambulatory blood pressure monitoring and 24-h ambulatory electrocardiography. RESULTS: Women had higher %SSAT (37 vs. 23% in men; P < 0.001) despite a similar mean waist circumference. Fasting plasma glucose (P = 0.046) and HbA1c (P = 0.006) were both lower with increased tertile of absolute SSAT. In regression models adjusted for age, waist circumference, and classes of medical treatments used in this patient population, increased %SSAT was significantly associated with decreased HbA1c (β = −0.317; P = 0.013), decreased daytime ambulatory blood pressure (β = −0.426; P = 0.008), and increased HDL cholesterol (β = 0.257; P = 0.042). In contrast, increased percent of deep SAT (DSAT) was associated with increased HbA1c (β = 0.266; P = 0.040) and poorer heart rate variability parameters (P = 0.030). Although total fat and energy intake were not correlated with fat tissue distribution, increased intake of trans fat tended to be associated with total SAT (r = 0.228; P = 0.05) and DSAT (r = 0.20; P = 0.093), but not with SSAT. CONCLUSIONS: Abdominal SAT is composed of two subdepots that associate differently with cardiometabolic parameters. Higher absolute and relative distribution of fat in abdominal SSAT may signify beneficial cardiometabolic effects in patients with type 2 diabetes

Carbapenemase type and mortality in blood-stream infections caused by carbapenemase-producing enterobacterales: a multicenter retrospective cohort study

Background: Previous studies analyzing differences in mortality associated with carbapenemase type in patients with a variety of infections caused by carbapenemase-producing Enterobacterales (CPE) have produced conflicting results. Methods: We performed a multinational multicenter retrospective cohort study. Adult patients with blood-stream infections (BSI) caused by CPE between 2015 and 2020 were included. The primary outcome was 14-day mortality; 28-day mortality and microbiological failure were secondary outcomes. Clinical and microbiological data were collected and analyzed using conditional logistic regression. Results: A total of 360 patients were identified of whom 226 had infections caused by KPC-producing isolates, 109 by NDM-producing isolates and 25 by other carbapenemases. Definitive therapy was colistin-based in 35.1% of patients, ceftazidime/avibactam ± aztreonam (CAZ/AVI ± A) in 28.2% and other in 23.4%. Overall 14-day mortality was 28.1%; carbapenemase type was unassociated with mortality in univariate or multivariate analyses. Antimicrobial therapy was significantly associated with 14-day mortality: patients treated with CAZ/AVI ± A had an adjusted hazard ratio of 0.172 (95% confidence interval 0.063–0.473) for death as compared to patients treated with colistin-based therapy. At 28 days, overall mortality was 35.3%; no association was observed between carbapenemase type and 28-day mortality or microbiological failure. Conclusion: After controlling for antimicrobial therapy, we did not find evidence of an association between carbapenemase type and mortality. Ceftazidime/avibactam was associated with a greater than 80% reduction in mortality as compared with colistin

A Unified Approach for Solving Sequential Selection Problems

In this paper we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as well as random problem horizons. The proposed framework is based on a reduction of the original selection problem to one of optimal stopping for a sequence of judiciously constructed independent random variables. We demonstrate that our approach allows exact and efficient computation of optimal policies and various performance metrics thereof for a variety of sequential selection problems, several of which have not been solved to date.The research was supported by the ISF grant No. 361/15.https://projecteuclid.org/journals/probability-surveys/volume-17/issue-none/A-unified-approach-for-solving-sequential-selection-problems/10.1214/19-PS333.ful

Optimal single threshold stopping rules and sharp prophet inequalities

This paper considers a finite horizon optimal stopping problem for a sequence of independent and identically distributed random variables. The objective is to design stopping rules that attempt to select the random variable with the highest value in the sequence. The performance of any stopping rule may be benchmarked relative to the selection of a “prophet” that has perfect foreknowledge of the largest value. Such comparisons are typically stated in the form of “prophet inequalities.” In this paper we characterize sharp prophet inequalities for single threshold stopping rules as solutions to infinite two person zero sum games on the unit square with special payoff kernels. The proposed game theoretic characterization allows one to derive sharp non-asymptotic prophet inequalities for different classes of distributions. This, in turn, gives rise to a simple and computationally tractable algorithmic paradigm for deriving optimal single threshold stopping rules.The research is supported by the BSF grant 2020063.http://arxiv.org/abs/2404.1294