105 research outputs found
The perimeter of uniform and geometric words: a probabilistic analysis
Let a word be a sequence of i.i.d. integer random variables. The
perimeter of the word is the number of edges of the word, seen as a
polyomino. In this paper, we present a probabilistic approach to the
computation of the moments of . This is applied to uniform and geometric
random variables. We also show that, asymptotically, the distribution of is
Gaussian and, seen as a stochastic process, the perimeter converges in
distribution to a Brownian motionComment: 13 pages, 7 figure
A Liouville theorem for some Bessel generalized operators
In this paper we establish a Liouville theorem in for a
wider class of operators in that generalizes the
-dimensional Bessel operator. We will present two different proofs, based in
two representation theorems for certain distributions "supported in zero"
Cardiorespiratory Fitness Attenuates the Impact of Risk Factors Associated With COVID-19 Hospitalization
Predicting diabetes mellitus using SMOTE and ensemble machine learning approach: The Henry Ford ExercIse Testing (FIT) project
Machine learning is becoming a popular and important approach in the field of medical research. In this study, we investigate the relative performance of various machine learning methods such as Decision Tree, Naïve Bayes, Logistic Regression, Logistic Model Tree and Random Forests for predicting incident diabetes using medical records of cardiorespiratory fitness. In addition, we apply different techniques to uncover potential predictors of diabetes. This FIT project study used data of 32,555 patients who are free of any known coronary artery disease or heart failure who underwent clinician-referred exercise treadmill stress testing at Henry Ford Health Systems between 1991 and 2009 and had a complete 5-year follow-up. At the completion of the fifth year, 5,099 of those patients have developed diabetes. The dataset contained 62 attributes classified into four categories: demographic characteristics, disease history, medication use history, and stress test vital signs. We developed an Ensembling-based predictive model using 13 attributes that were selected based on their clinical importance, Multiple Linear Regression, and Information Gain Ranking methods. The negative effect of the imbalance class of the constructed model was handled by Synthetic Minority Oversampling Technique (SMOTE). The overall performance of the predictive model classifier was improved by the Ensemble machine learning approach using the Vote method with three Decision Trees (Naïve Bayes Tree, Random Forest, and Logistic Model Tree) and achieved high accuracy of prediction (AUC = 0.92). The study shows the potential of ensembling and SMOTE approaches for predicting incident diabetes using cardiorespiratory fitness data
Relation of a Maximal Exercise Test to Change in Exercise Tolerance During Cardiac Rehabilitation
The purpose of this study was to test the hypothesis that an individualized exercise training target heart rate (HR) based on a maximal graded exercise test (GXT) is associated with greater improvements in exercise tolerance during cardiac rehabilitation (CR) compared with no GXT. In this retrospective study, we identified patients who completed 9 to 36 visits of CR between 2001 and 2016, with a length of stay ≤18 weeks and a visit frequency of 1 to 3 days per week. Patients were grouped based on whether their exercise was guided by a target HR determined from a GXT. To assess the relation between GXT and change in exercise training metabolic equivalents of task (METs), we used generalized linear models adjusted for age, gender, race, referral reason, CR visits, CR frequency, METs at start, CR location, and year of participation. Out of 4,455 patients (37% female, 48% White, median age = 62 years), 53% were prescribed a target HR based on a GXT. Compared with no GXT, a GXT was associated with a significantly greater increase in covariate-adjusted METs during CR and percentage change from start (+0.44 METs [95% confidence interval [CI] 0.38 to 0.51] and +17% [95% CI 14% to 19%], respectively). In a sensitivity analysis limited to patients with 24 to 36 visits at ≥2 days per week (n = 1,319), a GXT was associated with a significantly greater increase in covariate-adjusted exercise training METs (+0.51 [95% CI 0.36 to 0.66]; +19% [95% CI 13% to 24%]). In conclusion, to maximize the potential increase in exercise capacity during CR, patients should undergo a GXT to determine an individualized exercise training target HR
Chronotropic incompetence and long-term risk of heart failure: The henry ford exercise testing project
Background: Chronotropic incompetence (CI) has been associated with cardiovascular mortality. However, its relationship with long-term risk of heart failure (HF) is not well studied.
Methods: We included 43,098 participants (mean age 51.7±12.3 years, 47.5% females, 66.6% white) of the FIT project who completed a clinically indicated exercise test between 1991 and 2009. Patients with coronary artery disease, prior HF or on heart rate reducing medications were excluded. Incident HF was defined by having a documented diagnosis in 3 separate clinical encounters. CI was defined by inability to achieve 85% of maximal age predicted heart rate (calculated by 220 - age) with exercise. Multivariable adjusted Cox models were used to assess the independent association of CI with incident HF.
Results: At baseline, 5,249 (12.2%) had CI. After a mean follow-up duration of 10.9 ± 4.6 years, 1329 (3.2%) experienced new onset HF. The cumulative incidence of HF was 397 (7.6%) among CI patients compared with 992 (2.6%) among chronotropic competent patients. Figure 1 shows the cumulative incidence of heart failure by CI status. In multivariable Cox regression models, CI was associated with increased risk of incident heart failure (HR 1.73; 95% CI 1.48 – 2.03, p \u3c0.001) after adjusting for confounders. There were no interactions by age, sex, race, body mass index. Conclusions: Our study shows that CI is an independent risk factor for HF. Further research is needed to determine whether CI could be a therapeutic target for HF
Cardiorespiratory Fitness and Incident Stroke Types: The FIT (Henry Ford ExercIse Testing) Project
OBJECTIVE: To study the association between cardiorespiratory fitness (CRF) and incident stroke types.
PATIENTS AND METHODS: We studied a retrospective cohort of patients referred for treadmill stress testing in the Henry Ford Health System (Henry Ford ExercIse Testing Project) without history of stroke. CRF was expressed by metabolic equivalents of task (METs). Using appropriate International Classification of Diseases, Ninth Revision codes, incident stroke was ascertained through linkage with administrative claims files and classified as ischemic, hemorrhagic, and subarachnoid hemorrhage (SAH). Multivariable-adjusted Cox proportional hazards models examined the association between CRF and incident stroke.
RESULTS: Among 67,550 patients, mean ± SD age was 54±13 years, 46% (n=31,089) were women, and 64% (n=43,274) were white. After a median follow-up of 5.4 (interquartile range 2.7-8.5) years, a total of 7512 incident strokes occurred (6320 ischemic, 2481 hemorrhagic, and 275 SAH). Overall, there was a graded lower incidence of stroke with higher MET categories. Patients with METs of 12 or more had lower risk of overall stroke [0.42 (95% CI, 0.36-0.49)], ischemic stroke [0.69 (95% CI, 0.58-0.82)], and hemorrhagic stroke [0.71 (95% CI, 0.52-0.95)].
CONCLUSION: In a large ethnically diverse cohort of patients referred for treadmill stress testing, CRF is inversely associated with risk for ischemic and hemorrhagic stroke
Higher cardiorespiratory fitness predicts long-term survival in patients with heart failure and preserved ejection fraction: the Henry Ford Exercise Testing (FIT) Project
Introduction: Higher cardiorespiratory fitness (CRF) is associated with improved exercise capacity and quality of life in heart failure with preserved ejection fraction (HFpEF), but there are no large studies evaluating the association of HFpEF, CRF, and long-term survival. We therefore aimed to determine the association between CRF and all-cause mortality, in patients with HFpEF.
Material and methods: In the Henry Ford Exercise Testing (FIT) Project, 167 patients had baseline HFpEF, defined as a clinical diagnosis of heart failure with ejection fraction ≥ 50% on echocardiogram. The CRF was estimated from the peak workload (in METs) from a clinician-referred treadmill stress test and categorized as poor (1-4 METs), intermediate (5-6 METs), and moderate-high (≥ 7 METs). Additional analyses assessing the effect of HFpEF and CRF on mortality were also conducted, matching HFpEF patients to non-HFpEF patients using propensity scores.
Results: Mean age was 64 ±13 years, with 55% women, and 46% Black. Over a median follow-up of 9.7 (5.2-18.9) years, there were 103 deaths. In fully adjusted models, moderate-high CRF was associated with 63% lower mortality risk (HR = 0.37, 95% CI: 0.18-0.73) compared to the poor-CRF group. In the propensity-matched cohort, HFpEF was associated with a HR of 2.3 (95% CI: 1.7-3.2) for mortality compared to non-HFpEF patients, which was attenuated to 1.8 (95% CI: 1.3-2.5) after adjusting for CRF.
Conclusions: Moderate-high CRF in patients with HFpEF is associated with improved survival, and differences in CRF partly explain the intrinsic risk of HFpEF. Randomized trials of interventions aimed at improving CRF in HFpEF are needed
Use of Sex-Specific Clinical and Exercise Risk Scores to Identify Patients at Increased Risk for All-Cause Mortality
Importance Risk assessment tools for exercise treadmill testing may have limited external validity. Cardiovascular mortality has decreased in recent decades, and women have been underrepresented in prior cohorts.
Objectives To determine whether exercise and clinical variables are associated with differential mortality outcomes in men and women and to assess whether sex-specific risk scores better estimate all-cause mortality.
Design, Setting, and Participants This retrospective cohort study included 59 877 patients seen at the Cleveland Clinic Foundation (CCF cohort) from January 1, 2000, through December 31, 2010, and 49 278 patients seen at the Henry Ford Hospital (FIT cohort) from January 1, 1991, through December 31, 2009. All patients were 18 years or older and underwent exercise treadmill testing. Data were analyzed from January 1, 2000, to October 27, 2011, in the CCF cohort and from January 1, 1991, to April 1, 2013, in the FIT cohort.
Main Outcomes and Measurements The CCF cohort was divided randomly into derivation and validation samples, and separate risk scores were developed for men and women. Net reclassification, C statistics, and integrated discrimination improvement were used to compare the sex-specific risk scores with other tools that have all-cause mortality as the outcome. Discrimination and calibration were also evaluated with these sex-specific risk scores in the FIT cohort.
Results The CCF cohort included 59 877 patients (59.4% men; 40.5% women) with a median (interquartile range [IQR]) age of 54 (45-63) years and 2521 deaths (4.2%) during a median follow-up of 7 (IQR, 4.1-9.6) years. The FIT cohort included 49 278 patients (52.5% men; 47.4% women) with a median (IQR) age of 54 (46-64) years and 6643 deaths (13.5%) during a median (IQR) follow-up of 10.2 (7-13.4) years. C statistics for the sex-specific risk scores in the CCF validation sample were higher (0.79 in women and 0.81 in men) than C statistics using other tools in women (0.70 for Duke Treadmill Score; 0.74 for Lauer nomogram) and men (0.72 for Duke Treadmill Score; 0.75 for Lauer nomogram). Net reclassification and integrated discrimination improvement were superior with the sex-specific risk scores, mostly owing to correct reclassification of events. The sex-specific risk scores in the FIT cohort demonstrated similar discrimination (C statistic, 0.78 for women and 0.79 for men), and calibration was reasonable.
Conclusions and Relevance Sex-specific risk scores better estimate mortality in patients undergoing exercise treadmill testing. In particular, these sex-specific risk scores help to identify patients at the highest residual risk in the present era
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