A Mathematical Analysis of Benford's Law and its Generalization

We explain Kossovsky's generalization of Benford's law which is a formula that approximates the distribution of leftmost digits in finite sequences of natural data and apply it to six sequences of data including populations of US cities and towns and times between earthquakes. We model the natural logarithms of these two data sequences as samples of random variables having normal and reflected Gumbel densities respectively. We show that compliance with the general law depends on how nearly constant the periodized density functions are and that the models are generally more compliant than the natural data. This surprising result suggests that the generalized law might be used to improve density estimation which is the basis of statistical pattern recognition, machine learning and data science.Comment: 15 pages, 8 figure

Integrated care at home reduces unnecessary hospitalizations of community-dwelling frail older adults: a prospective controlled trial.

Care of frail and dependent older adults with multiple chronic conditions is a major challenge for health care systems. The study objective was to test the efficacy of providing integrated care at home to reduce unnecessary hospitalizations, emergency room visits, institutionalization, and mortality in community dwelling frail and dependent older adults. A prospective controlled trial was conducted, in real-life clinical practice settings, in a suburban region in Geneva, Switzerland, served by two home visiting nursing service centers. Three hundred and one community-dwelling frail and dependent people over 60 years old were allocated to previously randomized nursing teams into Control (N = 179) and Intervention (N = 122) groups: Controls received usual care by their primary care physician and home visiting nursing services, the Intervention group received an additional home evaluation by a community geriatrics unit with access to a call service and coordinated follow-up. Recruitment began in July 2009, goals were obtained in July 2012, and outcomes assessed until December 2012. Length of follow-up ranged from 5 to 41 months (mean 16.3). Primary outcome measure was the number of hospitalizations. Secondary outcomes were reasons for hospitalizations, the number and reason of emergency room visits, institutionalization, death, and place of death. The number of hospitalizations did not differ between groups however, the intervention led to lower cumulative incidence for the first hospitalization after the first year of follow-up (69.8%, CI 59.9 to 79.6 versus 87 · 6%, CI 78 · 2 to 97 · 0; p = .01). Secondary outcomes showed that the intervention compared to the control group had less frequent unnecessary hospitalizations (4.1% versus 11.7%, p = .03), lower cumulative incidence for the first emergency room visit, 8.3%, CI 2.6 to 13.9 versus 23.2%, CI 13.1 to 33.3; p = .01), and death occurred more frequently at home (44.4 versus 14.7%; p = .04). No significant differences were found for institutionalization and mortality. Integrated care that included a home visiting multidisciplinary geriatric team significantly reduced unnecessary hospitalizations, emergency room visits and allowed more patients to die at home. It is an effective tool to improve coordination and access to care for frail and dependent older adults. Clinical Trials.gov Identifier: NCT02084108 . Retrospectively registered on March 10(th) 2014

Reliability of the revised Swiss Emergency Triage Scale: a computer simulation study.

The Swiss Emergency Triage Scale (SETS) is a four-level emergency scale that previously showed moderate reliability and high rates of undertriage due to a lack of standardization. It was revised to better standardize the measurement and interpretation of vital signs during the triage process. The aim of this study was to explore the inter-rater and test-retest reliability, and the rate of correct triage of the revised SETS. Thirty clinical scenarios were evaluated twice at a 3-month interval using an interactive computerized triage simulator by 58 triage nurses at an urban teaching emergency department admitting 60 000 patients a year. Inter-rater and test-retest reliabilities were determined using κ statistics. Triage decisions were compared with a gold standard attributed by an expert panel. Rates of correct triage, undertriage, and overtriage were computed. A logistic regression model was used to identify the predictors of correct triage. A total of 3387 triage situations were analyzed. Inter-rater reliability showed substantial agreement [mean κ: 0.68; 95% confidence interval (CI): 0.60-0.78] and test-retest almost perfect agreement (mean κ: 0.86; 95% CI: 0.84-0.88). The rate of correct triage was 84.1%, and rates of undertriage and overtriage were 7.2 and 8.7%, respectively. Vital sign measurement was an independent predictor of correct triage (odds ratios for correct triage: 1.29 for each additional vital sign measured, 95% CI: 1.20-1.39). The revised SETS incorporating standardized vital sign measurement and interpretation during the triage process resulted in high reliability and low rates of mistriage

Variability in quality of care among dialysis units in western Switzerland

BACKGROUND: Quality indicators for dialysis care vary across countries and regions, but regional variability across centres has received little attention. We analysed variations in quality indicators among dialysis facilities in western Switzerland to identify opportunities for improving care for patients with end-stage kidney disease. METHODS: A cross-sectional study of 617 dialysis patients treated at 19 facilities examined the distribution of indicators of quality of care addressing: adequacy of dialysis (Kt/V > or =1.2 for haemodialysis, Kt/V > or =2 for peritoneal dialysis), anaemia control (haemoglobin > or =110 g/l), calcium and phosphate control (product < or =4.4 mmol2/l2), adequate nutrition (serum albumin >35 g/l), hypertension control (pre-dialysis blood pressure <140/90 mmHg) and type of vascular access. Centre quality targets were the following: achievement of quality criteria for 80% of their patients, except 85% for anaemia control and 60% for arterio-venous fistulae. RESULTS: Most centres fulfilled quality targets for dialysis adequacy, but substantial variations existed among centres (haemodialysis, 76%, range 36-100; peritoneal dialysis, 76%, range 33-100). Results were similar for anaemia (77%, range 35-100), calcium x phosphate product (69%, range 29-92), albumin (63%, range 26-95), hypertension control (33%, range 13-54) and arterio-venous fistula (61%, range 49-92). The between-centre variability was significantly greater than would be expected by chance, for all indicators. Dialysis facilities with >40 patients better fulfilled quality targets than university-based centres. Adjustment for patient characteristics did not modify these results. CONCLUSIONS: Substantial variations in quality indicators existed between dialysis centres in western Switzerland, which could not be attributed to different centre policies, or to differences in available measures of patient case mix. These findings indicate opportunities for improvement in dialysis practice which may translate into improved clinical outcomes

Unplanned readmission rates, length of hospital stay, mortality, and medical costs of ten common medical conditions: a retrospective analysis of Hong Kong hospital data

<p>Abstract</p> <p>Background</p> <p>Studies on readmissions attributed to particular medical conditions, especially heart failure, have generally not addressed the factors associated with readmissions and the implications for health outcomes and costs. This study aimed to investigate the factors associated with 30-day unplanned readmission for 10 common conditions and to determine the cost implications.</p> <p>Methods</p> <p>This population-based retrospective cohort study included patients admitted to all public hospitals in Hong Kong in 2007. The sample consisted of 337,694 hospitalizations in Internal Medicine. The disease-specific risk-adjusted odd ratio (OR), length of stay (LOS), mortality and attributable medical costs for the year were examined for unplanned readmissions for 10 medical conditions, namely malignant neoplasms, heart diseases, cerebrovascular diseases, pneumonia, injury and poisoning, nephritis and nephrosis, diabetes mellitus, chronic liver disease and cirrhosis, septicaemia, and aortic aneurysm.</p> <p>Results</p> <p>The overall unplanned readmission rate was 16.7%. Chronic liver disease and cirrhosis had the highest OR (1.62, 95% confidence interval (CI) 1.39-1.87). Patients with cerebrovascular disease had the longest LOS, with mean acute and rehabilitation stays of 6.9 and 3.0 days, respectively. Malignant neoplasms had the highest mortality rate (30.8%) followed by aortic aneurysm and pneumonia. The attributed medical cost of readmission was highest for heart disease (US$3 199 418, 95$2 579 443-803 393).</p> <p>Conclusions</p> <p>Our findings showed variations in readmission rates and mortality for different medical conditions which may suggest differences in the quality of care provided for various medical conditions. In-hospital care, comprehensive discharge planning, and post-discharge community support for patients need to be reviewed to improve the quality of care and patient health outcomes.</p

The immediate effects of the severe acute respiratory syndrome (SARS) epidemic on childbirth in Taiwan

BACKGROUND: When an emerging infectious disease like severe acute respiratory syndrome (SARS) strikes suddenly, many wonder the public's overwhelming fears of SARS may deterred patients from seeking routine care from hospitals and/or interrupt patient's continuity of care. In this study, we sought to estimate the influence of pregnant women's fears of severe acute respiratory syndrome (SARS) on their choice of provider, mode of childbirth, and length of stay (LOS) for the delivery during and after the SARS epidemic in Taiwan. METHODS: The National Health Insurance data from January 01, 2002 to December 31, 2003 were used. A population-based descriptive analysis was conducted to assess the changes in volume, market share, cesarean rate, and average LOS for each of the 4 provider levels, before, during and after the SARS epidemic. RESULTS: Compared to the pre-SARS period, medical centers and regional hospitals dropped 5.2% and 4.1% in market share for childbirth services during the peak SARS period, while district hospitals and clinics increased 2.1% and 7.1%, respectively. For changes in cesarean rates, only a significantly larger increase was observed in medical centers (2.2%) during the peak SARS period. In terms of LOS, significant reductions in average LOS were observed in all hospital levels except for clinics. Average LOS was shortened by 0.21 days in medical centers (5.6%), 0.21 days in regional hospitals (5.8%), and 0.13 days in district hospitals (3.8%). CONCLUSION: The large amount of patients shifting from the maternity wards of more advanced hospitals to those of less advanced hospitals, coupled with the substantial reduction in their length of maternity stay due to their fears of SARS could also lead to serious concerns for quality of care, especially regarding a patient's accessibility to quality providers and continuity of care

Reduction of missed appointments at an urban primary care clinic: a randomised controlled study

<p>Abstract</p> <p>Background</p> <p>Missed appointments are known to interfere with appropriate care and to misspend medical and administrative resources. The aim of this study was to test the effectiveness of a sequential intervention reminding patients of their upcoming appointment and to identify the profile of patients missing their appointments.</p> <p>Methods</p> <p>We conducted a randomised controlled study in an urban primary care clinic at the Geneva University Hospitals serving a majority of vulnerable patients. All patients booked in a primary care or HIV clinic at the Geneva University Hospitals were sent a reminder 48 hrs prior to their appointment according to the following sequential intervention: 1. Phone call (fixed or mobile) reminder; 2. If no phone response: a Short Message Service (SMS) reminder; 3. If no available mobile phone number: a postal reminder. The rate of missed appointment, the cost of the intervention, and the profile of patients missing their appointment were recorded.</p> <p>Results</p> <p>2123 patients were included: 1052 in the intervention group, 1071 in the control group. Only 61.7% patients had a mobile phone recorded at the clinic. The sequential intervention significantly reduced the rate of missed appointments: 11.4% (n = 122) in the control group and 7.8% (n = 82) in the intervention group (p < 0.005), and allowed to reallocate 28% of cancelled appointments. It also proved to be cost effective in providing a total net benefit of 1846. - EUR/3 months. A satisfaction survey conducted with 241 patients showed that 93% of them were not bothered by the reminders and 78% considered them to be useful. By multivariate analysis, the following characteristics were significant predictors of missed appointments: younger age (OR per additional decade 0.82; CI 0.71-0.94), male gender (OR 1.72; CI 1.18-2.50), follow-up appointment >1year (OR 2.2; CI: 1.15-4.2), substance abuse (2.09, CI 1.21-3.61), and being an asylum seeker (OR 2.73: CI 1.22-6.09).</p> <p>Conclusion</p> <p>A practical reminder system can significantly increase patient attendance at medical outpatient clinics. An intervention focused on specific patient characteristics could further increase the effectiveness of appointment reminders.</p

A predictive score to identify hospitalized patients' risk of discharge to a post-acute care facility

<p>Abstract</p> <p>Background</p> <p>Early identification of patients who need post-acute care (PAC) may improve discharge planning. The purposes of the study were to develop and validate a score predicting discharge to a post-acute care (PAC) facility and to determine its best assessment time.</p> <p>Methods</p> <p>We conducted a prospective study including 349 (derivation cohort) and 161 (validation cohort) consecutive patients in a general internal medicine service of a teaching hospital. We developed logistic regression models predicting discharge to a PAC facility, based on patient variables measured on admission (day 1) and on day 3. The value of each model was assessed by its area under the receiver operating characteristics curve (AUC). A simple numerical score was derived from the best model, and was validated in a separate cohort.</p> <p>Results</p> <p>Prediction of discharge to a PAC facility was as accurate on day 1 (AUC: 0.81) as on day 3 (AUC: 0.82). The day-3 model was more parsimonious, with 5 variables: patient's partner inability to provide home help (4 pts); inability to self-manage drug regimen (4 pts); number of active medical problems on admission (1 pt per problem); dependency in bathing (4 pts) and in transfers from bed to chair (4 pts) on day 3. A score ≥ 8 points predicted discharge to a PAC facility with a sensitivity of 87% and a specificity of 63%, and was significantly associated with inappropriate hospital days due to discharge delays. Internal and external validations confirmed these results.</p> <p>Conclusion</p> <p>A simple score computed on the 3rd hospital day predicted discharge to a PAC facility with good accuracy. A score > 8 points should prompt early discharge planning.</p

Hospital Readmission in General Medicine Patients: A Prediction Model

Background: Previous studies of hospital readmission have focused on specific conditions or populations and generated complex prediction models. Objective: To identify predictors of early hospital readmission in a diverse patient population and derive and validate a simple model for identifying patients at high readmission risk. Design: Prospective observational cohort study. Patients: Participants encompassed 10,946 patients discharged home from general medicine services at six academic medical centers and were randomly divided into derivation (n = 7,287) and validation (n = 3,659) cohorts. Measurements: We identified readmissions from administrative data and 30-day post-discharge telephone follow-up. Patient-level factors were grouped into four categories: sociodemographic factors, social support, health condition, and healthcare utilization. We performed logistic regression analysis to identify significant predictors of unplanned readmission within 30 days of discharge and developed a scoring system for estimating readmission risk. Results: Approximately 17.5% of patients were readmitted in each cohort. Among patients in the derivation cohort, seven factors emerged as significant predictors of early readmission: insurance status, marital status, having a regular physician, Charlson comorbidity index, SF12 physical component score, ≥1 admission(s) within the last year, and current length of stay >2 days. A cumulative risk score of ≥25 points identified 5% of patients with a readmission risk of approximately 30% in each cohort. Model discrimination was fair with a c-statistic of 0.65 and 0.61 for the derivation and validation cohorts, respectively. Conclusions: Select patient characteristics easily available shortly after admission can be used to identify a subset of patients at elevated risk of early readmission. This information may guide the efficient use of interventions to prevent readmission