Statistical auditing and randomness test of lotto k/N-type games

One of the most popular lottery games worldwide is the so-called ``lotto k/N''. It considers N numbers 1,2,...,N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those players whose selected numbers match all of the k randomly drawn. Exact rules may vary in different countries. In this paper, mean values and covariances for the random variables representing the numbers drawn from this kind of game are presented, with the aim of using them to audit statistically the consistency of a given sample of historical results with theoretical values coming from a hypergeometric statistical model. The method can be adapted to test pseudorandom number generators.Comment: 10 pages, no figure

The Cholecystectomy As A Day Case (CAAD) Score: A Validated Score of Preoperative Predictors of Successful Day-Case Cholecystectomy Using the CholeS Data Set

Background Day-case surgery is associated with significant patient and cost benefits. However, only 43% of cholecystectomy patients are discharged home the same day. One hypothesis is day-case cholecystectomy rates, defined as patients discharged the same day as their operation, may be improved by better assessment of patients using standard preoperative variables. Methods Data were extracted from a prospectively collected data set of cholecystectomy patients from 166 UK and Irish hospitals (CholeS). Cholecystectomies performed as elective procedures were divided into main (75%) and validation (25%) data sets. Preoperative predictors were identified, and a risk score of failed day case was devised using multivariate logistic regression. Receiver operating curve analysis was used to validate the score in the validation data set. Results Of the 7426 elective cholecystectomies performed, 49% of these were discharged home the same day. Same-day discharge following cholecystectomy was less likely with older patients (OR 0.18, 95% CI 0.15–0.23), higher ASA scores (OR 0.19, 95% CI 0.15–0.23), complicated cholelithiasis (OR 0.38, 95% CI 0.31 to 0.48), male gender (OR 0.66, 95% CI 0.58–0.74), previous acute gallstone-related admissions (OR 0.54, 95% CI 0.48–0.60) and preoperative endoscopic intervention (OR 0.40, 95% CI 0.34–0.47). The CAAD score was developed using these variables. When applied to the validation subgroup, a CAAD score of ≤5 was associated with 80.8% successful day-case cholecystectomy compared with 19.2% associated with a CAAD score >5 (p < 0.001). Conclusions The CAAD score which utilises data readily available from clinic letters and electronic sources can predict same-day discharges following cholecystectomy

Combining heterogeneous across-country data for prediction of enteric methane from proxies in dairy cattle

Large-scale measurement of enteric methane (CH4) from individual animals is a requisite for estimation of genetic parameters and prediction of breeding values. Direct measurement of individual CH4 emissions is logistically demanding and expensive, and correlated traits (proxies) or models can be used instead as a means to predict emissions. However, most predictive models tend to be specific and are valid mainly within the circumstances under which they were developed. Robust prediction models that work across countries and production environments may be built by combining heterogeneous data from several sources. However, combining heterogeneous individual animal observations on CH4 proxies from several sources is challenging and reports are scant in literature. The main objective of this study was to combine heterogeneous individual animal observations on CH4 proxies to develop robust enteric CH4 prediction models. Data on dairy cattle CH4 emissions and related proxies from 16 herds were made available by 13 research centers across 9 European countries within the Methagene EU COST Action FA1302 consortium on “Large-scale methane measurements on individual ruminants for genetic evaluations”. After a through edition and harmonization, the final dataset comprised 48,804 observations from 2,391 cows. Random Forest (RF) models were used to predict CH4 emissions and to estimate the relative importance of proxies for across-country predictions. Principal component analysis (PCA) was used to detect potential data stratifications. Milk yield, milk fat, DIM, BW, herd and country of origin appeared to be the most relevant proxies in the prediction model. An overall prediction accuracy of 0.81 was estimated from the combined heterogeneous data. This study is a first attempt to develop methods and approaches to combine heterogeneous individual animal data on proxies for CH4 to build robust models for prediction of CH4 emissions across diverse production systems and environments. The methodology outlined here can be extended to combining heterogeneous data, pedigree information and genome-wide dense marker information for estimation of genetic parameters and prediction of breeding values for traits related to dairy system CH4 emissions. Keywords: enteric methane, heterogeneous data, prediction accuracy, methane proxies, random forest, dairy cattle

Combining heterogeneous across-country data for prediction of enteric methane from proxies in dairy cattle

Large-scale measurement of enteric methane (CH4) from individual animals is a requisite for estimation of genetic parameters and prediction of breeding values. Direct measurement of individual CH4 emissions is logistically demanding and expensive, and correlated traits (proxies) or models can be used instead as a means to predict emissions. However, most predictive models tend to be specific and are valid mainly within the circumstances under which they were developed. Robust prediction models that work across countries and production environments may be built by combining heterogeneous data from several sources. However, combining heterogeneous individual animal observations on CH4 proxies from several sources is challenging and reports are scant in literature. The main objective of this study was to combine heterogeneous individual animal observations on CH4 proxies to develop robust enteric CH4 prediction models. Data on dairy cattle CH4 emissions and related proxies from 16 herds were made available by 13 research centers across 9 European countries within the Methagene EU COST Action FA1302 consortium on “Large-scale methane measurements on individual ruminants for genetic evaluations”. After a through edition and harmonization, the final dataset comprised 48,804 observations from 2,391 cows. Random Forest (RF) models were used to predict CH4 emissions and to estimate the relative importance of proxies for across-country predictions. Principal component analysis (PCA) was used to detect potential data stratifications. Milk yield, milk fat, DIM, BW, herd and country of origin appeared to be the most relevant proxies in the prediction model. An overall prediction accuracy of 0.81 was estimated from the combined heterogeneous data. This study is a first attempt to develop methods and approaches to combine heterogeneous individual animal data on proxies for CH4 to build robust models for prediction of CH4 emissions across diverse production systems and environments. The methodology outlined here can be extended to combining heterogeneous data, pedigree information and genome-wide dense marker information for estimation of genetic parameters and prediction of breeding values for traits related to dairy system CH4 emissions. Keywords: enteric methane, heterogeneous data, prediction accuracy, methane proxies, random forest, dairy cattle

Imperfezioni del Mercato e Tassazione d'Impresa

Background Whether the clinical or pathophysiologic significance of the “treatable trait” high blood eosinophil count in COPD is the same as for asthma remains controversial. We sought to determine the relationship between the blood eosinophil count, clinical characteristics and gene expression from bronchial brushings in COPD and asthma. Methods Subjects were recruited into a COPD (emphysema versus airway disease [EvA]) or asthma cohort (Unbiased BIOmarkers in PREDiction of respiratory disease outcomes, U‐BIOPRED). We determined gene expression using RNAseq in EvA (n = 283) and Affymetrix microarrays in U‐BIOPRED (n = 85). We ran linear regression analysis of the bronchial brushings transcriptional signal versus blood eosinophil counts as well as differential expression using a blood eosinophil > 200 cells/μL as a cut‐off. The false discovery rate was controlled at 1% (with continuous values) and 5% (with dichotomized values). Results There were no differences in age, gender, lung function, exercise capacity and quantitative computed tomography between eosinophilic versus noneosinophilic COPD cases. Total serum IgE was increased in eosinophilic asthma and COPD. In EvA, there were 12 genes with a statistically significant positive association with the linear blood eosinophil count, whereas in U‐BIOPRED, 1197 genes showed significant associations (266 positive and 931 negative). The transcriptome showed little overlap between genes and pathways associated with blood eosinophil counts in asthma versus COPD. Only CST1 was common to eosinophilic asthma and COPD and was replicated in independent cohorts. Conclusion Despite shared “treatable traits” between asthma and COPD, the molecular mechanisms underlying these clinical entities are predominately different