José María Pérez Sánchez

Bayesian Analysis of Nosocomial Infection Risk and Length of Stay in a Department of General and Digestive Surgery

OBJECTIVE Nosocomial infection is one of the main causes of morbidity and mortality in patients admitted to hospital. One aim of this study is to determine its intrinsic and extrinsic risk factors. Nosocomial infection also increases the duration of hospital stay. We quantify, in relative terms, the increased duration of the hospital stay when a patient has the infection. METHODS We propose the use of logistic regression models with an asymmetric link to estimate the probability of a patient suffering a nosocomial infection. We use Poisson-Gamma regression models as a multivariate technique to detect the factors that really influence the average hospital stay of infected and noninfected patients. For both models, frequentist and Bayesian estimations were carried out and compared. RESULTS The models are applied to data from 1039 patients operated on in a Spanish hospital. Length of stay, the existance of a preoperative stay and obesity were found the main risk factors for a nosomial infection. The existence of a nosocomial infection multiplies the length of stay in the hospital by a factor of 2.87. CONCLUSION The results show that the asymmetric logit improves the predictive capacity of conventional logistic regressions.

Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model

The distribution of the aggregate claims in one year plays an important role in Actuarial Statistics for computing, for example, insurance premiums when both the number and size of the claims must be implemented into the model. When the number of claims follows a Poisson distribution the aggregated distribution is called the compound Poisson distribution. In this article we assume that the claim size follows an exponential distribution and later we make an extensive study of this model by assuming a bidimensional prior distribution for the parameters of the Poisson and exponential distribution with marginal gamma. This study carries us to obtain expressions for net premiums, marginal and posterior distributions in terms of some well-known special functions used in statistics. Later, a Bayesian robustness study of this model is made. Bayesian robustness on bidimensional models was deeply treated in the 1990s, producing numerous results, but few applications dealing with this problem can be found in the literature.

Expected number of goals depending on intrinsic and extrinsic factors of a football player. An application to professional Spanish football league

Abstract A Bayesian regression model for the number of goals scored by players in the Spanish football league during nine seasons is fitted. The model handles overdispersion in such a way that individual footballers ability for scoring may be estimated regardless of the number of minutes played, the position in the field and the team in which they play. Additionally, the posterior predictive distributions of the fitted model allow to obtain an estimation of the performance of any player in each season with reference to the number of goals scored, locating that number as a quantile in the expected distribution of the goals scored by this player in this season. The results show how the model awards the fact that defenders and midfielders score goals because it does not expect that they score many goals and evaluates a forward more strictly in relation to the expected number of goals.Abstract A Bayesian regression model for the number of goals scored by players in the Spanish football league during nine seasons is fitted. The model handles overdispersion in such a way that individual footballers ability for scoring may be estimated regardless of the number of minutes played, the position in the field and the team in which they play. Additionally, the posterior predictive distributions of the fitted model allow to obtain an estimation of the performance of any player in each season with reference to the number of goals scored, locating that number as a quantile in the expected distribution of the goals scored by this player in this season. The results show how the model awards the fact that defenders and midfielders score goals because it does not expect that they score many goals and evaluates a forward more strictly in relation to the expected number of goals.

A Comparative Study of Logistic Models Using an Asymmetric Link: Modelling the Away Victories in Football

The target of this paper is to study the relevant factors affecting the victories away from home of football teams in order to fit the probability of winning an away match. The paper addressed the following research issues: (a) Is the identification of the significant variables underlying the results plausible? (b) Can information of these factors increase the probability of winning away from home and assist coaches in their decisions? Empirically, it is shown that there are more home victories and draws than away victories in the professional football leagues in Europe and this fact has to be taken into account. Thus, the classical logistic and Bayesian regression models do not seem to be adequate in this case and an asymmetric logistic regression model is therefore considered. This paper analyses 380 games played in the First Division of the Spanish Football League during the 2013–2014 season. Asymmetric logistic regression from a Bayesian point of view is chosen as the best model. This model detects new relevant factors undetected by standard logistic regressions. In view of the paper’s findings, various practical recommendations were made in order to improve decision-making in this field. The Asymmetric logit link is a helpful device that can assist coaches in their game strategies.