## 1. Introduction

Nosocomial infections (NI) are infections that develop during hospitalization and are neither present nor incubating at the time of the patient's admission. Currently, hospital infection or NI remains a major problem, constituting one of the main causes of morbidity and mortality in patients admitted to hospital. Although the figure varies considerably among countries, some studies estimate that approximately one in ten hospitalized patients will acquire an infection after admission [1]. In Spain, the overall prevalence rate of patients with NI has decreased from 8.5% in 1990 to 7% in 2007 [2–4].

For this reason, determining the intrinsic and extrinsic risk factors to which these patients are exposed and predicting NI are important aims of research. Furthermore, NI clearly increases the duration of hospital stay, causing direct economic costs and other costs derived from specific laboratory and isolation techniques and from lengthy antibiotic treatments. Estimates of the cost of these infections, in 2002 prices, suggest that the annual economic burden is $6.7 billion per year in the United States [5] and £1.06 billion in the United Kingdom [6].

In view of the foregoing, the first aim of this article is to estimate the risk factors for NI in a hospital's general surgery and digestive department ([7–10], among others). One of the statistical techniques that has traditionally been used to predict NI is the logistic regression, which not only allows the effect of each risk factor to be evaluated, but also makes it possible to quantify the NI probability of a given patient. We carried out the Bayesian estimation of these regression models. Recently, there has been great interest in Bayesian regression techniques for dichotomous response variables in many fields of application [11–16]. Chen et al. [17] also apply a Bayesian approach in their proposal to use an asymmetric link for analyzing binary response data when one response is much more frequent than the other. We compare the results of applying a Bayesian estimation with those obtained by the frequentist estimation for logistic regression models.

Patients with hospital-acquired infections suffer a prolonged stay, during which time they occupy scarce bed-days and require additional diagnostic and therapeutic interventions [18]. As a second objective of this study, we set out to determine the factors that influence hospital stay, using a Poisson-Gamma regression model. A particular aim is to quantify, in relative terms, the increased duration of the hospital stay when a patient has NI. Frequentist and Bayesian estimations for this model are compared.

The article is organized as follows: section 2 describes the data, introducing the covariates used in the study and section 3 addresses the analysis of the methodology to be considered. The results of the article are shown in section 4, and section 5 is devoted to a discussion of the results and to summarizing the conclusions reached.