A. J. Sáez-Castillo

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.

A hyper-Poisson regression model for overdispersed and underdispersed count data

The Poisson regression model is the most common framework for modeling count data, but it is constrained by its equidispersion assumption. The hyper-Poisson regression model described in this paper generalizes it and allows for over- and under-dispersion, although, unlike other models with the same property, it introduces the regressors in the equation of the mean. Additionally, regressors may also be introduced in the equation of the dispersion parameter, in such a way that it is possible to fit data that present overdispersion and underdispersion in different levels of the observations. Two applications illustrate that the model can provide more accurate fits than those provided by alternative usual models.

A generalized Waring regression model for count data

A regression model for count data based on the generalized Waring distribution is developed. This model allows the observed variability to be split into three components: randomness, internal differences between individuals and the presence of other external factors that have not been included as covariates in the model. An application in the field of sports illustrates its capacity for modelling data sets with great accuracy. Moreover, this yields more information than a model based on the negative binomial distribution.

A triparametric discrete distribution with complex parameters

Rodríguez-Aviet al. (2002) give a general description of a discrete distribution generated by the Gaussian hypergeometric function with complex parameters and provide a detailed study of a biparametric distribution, namedCBPD, under conditions where the complex parameters have no real part. In this paper we present a more complete study of the discrete distribution obtained in the general case. Thus, its main probabilistic properties are described, convergence results are generalized and, finally, methods of estimation are developed with some examples of applications.

Estimation of Parameters in Gaussian Hypergeometric Distributions

Abstract Some methods for estimating parameters in distributions generated by the Gaussian hypergeometric function are developed in this article: specifically, methods based on relations between moments and/or frequencies, estimators obtained by the minimum chi-square procedure and the method of maximum likelihood are considered. The asymptotic relative efficiencies of estimators with explicit formulae are compared. Finally, two real examples are given in order to illustrate these methods.

A new generalization of the Waring distribution

A tetraparametric univariate distribution generated by the Gaussian hypergeometric function that includes the Waring and the generalized Waring distributions as particular cases is presented. This distribution is expressed as a generalized beta type I mixture of a negative binomial distribution, in such a way that the variance of the tetraparametric model can be split into three components: randomness, proneness and liability. These results are extensions of known analogous properties of the generalized Waring distribution. Two applications in the fields of sport and economy are included in order to illustrate the utility of the new distribution compared with the generalized Waring distribution.

Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes

The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This studys objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model.

Gaussian Hypergeometric Probability Distributions for Fitting Discrete Data

The distributions generated by the Gaussian hypergeometric function compose a tetraparametric family that includes many of the most common discrete distributions in the literature. In this article, probability aspects related to the whole family are reviewed and methods of estimation for fitting them to real data are developed. Several applied examples are also provided to illustrate the procedures and compare the methods of estimation.

Estimation and Inference in Complex Triparametric Pearson Distributions

Abstract The complex triparametric Pearson distribution is an extension of the Gaussian hypergeometric probability distribution with complex parameters that provides adequate random models for data originating from different fields. In the present article, relations between moments and probabilities are employed to obtain minimum χ2 estimators of the parameters. We compare the asymptotic relative efficiency of these estimators with those obtained by several methods. We also develop a test of hypotheses in selecting a two-parameter family from a three-parameter family of distributions. Finally, some examples are provided to illustrate these methods.

Modelling using an extended Yule distribution

A biparametric discrete distribution that extends the Yule distribution is presented. It belongs to the family of distributions generated by the Gaussian hypergeometric function and it can be expressed as a generalized beta mixture of a geometric distribution. The introduction of a new parameter makes the model very suitable to fit the empiric distribution tails and the effect of infinite variance is not possible. Several examples show more accurate fits when the extended distribution is used and the results are compared with other biparametric extensions of the Yule distribution.