The Role of Classification Trees and Expert Knowledge in Building Bayesian Networks: A Case Study in Medicine

In clinical research an early and prompt detection of the risk class of a new patient may really play a crucial role in determining the effectiveness of the treatment and, consequently, achieving a satisfying prognosis of the patient's chances. There exists a number of popular rule-based algorithms for classification, whose performances are very attractive whenever data of large number of patients are available. However, when datasets only include data of a few hundred patients, the most common approaches give unstable results and developing effective decision-support systems become scientifically challenging. Since rules can be derived from different models as well as expert knowledge resources, each of them having its advantages and weaknesses, this article suggests a “hybrid” approach to address the classification problem when the number of patients is too small to effectively use a single technique only. The hybrid strategy was applied to a case study and its predictive performance was compared with performances of each single approach: due to the seriousness of a misclassification of high-risk patients, special attention was paid on the specificity. The results show that the hybrid strategy outperforms each single strategy involved.     

The Use of Working Variables in the Bayesian Modeling of Mean and Dispersion Parameters in Generalized Nonlinear Models with Random Effects

This article is aimed at reviewing a novel Bayesian approach to handle inference and estimation in the class of generalized nonlinear models. These models include some of the main techniques of statistical methodology, namely generalized linear models and parametric nonlinear regression. In addition, this proposal extends to methods for the systematic treatment of variation that is not explicitly predicted within the model, through the inclusion of random effects, and takes into account the modeling of dispersion parameters in the class of two-parameter exponential family. The methodology is based on the implementation of a two-stage algorithm that induces a hybrid approach based on numerical methods for approximating the likelihood to a normal density using a Taylor linearization around the values of current parameters in an MCMC routine.     

The posterior distribution of the fixed and random effects in a mixed-effects linear model

The subject of this paper is Bayesian inference about the fixed and random effects of a mixed-effects linear statistical model with two variance components. It is assumed that a priori the fixed effects have a noninformative distribution and that the reciprocals of the variance components are distributed independently (of each other and of the fixed effects) as gamma random variables. It is shown that techniques similar to those employed in a ridge analysis of a response surface can be used to construct a one-dimensional curve that contains all of the stationary points of the posterior density of the random effects. The “ridge analysis” (of the posterior density) can be useful (from a computational standpoint) in finding the number and the locations of the stationary points and can be very informative about various features of the posterior density. Depending on what is revealed by the ridge analysis, a multivariate normal or multivariate-t distribution that is centered at a posterior mode may provide a satisfactory approximation to the posterior distribution of the random effects (which is of the poly-t form).