Jean-François Angers

The Use of the Bootstrap Statistical Method for the Pharmacoeconomic Cost Analysis of Skewed Data

SummaryIn pharmacoeconomics, the comparison of the costs of 2 different drugs used for the same treatment is of great interest. The problem is especially challenging when the drugs are likely to produce costly adverse effects in a small number of patients, which is often the case. The data are then skewed and traditional statistical methods to analyse the difference in the mean costs produced by 2 treatments may be inappropriate. The bootstrap method is presented as an alternative approach. A pharmacoeconomic cost-analysis example is presented and used throughout this article.

A Bayesian analysis of zero-inflated generalized Poisson model

In several real-life examples one encounters count data where the number of zeros is such that the usual Poisson distribution does not fit the data. Quite often the number of zeros is large, and hence the data is zero inflated. In this situation, a zero-inflated generalized Poisson model can be considered and a Bayesian analysis can be carried out. Some appropriate priors are discussed and the posteriors are obtained using Monte-Carlo integration with importance sampling. The predictive density of the future observation is also obtained. The techniques are illustrated using a real-life data set. Computations largely support the methodology.

A stochastic method for Bayesian estimation of hidden Markov random field models with application to a color model

We propose a new stochastic algorithm for computing useful Bayesian estimators of hidden Markov random field (HMRF) models that we call exploration/selection/estimation (ESE) procedure. The algorithm is based on an optimization algorithm of O. Francois, called the exploration/selection (E/S) algorithm. The novelty consists of using the a posteriori distribution of the HMRF, as exploration distribution in the E/S algorithm. The ESE procedure computes the estimation of the likelihood parameters and the optimal number of region classes, according to global constraints, as well as the segmentation of the image. In our formulation, the total number of region classes is fixed, but classes are allowed or disallowed dynamically. This framework replaces the mechanism of the split-and-merge of regions that can be used in the context of image segmentation. The procedure is applied to the estimation of a HMRF color model for images, whose likelihood is based on multivariate distributions, with each component following a Beta distribution. Meanwhile, a method for computing the maximum likelihood estimators of Beta distributions is presented. Experimental results performed on 100 natural images are reported. We also include a proof of convergence of the E/S algorithm in the case of nonsymmetric exploration graphs.

Fusion of Hidden Markov Random Field Models and Its Bayesian Estimation

In this paper, we present a Hidden Markov Random Field (HMRF) data-fusion model. The proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into Julesz ensembles. The corresponding Exploration/Selection/Estimation (ESE) procedure for the estimation of the parameters is presented. This method achieves the estimation of the parameters of the Gaussian kernels, the mixture proportions, the region labels, the number of regions, and the Markov hyper-parameter. Meanwhile, we present a new proof of the asymptotic convergence of the ESE procedure, based on original finite time bounds for the rate of convergence

Localization of Shapes Using Statistical Models and Stochastic Optimization

In this paper, we present a new model for deformations of shapes. A pseudolikelihood is based on the statistical distribution of the gradient vector field of the gray level. The prior distribution is based on the probabilistic principal component analysis (PPCA). We also propose a new model based on mixtures of PPCA that is useful in the case of greater variability in the shape. A criterion of global or local object specificity based on a preliminary color segmentation of the image is included into the model. The localization of a shape in an image is then viewed as minimizing the corresponding Gibbs field. We use the exploration/selection (E/S) stochastic algorithm in order to find the optimal deformation. This yields a new unsupervised statistical method for localization of shapes. In order to estimate the statistical parameters for the gradient vector field of the gray level, we use an iterative conditional estimation (ICE) procedure. The color segmentation of the image can be computed with an exploration/selection/estimation (ESE) procedure.

Multivariate Bayesian function estimation

Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries on the multivariate nonparametric regression function. The Bayesian approach then allows one to incorporate hierarchical Bayesian methods directly into the spectral structure, thus providing a symmetry-adaptive multivariate Bayesian function estimator. One can also diffuse away some prior information in which the limiting case is a smoothing spline on the manifold. This, together with the result that the smoothing spline solution obtains the minimax rate of convergence in the multivariate nonparametric regression problem, provides good frequentist properties for the Bayes estimators. An application to astronomy is included.

A Bayesian adaptive design in clinical trials for continuous responses

Adaptive design is a popular concept in several clinical trials, especially in phase III trials. The idea is to allocate treatments to the entering patients according to the state of art of the present data, i.e., to allocate a larger number of patients to the better treatment. The present paper provides a Bayesian formulation of an adaptive allocation design for clinical trials that considers all the continuous responses along with the associated covariates for future allocation. Some Bayesian inferences followed by the allocation are discussed along with a Bayesian prediction for future allocation. The convergence of the allocation probabilities is also discussed along with some related logistics of the design.

Air pollution effects on clinic visits in small areas of Taiwan revisited

We revisit the complete daily clinic visit records and environmental monitoring data at 50 townships and city districts of Taiwan, considered by Angers et al. (Commun Stat Simul Comput 38:1535–1550, 2009). Extending the earlier analysis, we consider a Bayesian analysis using regression spline model where instead of principal components we consider all the seven covariates for all 50 monitoring stations. We find that NO

Bivariate versus univariate ordinal categorical data with reference to an ophthalmologic study

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