Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics

The purpose of this paper is to develop a Bayesian analysis for nonlinear regression models under scale mixtures of skew-normal distributions. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the error distributions cover both skewness and heavy-tailed distributions such as the skew-t, skew-slash and the skew-contaminated normal distributions. The main advantage of these class of distributions is that they have a nice hierarchical representation that allows the implementation of Markov chain Monte Carlo (MCMC) methods to simulate samples from the joint posterior distribution. In order to examine the robust aspects of this flexible class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. Further, some discussions on the model selection criteria are given. The newly developed procedures are illustrated considering two simulations study, and a real data previously analyzed under normal and skew-normal nonlinear regression models. (C) 2010 Elsevier B.V. All rights reserved.

Augmented Mixed Models For Clustered Proportion Data.

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, controlling for the clustering. Our approach is Bayesian and presents a computationally convenient framework amenable to available freeware. Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

On estimation and influence diagnostics for log-Birnbaum-Saunders Student-t regression models: Full Bayesian analysis

The purpose of this paper is to develop a Bayesian approach for log-Birnbaum-Saunders Student-t regression models under right-censored survival data. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the considered model. In order to attenuate the influence of the outlying observations on the parameter estimates, we present in this paper Birnbaum-Saunders models in which a Student-t distribution is assumed to explain the cumulative damage. Also, some discussions on the model selection to compare the fitted models are given and case deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback-Leibler divergence. The developed procedures are illustrated with a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Influence Diagnostics for a Skew Extension of the Grubbs Measurement Error Model

Influence diagnostics methods are extended in this article to the Grubbs model when the unknown quantity x (latent variable) follows a skew-normal distribution. Diagnostic measures are derived from the case-deletion approach and the local influence approach under several perturbation schemes. The observed information matrix to the postulated model and Delta matrices to the corresponding perturbed models are derived. Results obtained for one real data set are reported, illustrating the usefulness of the proposed methodology.

The zero-inflated Conway-Maxwell-Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The FGM bivariate lifetime copula model: a bayesian approach

In this paper, we propose a bivariate distribution for the bivariate survival times based on Farlie-Gumbel-Morgenstern copula to model the dependence on a bivariate survival data. The proposed model allows for the presence of censored data and covariates. For inferential purpose a Bayesian approach via Markov Chain Monte Carlo (MCMC) is considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated via a simulation study and a real dataset.

Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

Influence Assessment in an Heteroscedastic Errors-in-Variables Model

The main goal of this article is to consider influence assessment in models with error-prone observations and variances of the measurement errors changing across observations. The techniques enable to identify potential influential elements and also to quantify the effects of perturbations in these elements on some results of interest. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.

Distal 22q11.2 Microduplication Combined With Typical 22q11.2 Proximal Deletion: A Case Report.

The 22q11 chromosomal region contains low copy repeats (LCRs) sequences that mediate non-allelic homologous recombination, which predisposes to copy number variations (CNVs) at this locus. Hemizygous deletions of the proximal 22q11.2 region result in the 22q11.2 deletion syndrome (22q11.2 DS). In addition, 22q11.2 duplications involving the distal LCR22s have been reported. This article describes a patient presenting a 2.5-Mb de novo deletion at proximal 22q11.21 region (between LCRs A-D), combined with a 1.3-Mb maternally inherited duplication at distal 22q11.23 region (between LCRs F-H). The presence of concomitant chromosomal imbalances found in this patient has not been reported previously. Clinical and molecular data were compared with literature, in order to contribute to genotype-phenotype correlation. These findings exemplify the complexity and genetic heterogeneity observed in 22q11.2 deletion syndrome and highlights the difficulty to make genetic counseling and predict phenotypic consequences in these situations.

Familial deletion 18p syndrome: case report

Affiliation: CHU Ste-Justine, Université de Montréal

A case of terminal long arm deletion of chromosome 6

A four-year-old girl with deletion of chromosomal band 6q24 → qter is described. Clinical features include growth and psychomotor retardation, microcephaly, convergent strabismus, bulbous nose, long philtrum, short neck and cardiopathy.

A familial case with interstitial 2q36 deletion: Variable phenotypic expression in full and mosaic state

Submicroscopic chromosomal anomalies play an important role in the etiology of craniofacial malformations, including midline facial defects with hypertelorism (MFDH). MFDH is a common feature combination in several conditions, of which Frontonasal Dysplasia is the most frequently encountered manifestation; in most cases the etiology remains unknown. We identified a parent to child transmission of a 6.2 Mb interstitial deletion of chromosome region 2q36.1q36.3 by array-CGH and confirmed by FISH and microsatellite analysis. The patient and her mother both presented an MFDH phenotype although the phenotype in the mother was much milder than her daughter. Inspection of haplotype segregation within the family of 2q36.1 region suggests that the deletion arose on a chromosome derived from the maternal grandfather. Evidences based on FISH, microsatellite and array-CGH analysis point to a high frequency mosaicism for presence of a deleted region 2q36 occurring in blood of the mother. The frequency of mosaicism in other tissues could not be determined. We here suggest that the milder phenotype observed in the proband's mother can be explained by the mosaic state of the deletion. This most likely arose by an early embryonic deletion in the maternal embryo resulting in both gonadal and somatic mosaicism of two cell lines, with and without the deleted chromosome. The occurrence of gonadal mosaicism increases the recurrence risk significantly and is often either underestimated or not even taken into account in genetic counseling where new mutation is suspected. (C) 2012 Elsevier Masson SAS. All rights reserved.