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.

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.

Delineation of a recognisable phenotype of interstitial deletion 3 (q22.3q25.1) in a case with previously unreported truncus arteriosus

Interstitial deletions of chromosome 3q22.3e25.1 are very rare with only five previous reports of deletions in this region [1,2,4,7,9]. We describe a case of a female infant with a de novo deletion. Dysmorphic features and congenital heart disease led to a clinical genetics assessment on day 1 of life. Chromosomal analysis showed an interstitial deletion with a female karyotype 46,XX,del (3)(q23q25.1) dn. Subsequent array CGH demonstrated the breakpoints as 3q22.3q25.1. This is the first documented association with a truncus arteriosus. We identify an emerging clinical phenotype of microphthalmia, microcephaly, congenital heart disease, slow feeding, skeletal abnormalities, with an abnormal facies and developmental delay. Array CGH demonstrated that the FOXL2 gene responsible for BPES was not deleted in this patient. (C) 2010 Elsevier Masson SAS. All rights reserved.

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.

A 1.77 Mb deletion in 3p26.3 encompassing CNTN6 and CNTN4 genes: case report

Chromosome microarray analysis is a powerful diagnostic tool and is being used as a first-line approach to detect chromosome imbalances associated with intellectual disability, dysmorphic features and congenital abnormalities. This test enables the identification of new copy number variants (CNVs) and their association with new microdeletion/microduplication syndromes in patients previously without diagnosis. We report the case of a 7 year-old female with moderate intellectual disability, severe speech delay and auto and hetero aggressivity with a previous 45,XX,der(13;14)mat karyotype performed at a younger age. Affymetrix CytoScan 750K chromosome microarray analysis was performed detecting a 1.77 Mb deletion at 3p26.3, encompassing 2 OMIM genes, CNTN6 and CNTN4. These genes play an important role in the formation, maintenance, and plasticity of functional neuronal networks. Deletions or mutations in CNTN4 gene have been implicated in intellectual disability and learning disabilities. Disruptions or deletions in the CNTN6 gene have been associated with development delay and other neurodevelopmental disorders. The haploinsufficiency of these genes has been suggested to participate to the typical clinical features of 3p deletion syndrome. Nevertheless inheritance from a healthy parent has been reported, suggesting incomplete penetrance and variable phenotype for this CNV. We compare our patient with other similar reported cases, adding additional value to the phenotype-genotype correlation of deletions in this region.

Association between a 19 bp deletion polymorphism at the dopamine beta-hydroxylase (DBH) locus and migraine with aura

Migraine is a debilitating neurological disorder, affecting 12% of Caucasian populations. It is well known that migraine has a strong genetic component, although the type and number of genes involved is unclear. Our previous work has investigated dopamine related migraine candidate genes and has reported a significant allelic association with migraine of a microsatellite localised to the promoter region of the dopamine beta-hydroxylase (DBH) gene. The present study performed an association analysis in a larger population of case-controls (275 unrelated Caucasian migraineurs versus 275 controls) examining two different genetic DBH polymorphisms (a functional insertion/deletion promoter and a coding SNP A444G polymorphism). Although no significant association was found for the SNP polymorphism, the results showed a significant association between the insertion/deletion variant and disease (chi(2)=8.92, P=0.011), in particular in migraine with aura (chi(2)=11.53, P=0.003) compared to the control group. Furthermore, the analysis of this polymorphism stratified by gender, revealed that male individuals with the homozygote deletion genotype had three times the risk of developing migraine, compared to females. The DBH insertion/deletion polymorphism is in linkage disequilibrium with the previously reported migraine associated DBH microsatellite and this insertion/deletion polymorphism is functional, which may explain a potential role in susceptibility to migraine.