Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

Framework for Skew-Probit Links in Binary Regression

We review several asymmetrical links for binary regression models and present a unified approach for two skew-probit links proposed in the literature. Moreover, under skew-probit link, conditions for the existence of the ML estimators and the posterior distribution under improper priors are established. The framework proposed here considers two sets of latent variables which are helpful to implement the Bayesian MCMC approach. A simulation study to criteria for models comparison is conducted and two applications are made. Using different Bayesian criteria we show that, for these data sets, the skew-probit links are better than alternative links proposed in the literature.

Regression analysis of mean quality-adjusted survival time based on pseudo-observations

Regression models for the mean quality-adjusted survival time are specified from hazard functions of transitions between two states and the mean quality-adjusted survival time may be a complex function of covariates. We discuss a regression model for the mean quality-adjusted survival (QAS) time based on pseudo-observations, which has the advantage of directly modeling the effect of covariates in the QAS time. Both Monte Carlo Simulations and a real data set are studied. Copyright (C) 2009 John Wiley & Sons, Ltd.

A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

Some restriction tests in a new class of regression models for proportions

The main purpose of this work is to study the behaviour of Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian journal of Probability and Statistics 19,13-31]. We show that, for our model, Skovgaard`s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed. (C) 2009 Elsevier B.V. All rights reserved.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

O risco espacial e fatores associados ao edentulismo em idosos em município do Sudeste do Brasil

Objetivou-se identificar fatores associados ao edentulismo e o seu risco espacial em idosos. Foi realizado um estudo transversal em uma amostra de 372 indivíduos de 60 anos e mais, no Município de Botucatu, São Paulo, Brasil, em 2005. Razões de prevalência brutas e ajustadas foram estimadas por meio de regressão de Poisson, com estimativa robusta da variância e procedimentos de modelagem hierárquica. A análise espacial foi realizada por estimativas de densidade de Kernel. A prevalência de edentulismo foi de 63,17%. Os fatores sociodemográficos associados ao edentulismo foram a baixa escolaridade, o aumento do número de pessoas por cômodo, não possuir automóvel e idade mais avançada, presença de comorbidades, ausência de um cirurgião-dentista regular e ter realizado a última consulta há três anos ou mais. A análise espacial mostrou maior risco nas áreas periféricas. Obteve-se uma melhor compreensão da perda dentária entre os idosos, subsidiando o planejamento de ações em saúde coletiva.

Survival and quality of life of patients with oral and oropharyngeal cancer at 1-year follow-up of tumor resection

OBJECTIVE: This study aimed to assess the survival and life quality evolution of patients subjected to surgical excision of oral and oropharyngeal squamous cell carcinoma. MATERIAL AND METHODS: Forty-seven patients treated at a Brazilian healthcare unit specialized in head and neck surgery between 2006 and 2007 were enrolled in the study. The gathering of data comprised reviewing hospital files and applying the University of Washington Quality of Life (UW-QOL) questionnaire previously and 1 year after the surgery. Comparative analysis used Poisson regression to assess factors associated with survival and a paired t-test to compare preoperative and 1-year postoperative QOL ratings. RESULTS: 1 year after surgery, 7 patients were not found (dropout of the cohort); 15 had died and 25 fulfilled the UW-QOL again. The risk of death was associated with having regional metastasis previously to surgery (relative risk=2.18; 95% confidence interval=1.09-5.17) and tumor size T3 or T4 (RR=2.30; 95%CI=1.05-5.04). Survivors presented significantly (p<0.05) poorer overall and domain-specific ratings of quality of life. Chewing presented the largest reduction: from 74.0 before surgery to 34.0 one year later. Anxiety was the only domain whose average rating increased (from 36.0 to 70.7). CONCLUSIONS: The prospective assessment of survival and quality of life may contribute to anticipate interventions aimed at reducing the incidence of functional limitations in patients with oral and oropharyngeal cancer.

Inequalities in the distribution of dental caries among 12-year-old Brazilian schoolchildren

We assessed the inequality in the distribution of dental caries and the association between indicators of socioeconomic status and caries experience in a representative sample of schoolchildren. This study followed a cross-sectional design, with a sample of 792 schoolchildren aged 12 years, representative of this age group in Santa Maria, RS, Brazil. Guardians answered questions on socioeconomic status and a dental examination provided information on the dental caries experience (DMF-T). Inequality in dental caries distribution was measured by the Gini coefficient and the Significant Caries Index (SiC). The assessment of association used Poisson regression models. Socioeconomic factors were associated with prevalence of dental caries for the whole sample and also for individuals with a high-caries level. Children from low-income households had the highest prevalence of dental caries. The Gini coefficient was 0.7 and the SiC Index 2.5. The percentage of caries prevalence was 39.3% (95% CI: 35.8%-42.8%) and the mean for DMF-T was 0.9 (± SD 1.5). Inequalities in the distribution of dental caries were observed and socioeconomic factors were found to be strong predictors of the prevalence of oral disease in children of this age group.

Dor nos dentes e gengivas e fatores associados em adolescentes brasileiros: análise do inquérito nacional de saúde bucal SB-Brasil 2002-2003

Estimou-se a prevalência de dor nos dentes e gengivas e fatores associados em adolescentes brasileiros de 15 a 19 anos de idade. Foram utilizadas informações de 16.126 adolescentes participantes do levantamento epidemiológico nacional de saúde bucal - SB Brasil 2002-2003. O desfecho foi o relato de dor nos dentes e gengivas nos últimos seis meses. As variáveis exploratórias foram: renda per capita, escolaridade, condição de estudo, sexo, cor da pele, idade, localização geográfica da residência, tipo de serviço odontológico utilizado pela última vez, tempo decorrido da última consulta odontológica, índice CPO-D e seus componentes, cálculo dentário e o índice de estética dental. Foram realizadas análises brutas e múltiplas utilizando a regressão de Poisson. A prevalência da dor de dentes e gengivas foi de 35,6% (IC95%: 34,8-36,4). A prevalência de dor foi maior nas meninas, naqueles pertencentes a famílias com baixa renda per capita, nos não estudantes e estudantes de escola pública e naqueles com baixa escolaridade para a idade. Indivíduos que apresentaram altos níveis de cárie e cálculo dentário também apresentaram maiores prevalências do desfecho. A dor nos dentes e gengivas em adolescentes pode ser considerada um problema relevante em saúde pública sugerindo a necessidade de ações preventivas e de promoção da saúde.

Wives of pathological gamblers: personality traits, depressive symptoms and social adjustment

Objective: Wives of pathological gamblers tend to endure long marriages despite financial and emotional burden. Difficulties in social adjustment, personality psychopathology, and comorbidity with psychiatric disorders are pointed as reasons for remaining on such overwhelming relationships. The goal was to examine the social adjustment, personality and negative emotionality of wives of pathological gamblers. Method: The sample consisted of 25 wives of pathological gamblers, mean age 40.6, SD = 9.1 from a Gambling Outpatient Unit and at GAM-ANON, and 25 wives of non-gamblers, mean age 40.8, SD = 9.1, who answered advertisements placed at the Universidade de São Paulo hospital and medical school complex. They were selected in order to approximately match demographic characteristics of the wives of pathological gamblers. Subjects were assessed by the Social Adjustment Scale, Temperament and Character Inventory, Beck Depression Inventory and State-Trait Anxiety Inventory. Results: Three variables remained in the final Multiple Logistic Regression model, wives of pathological gamblers presented greater dissatisfaction with their marital bond, and higher scores on Reward Dependence and Persistence temperament factors. Both, Wives of pathological gamblers and wives of non-gamblers presented well-structured character factors excluding personality disorders. Conclusion: This personality profile may explain wives of pathological gamblers emotional resilience and their marriage longevity. Co-dependence and other labels previously used to describe them may work as a double edged sword, legitimating wives of pathological gamblers problems, while stigmatizing them as inapt and needy.