Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.

A nonlinear regression model with skew-normal errors

In this paper we have discussed inference aspects of the skew-normal nonlinear regression models following both, a classical and Bayesian approach, extending the usual normal nonlinear regression models. The univariate skew-normal distribution that will be used in this work was introduced by Sahu et al. (Can J Stat 29:129-150, 2003), which is attractive because estimation of the skewness parameter does not present the same degree of difficulty as in the case with Azzalini (Scand J Stat 12:171-178, 1985) one and, moreover, it allows easy implementation of the EM-algorithm. As illustration of the proposed methodology, we consider a data set previously analyzed in the literature under normality.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

Bias-corrected Pearson estimating functions for Taylor`s power law applied to benthic macrofauna data

Estimation of Taylor`s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.

A Model for comparing reduced impact logging with conventional logging for an Eastern Amazonian Forest

Using data from a logging experiment in the eastern Brazilian Amazon region, we develop a matrix growth and yield model that captures the dynamic effects of harvest system choice on forest structure and composition. Multinomial logistic regression is used to estimate the growth transition parameters for a 10-year time step, while a Poisson regression model is used to estimate recruitment parameters. The model is designed to be easily integrated with an economic model of decisionmaking to perform tropical forest policy analysis. The model is used to compare the long-run structure and composition of a stand arising from the choice of implementing either conventional logging techniques or more carefully planned and executed reduced-impact logging (RIL) techniques, contrasted against a baseline projection of an unlogged forest. Results from log and leave scenarios show that a stand logged according to Brazilian management requirements will require well over 120 years to recover its initial commercial volume, regardless of logging technique employed. Implementing RIL, however, accelerates this recovery. Scenarios imposing a 40-year cutting cycle raise the possibility of sustainable harvest volumes, although at significantly lower levels than is implied by current regulations. Meeting current Brazilian forest policy goals may require an increase in the planned total area of permanent production forest or the widespread adoption of silvicultural practices that increase stand recovery and volume accumulation rates after RIL harvests. Published by Elsevier B.V.

E-Learning Used in a Training Course on Atraumatic Restorative Treatment (ART) for Brazilian Dentists

The purpose of this study was to assess the benefits of using e-learning resources in a dental training course on Atraumatic Restorative Treatment (ART). This e-course was given in a DVD format, which presented the ART technique and philosophy. The participants were twenty-four dentists from the Brazilian public health system. Prior to receiving the DVD, the dentists answered a questionnaire regarding their personal data, previous knowledge about ART, and general interest in training courses. The dentists also participated in an assessment process consisting of a test applied before and after the course. A single researcher corrected the tests, and intraexaminer reproducibility was calculated (kappa=0.89). Paired t-tests were carried out to compare the means between the assessments, showing a significant improvement in the performance of the subjects on the test taken after the course (p<0.05). A linear regression model was used with the difference between the means as the outcome. A greater improvement on the test results was observed among female dentists (p=0.034), dentists working for a shorter period of time in the public health system (p=0.042), and dentists who used the ART technique only for urgent and/or temporary treatment (p=0.010). In conclusion, e-learning has the potential of improving the knowledge that dentists working in the public health system have about ART, especially those with less clinical experience and less knowledge about the subject.

Association Between Urinary Incontinence in Elderly Patients and Caregiver Burden in the City of Sao Paulo/Brazil: Health, Wellbeing, and Ageing Study

Aim: Some elderly patients with incontinence require the care of third parties, known as caregivers. Such care can occur on a daily basis leaving little opportunity for the caregiver to take care of himself/herself. The aims are to assess the association between urinary incontinence in elderly patients and caregiver burden and identify independent factors for caregiver`s burden in the city of Sao Paulo, Brazil. Methods: The Pan-American Health Organization and World Health Organization coordinated a multicenter study named Health, Wellbeing and Aging (SABE Study) in elderly people living in seven countries of Latin America and the Caribbean. In Brazil, the study population carried out in Sao Paulo in the year 2000 and reassessed in 2006 (COHORT A). Urinary incontinence was assessed by ICIQ-SF and caregiver burden by means of Zarit Burden Scale. Results: A total of 327 patients with caregivers were included in the study. The general prevalence of urinary incontinence was 25.8%, higher among the women. There was a significant positive association between caregiver burden and incontinent patients, demonstrating that urinary incontinence in elderly patients produced greater caregiver burden. In the present study, the variables with significant correlations were assessed using the multivariate logistic regression model. Category 2 of the ICIQ-SF (incontinent patients) increased the chances of caregiver burden 1.96-fold in comparison to Category 1 (continent patients). Likewise, the category of impaired cognition increased the chances of caregiver burden 2.34-fold. Conclusions: Urinary incontinence and cognitive impairment in elderly patients were associated to an increase in caregiver burden. Neurourol. Urodynam. 30:1281-1285, 2011. (C) 2011 Wiley-Liss, Inc.