Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

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.

Quantification of chlorpheniramine maleate enantiomers by ultraviolet spectroscopy and chemometric methods

Chlorpheniramine maleate (CLOR) enantiomers were quantified by ultraviolet spectroscopy and partial least squares regression. The CLOR enantiomers were prepared as inclusion complexes with beta-cyclodextrin and 1-butanol with mole fractions in the range from 50 to 100%. For the multivariate calibration the outliers were detected and excluded and variable selection was performed by interval partial least squares and a genetic algorithm. Figures of merit showed results for accuracy of 3.63 and 2.83% (S)-CLOR for root mean square errors of calibration and prediction, respectively. The ellipse confidence region included the point for the intercept and the slope of 1 and 0, respectively. Precision and analytical sensitivity were 0.57 and 0.50% (S)-CLOR, respectively. The sensitivity, selectivity, adjustment, and signal-to-noise ratio were also determined. The model was validated by a paired t test with the results obtained by high-performance liquid chromatography proposed by the European pharmacopoeia and circular dichroism spectroscopy. The results showed there was no significant difference between the methods at the 95% confidence level, indicating that the proposed method can be used as an alternative to standard procedures for chiral analysis.

Exploratory Approach to the use of Techniques of Regression Analysis and Pooled Analysis in Studies of Consumer Behavior

This paper is part of a large study to assess the adequacy of the use of multivariate statistical techniques in theses and dissertations of some higher education institutions in the area of marketing with theme of consumer behavior from 1997 to 2006. The regression and conjoint analysis are focused on in this paper, two techniques with great potential of use in marketing studies. The objective of this study was to analyze whether the employement of these techniques suits the needs of the research problem presented in as well as to evaluate the level of success in meeting their premisses. Overall, the results suggest the need for more involvement of researchers in the verification of all the theoretical precepts of application of the techniques classified in the category of investigation of dependence among variables.

Validated spectrophotometric and spectrofluorimetric methods for determination of chloroaluminum phthalocyanine in nanocarriers

UV-VIS-Spectrophotometric and spectrofluorimetric methods have been developed and validated allowing the quantification of chloroaluminum phthalocyanine (CIAIPc) in nanocarriers. In order to validate the methods, the linearity, limit of detection (LOD), limit of quantification (LOQ), precision, accuracy, and selectivity were examined according to USP 30 and ICH guidelines. Linearities range were found between 0.50-3.00 mu g.mL(-1) (Y=0.3829 X [CIAIPc, mu g.mL(-1)] + 0.0126; r=0.9992) for spectrophotometry, and 0.05-1.00 mu g.mL(-1) (Y=2.24 x 10(6) X [CIAIPc, mu g.L(-1)] + 9.74 x 10(4); r=0.9978) for spectrofluorimetry. In addition, ANOVA and Lack-of-fit tests demonstrated that the regression equations were statistically significant (p<0.05), and the resulting linear model is fully adequate for both analytical methods. The LOD values were 0.09 and 0.01 mu g.mL(-1), while the LOCI were 0.27 and 0.04 mu g.mL(-1) for spectrophotometric and spectrofluorimetric methods, respectively. Repeatability and intermediate precision for proposed methods showed relative standard deviation (RSD) between 0.58% to 4.80%. The percent recovery ranged from 98.9% to 102.7% for spectrophotometric analyses and from 94.2% to 101.2% for spectrofluorimetry. No interferences from common excipients were detected and both methods were considered specific. Therefore, the methods are accurate, precise, specific, and reproducible and hence can be applied for quantification of CIAIPc in nanoemulsions (NE) and nanocapsules (NC).

Methods for exploring the morpho-functional relations of the aortic depressor nerve in experimental diabetes

The present study investigated morpho-functional relations of the aortic depressor nerve (ADN) 5, 15 and 120 days after the onset of streptozotocin-induced diabetes in rats. Time control animals received vehicle. Under pentobarbital anesthesia, ADN activity was recorded simultaneously with arterial pressure. After the recordings, nerves were prepared for light microscopy study and morphometry. ADN function was accessed by means of pressure-nerve activity curve (fitted by sigmoidal regression) and cross-spectral analysis between mean arterial pressure (MAP) and ADN activity. The relation between morphological (myelinated fibers number and density, total myelin area, total fiber area and percentage of occupancy) and functional (gain, signal/noise relation, frequency) parameters were accessed by linear regression analysis and correlation coefficient calculations. Functional parameters obtained by means of the sigmoidal regression curve as well as by cross-spectral analysis were similar in diabetic and control rats. Morphometric parameters of the ADN were similar between groups 5 days after the onset of diabetes. Average myelin area and myelinated fiber area were significantly smaller on diabetic rats 15 and 120 days after the onset of diabetes, being the myelinated fiber and respective axons area and diameter also smaller on 120 days group. Nevertheless, G ratio (ratio between axon and fiber diameter) was nearly 0.6 and not different between groups or experimental times. No significant relationship between morphological and functional parameters was detected in all experimental groups. The present study suggests that ADN diabetic neuropathy was time-dependent, with damage to myelinated fibers to be the primary event, not evidenced by physiological methods. (C) 2010 Elsevier B.V. All rights reserved.

Heteroscedastic Nonlinear Regression Models

In this article, we present a generalization of the Bayesian methodology introduced by Cepeda and Gamerman (2001) for modeling variance heterogeneity in normal regression models where we have orthogonality between mean and variance parameters to the general case considering both linear and highly nonlinear regression models. Under the Bayesian paradigm, we use MCMC methods to simulate samples for the joint posterior distribution. We illustrate this algorithm considering a simulated data set and also considering a real data set related to school attendance rate for children in Colombia. Finally, we present some extensions of the proposed MCMC algorithm.

Regression Models with Heteroscedasticity using Bayesian Approach

In this paper, we compare the performance of two statistical approaches for the analysis of data obtained from the social research area. In the first approach, we use normal models with joint regression modelling for the mean and for the variance heterogeneity. In the second approach, we use hierarchical models. In the first case, individual and social variables are included in the regression modelling for the mean and for the variance, as explanatory variables, while in the second case, the variance at level 1 of the hierarchical model depends on the individuals (age of the individuals), and in the level 2 of the hierarchical model, the variance is assumed to change according to socioeconomic stratum. Applying these methodologies, we analyze a Colombian tallness data set to find differences that can be explained by socioeconomic conditions. We also present some theoretical and empirical results concerning the two models. From this comparative study, we conclude that it is better to jointly modelling the mean and variance heterogeneity in all cases. We also observe that the convergence of the Gibbs sampling chain used in the Markov Chain Monte Carlo method for the jointly modeling the mean and variance heterogeneity is quickly achieved.

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.

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.

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.

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.

Prediction in Multilevel Logistic Regression

The purpose of this article is to present a new method to predict the response variable of an observation in a new cluster for a multilevel logistic regression. The central idea is based on the empirical best estimator for the random effect. Two estimation methods for multilevel model are compared: penalized quasi-likelihood and Gauss-Hermite quadrature. The performance measures for the prediction of the probability for a new cluster observation of the multilevel logistic model in comparison with the usual logistic model are examined through simulations and an application.

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.

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.