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.

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.

Measuring time series predictability using support vector regression

Most studies involving statistical time series analysis rely on assumptions of linearity, which by its simplicity facilitates parameter interpretation and estimation. However, the linearity assumption may be too restrictive for many practical applications. The implementation of nonlinear models in time series analysis involves the estimation of a large set of parameters, frequently leading to overfitting problems. In this article, a predictability coefficient is estimated using a combination of nonlinear autoregressive models and the use of support vector regression in this model is explored. We illustrate the usefulness and interpretability of results by using electroencephalographic records of an epileptic patient.

Nutritional intervention programme among a Japanese-Brazilian community: procedures and results according to gender

Objective: To describe the results of a nutritional intervention programme among Japanese-Brazilians according to gender. Design: A non-controlled experimental study. Setting: The research included three points of clinical, nutritional and physical activity evaluation: at baseline (in 2005), after the first year and at the end of the second year (in 2007). The paired Student t test and multiple linear regression analysis were used to evaluate changes in the subjects` profile (clinical, nutritional and physical activity variables). Subjects: Japanese-Brazilians (n 575) of both genders, aged over 30 years. Results: We verified statistically significant reductions in body weight (0.9 kg), waist circumference (2.9 cm), blood pressure, fasting blood glucose (>3 mg/dl) and total cholesterol (>20 mg/dl) and its fractions, in both genders. We also found reductions in intake of energy (among men), protein (among women) and fat (both genders) and increases in intake of total fibre (among women) and carbohydrate (among men). Conclusions: The intervention programme indicated meaningful benefits for the intervention subjects, with changes in their habits that led to a `healthier` lifestyle positively impacting their nutritional and metabolic profile.

Explaining sleep duration in adolescents: The impact of socio-demographic and lifestyle factors and working status

Previous studies found students who both work and attend school undergo a partial sleep deprivation that accumulates across the week. The aim of the present study was to obtain information using a questionnaire on a number of variables (e.g., socio-demographics, lifestyle, work timing, and sleep-wake habits) considered to impact on sleep duration of working (n = 51) and non-working (n = 41) high-school students aged 14-21 yrs old attending evening classes (19:00-22:30h) at a public school in the city of Sao Paulo, Brazil. Data were collected for working days and days off. Multiple linear regression analyses were performed to assess the factors associated with sleep duration on weekdays and weekends. Work, sex, age, smoking, consumption of alcohol and caffeine, and physical activity were considered control variables. Significant predictors of sleep duration were: work (p < 0.01), daily work duration (8-10h/day; p < 0.01), sex (p = 0.04), age 18-21 yrs (0.01), smoking (p = 0.02) and drinking habits (p = 0.03), irregular physical exercise (p < 0.01), ease of falling asleep (p = 0.04), and the sleep-wake cycle variables of napping (p < 0.01), nocturnal awakenings (p < 0.01), and mid-sleep regularity (p < 0.01). The results confirm the hypotheses that young students who work and attend school showed a reduction in night-time sleep duration. Sleep deprivation across the week, particularly in students working 8-10h/day, is manifested through a sleep rebound (i.e., extended sleep duration) on Saturdays. However, the different roles played by socio-demographic and lifestyle variables have proven to be factors that intervene with nocturnal sleep duration. The variables related to the sleep-wake cyclenaps and night awakeningsproved to be associated with a slight reduction in night-time sleep, while regularity in sleep and wake-up schedules was shown to be associated with more extended sleep duration, with a distinct expression along the week and the weekend. Having to attend school and work, coupled with other socio-demographic and lifestyle factors, creates an unfavorable scenario for satisfactory sleep duration.

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions. (C) 2011 Elsevier Inc. All rights reserved.

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.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Influence diagnostics in Birnbaum-Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.

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 reduction of CETP activity, not an increase, is associated with modestly impaired postprandial lipemia and increased HDL-Cholesterol in adult asymptomatic women

Background: The relationship between CETP and postprandial hyperlipemia is still unclear. We verified the effects of varying activities of plasma CETP on postprandial lipemia and precocious atherosclerosis in asymptomatic adult women. Methods: Twenty-eight women, selected from a healthy population sample (n = 148) were classified according to three CETP levels, all statistically different: CETP deficiency (CETPd <= 4.5%, n = 8), high activity (CETPi >= 23.8, n = 6) and controls (CTL, CETP >= 4.6% and <= 23.7%, n = 14). After a 12 h fast they underwent an oral fat tolerance test (40 g of fat/m(2) of body surface area) for 8 hours. TG, TG-rich-lipoproteins (TRL), cholesterol and TRL-TG measurements (AUC, AUIC, AR, RR and late peaks) and comparisons were performed on all time points. Lipases and phospholipids transfer protein (PLTP) were determined. Correlation between carotid atherosclerosis (c-IMT) and postprandial parameters was determined. CETP TaqIB and I405V and ApoE-epsilon 3/epsilon 2/epsilon 4 polymorphisms were examined. To elucidate the regulation of increased lipemia in CETPd a multiple linear regression analysis was performed. Results: In the CETPi and CTL groups, CETP activity was respectively 9 and 5.3 higher compared to the CETPd group. Concentrations of all HDL fractions and ApoA-I were higher in the CETPd group and clearance was delayed, as demonstrated by modified lipemia parameters (AUC, AUIC, RR, AR and late peaks and meal response patterns). LPL or HL deficiencies were not observed. No genetic determinants of CETP deficiency or of postprandial lipemia were found. Correlations with c-IMT in the CETPd group indicated postprandial pro-atherogenic associations. In CETPd the regression multivariate analysis (model A) showed that CETP was largely and negatively predicted by VLDL-C lipemia (R(2) = 92%) and much less by TG, LDL-C, ApoAI, phospholipids and non-HDL-C. CETP (model B) influenced mainly the increment in ApoB-100 containing lipoproteins (R(2) = 85% negatively) and phospholipids (R(2) = 13%), at the 6(th)h point. Conclusion: The moderate CETP deficiency phenotype included a paradoxically high HDL-C and its sub fractions (as earlier described), positive associations with c-IMT, a postprandial VLDL-C increment predicting negatively CETP activity and CETP activity regulating inversely the increment in ApoB100-containing lipoproteins. We hypothesize that the enrichment of TG content in triglyceride-rich ApoB-containing lipoproteins and in TG rich remnants increases lipoproteins` competition to active lipolysis sites, reducing their catabolism and resulting on postprandial lipemia with atherogenic consequences.