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.

Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. 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. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is 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 for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 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.

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.

Aquisição de açúcar e perfil de macronutrientes na cesta de alimentos adquirida pelas famílias brasileiras (2002-2003)

Avaliou-se a influência exercida pela aquisição de calorias de açúcar sobre a participação calórica dos demais macronutrientes da dieta. As estimativas deste estudo são baseadas em dados da Pesquisa de Orçamentos Familiares realizada no Brasil pelo Instituto Brasileiro de Geografia e Estatística entre julho de 2002 e junho de 2003. Modelos de regressão linear múltiplos foram utilizados para estudar a influência das calorias de açúcar sobre a participação calórica de cada um dos macronutrientes na aquisição domiciliar de alimentos com o controle do valor calórico total da aquisição de alimentos e variáveis sócio-demográficas. Cada caloria adquirida de açúcar eleva em 0,3 caloria a participação de gorduras na aquisição domiciliar de alimentos e diminui em 0,07 a participação de proteínas. Cada caloria de açúcar procedente de alimentos processados aumenta em 1,6 caloria a participação de gorduras e em 0,4 caloria de ácidos graxos saturados e diminui em 0,8 caloria a participação de outros carboidratos que não o açúcar. Os resultados encontrados trazem novas evidências sobre o papel prejudicial do açúcar à saúde humana.

Preditores sócio-demográficos, de estilo de vida e gineco-obstétricos das concentrações séricas ou plasmáticas de homocisteína, ácido fólico e vitaminas B12 e B6 em mulheres de baixa renda de São Paulo, Brasil

O presente estudo investigou fatores sócio-demográficos, de estilo de vida e gineco-obstétricos associados às concentrações séricas ou plasmáticas de homocisteína, ácido fólico, vitaminas B12 e B6 em mulheres de baixa renda de São Paulo, Brasil. Concentrações séricas de ácido fólico e vitamina B12 foram analisadas por fluoroimunoensaio; concentrações plasmáticas de homocisteína e vitamina B6, por cromatografia líquida de alta performance em fase reversa. Variáveis independentes foram inicialmente selecionadas segundo pressupostos teóricos, correlação de Pearson ou teste Kruskal-Wallis (p < 0,20). Concentrações alteradas segundo pontos de corte para homocisteína, ácido fólico, vitaminas B12 e B6 foram observadas em 20%, 6%, 11% e 67% das participantes, respectivamente. Idade foi positivamente correlacionada à vitamina B6 e homocisteína plasmáticas (p < 0,001). Índice de massa corporal foi positivamente correlacionado à vitamina B6 plasmática (p < 0,001). Modelos de regressão linear múltiplos explicaram 10,2%, 5,8%, 14,4% e 9,4% das concentrações de ácido fólico, vitamina B12, vitamina B6 e homocisteína, respectivamente. No presente estudo, variáveis sócio-demográficas, de estilo de vida e gineco-obstétricas apresentaram contribuição importante na variação das concentrações dos indicadores bioquímicos avaliados.

Sugar and total energy content of household food purchases in Brazil

Objective To study the role of energy derived from sugar (both table sugar and sugar added to processed foods) in the total energy content of food purchases in Brazil.Design Food purchase data were collected during a national household budget survey carried out between June 2002 and July 2003 on a probabilistic sample representative of all households in the country. The amount of food purchased in this 12-month period was transformed into energy and energy from sugar using food composition tables. Multiple linear regression models were used to study the association between amount of energy from sugar and total energy content of food purchases, controlling for sociodemographic variables and potential interactions between these variables and sugar purchases.Results There was a positive and significant association between energy from sugar and total household energy purchases. A 1 kJ increase in sugar purchase corresponded to a 3·637 kJ increase in total energy. In the absence of expenditure on meals outside the home, i.e. when household food purchases tend to approximate actual food consumption by household members, sugar purchase of 1926·35 kJ/d (the 90th percentile of the distribution of sugar purchases in Brazil) was associated, depending on income strata, with total energy purchase over 40\201360 per cent of the recommended daily value for energy intake in Brazil.Conclusions The present results corroborate the recommendations of the WHO and the Brazilian Ministry of Health regarding limiting the consumption of sugar

Relationships of blood lead to calcium, iron, and vitamin C intakes in Brazilian pregnant women

Background & aims. This study aimed to determine the relationship between blood lead concentrations and calcium, iron and vitamin C dietary intakes of pregnant women. Methods. Included in the study were 55 women admitted to a hospital, for delivery, from June to August 2002. A food frequency questionnaire was applied to determine calcium, iron and vitamin C intakes, and a general questionnaire to obtain data on demographic-socioeconomic condition, obstetric history, smoking habit, and alcohol intake. Blood lead and haemoglobin were determined, respectively, by atomic absorption spectrometry and by the haemoglobinometer HemoCue®. Multiple linear regression models were used to determine the relationship between blood lead and calcium, iron and vitamin C intakes, and haemoglobin levels, controlling for confounders. Results. The final model of the regression analysis detected an inverse relationship between blood lead and age of the women (p=0.011), haemoglobin (p=0.001), vitamin C (p=0.012), and calcium intake (p<0.001) (R2=0.952). One hundred percent, 98.2% and 43.6% of the women were below the adequate intake (AI) for calcium, and below the recommended dietary allowances (RDA) for iron, and vitamin C, respectively. Conclusion. Despite the small sample size, the results of this study suggest that maternal age, haemoglobin, vitamin C intake, and calcium intake may interfere with blood concentrations of lead

Espacialização da temperatura do ar anual no estado de Alagoas com diferentes modelos digitais de elevação e resoluções espaciais

The aim of this study was to establish a digital elevation model and its horizontal resolution to interpolate the annual air temperature for the Alagoas State by means of multiple linear regression models. A multiple linear regression model was adjusted to series (11 to 34 years) of annual air temperatures obtained from 28 weather stations in the states of Alagoas, Bahia, Pernambuco and Sergipe, in the Northeast of Brazil, in function of latitude, longitude and altitude. The elevation models SRTM and GTOPO30 were used in the analysis, with original resolutions of 90 and 900 m, respectively. The SRTM was resampled for horizontal resolutions of 125, 250, 500, 750 and 900 m. For spatializing the annual mean air temperature for the state of Alagoas, a multiple linear regression model was used for each elevation and spatial resolution on a grid of the latitude and longitude. In Alagoas, estimates based on SRTM data resulted in a standard error of estimate (0.57 degrees C) and dispersion (r(2) = 0.62) lower than those obtained from GTOPO30 (0.93 degrees C and 0.20). In terms of SRTM resolutions, no significant differences were observed between the standard error (0.55 degrees C; 750 m - 0.58 degrees C; 250m) and dispersion (0.60; 500 m - 0.65; 750 m) estimates. The spatialization of annual air temperature in Alagoas, via multiple regression models applied to SRTM data showed higher concordance than that obtained with the GTOPO30, independent of the spatial resolution.

Understanding Pain and Quality of Life for Patients With Chronic Venous Ulcers

Aim. To identify the impact of pain on quality of life (QOL) of patients with chronic venous ulcers. Methods. A cross-sectional study was performed on 40 outpatients with chronic venous ulcers who were recruited at one outpatient care center in Sao Paulo, Brazil. WHOQOL-Bref was used to assess QOL, the McGill Pain Questionnarie-Short Form (MPQ) to identify pain characteristics, and an 11-point numerical pain rating scale to measure pain intensity. Kruskall-Wallis or ANOVA test, with post-hoc correction (Tukey test) was applied to compare groups. Multiple linear regression models were used. Results. The mean age of the patients was 67 +/- 11 years (range, 39-95 years), and 26 (65%) were women. The prevalence of pain was 90%, with worst pain mean intensity of 6.2 +/- 3.5. Severe pain was the most prevalent (21 patients, 52.5%). Pain most frequently reported was sensory-discriminative and evaluate in quality. Pain was significantly and negatively correlated with physical (PY), environmental (EV), and overall QOL. Compared to a no-pain group, those with pain had lower overall QOL. On multiple analyses, pain remained as a predictor of overall QOL (beta = -0.73, P = 0.03) and was also predictive of social QOL, whereas pain did not have any impact on physical, emotional, or social relationships QOL (beta = -3.85, P = 0.00) when adjusted for age, number, duration and frequency of wounds, pain dimension (MPQ), partnership, and economic status. Conclusion. To improve QOL of out-patients with chronic venous ulcers, the qualities and the intensity of pain must be considered differently.

The association of prevalent medial meniscal pathology with cartilage loss in the medial tibiofemoral compartment over a 2-year period

Objective: To investigate the association of different types of magnetic resonance imaging (MRI)-detected medial meniscal pathology with subregional cartilage loss in the medial tibiofemoral compartment. Methods: A total of 152 women aged >= 40 years, with and without knee osteoarthritis (OA) were included in a longitudinal 24-month observational study. Spoiled gradient recalled acquisitions at steady state (SPGR) and T2-weighted fat-suppressed MRI sequences were acquired. Medial meniscal status of the anterior horn (AH), body, and posterior horn (PH) was graded at baseline: 0 (normal), 1 (intrasubstance meniscal signal changes), 2 (single tears), and 3 (complex tears/maceration). Cartilage segmentation was performed at baseline and 24-month follow-up in various tibiofemoral subregions using computation software. Multiple linear regression models were applied for the analysis with cartilage loss as the outcome. In a first model, the results were adjusted for age and body mass index (BMI). In a second model, the results were adjusted for age, BMI and medial meniscal extrusion. Results: After adjusting for age, BMI, and medial meniscal extrusion, cartilage loss in the total medial tibia (MT) (0.04 mm, P=0.04) and the external medial tibia (eMT) (0.068 mm, P=0.04) increased significantly for compartments with grade 3 lesions. Cartilage loss in the total central medial femoral condyle (cMF) (0.071 mm, P=0.03) also increased significantly for compartments with grade 2 lesions. Cartilage loss at the eMT was significantly related to tears of the PH (0.074 mm; P=0.03). Cartilage loss was not significantly increased for compartments with grade 1 lesions. Conclusion: The protective function of the meniscus appears to be preserved in the presence of intrasubstance meniscal signal changes. Prevalent single tears and meniscal maceration were found to be associated with increased cartilage loss in the same compartment, especially at the PH. (C) 2009 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

Birth weight and bone mass in young adults from Brazil

Background: Birth weight is positively associated with adult bone mass. However, it is not clear if its effect is already evident in early adulthood. Objective: To investigate the association between birth weight, adult body size, the interaction between them and bone mass in young adults. Methods: Bone densitometry by DXA was performed on 496 individuals (240 men) aged 23-24 years from the 1978/79 Ribeirao Preto (southern Brazil) birth cohort, who were born and still residing in the city in 2002. Birth weight and length as well as adult weight and height were directly measured and converted to z-scores. The influence of birth weight and length, and adult weight and height on bone area (BA), bone mineral content (BMC) and bone mineral density (BMD) at the lumbar spine, proximal femur and femoral neck were investigated through simple and multiple linear regression models. Adjustments were made for sex, skin color, gestational age, physical activity level, smoking status and dietary consumption of protein, calcium and alcohol. Interaction terms between birth weight and adult weight, and birth length and adult height were tested. Results: Men in the highest fertile of birth weight distribution had greater BA and BMC at all three bone sites when compared with their counterparts in the lowest tertiles (p<0.008). For BMD, this trend was observed only in the lumbar spine. Adult weight and height were positively associated with BA and BMC at all three bone sites (p<0.05). For BMD, these associations were seen for adult weight, but for adult height an association was observed only in the lumbar spine. Birth weight retained positive associations with proximal femur BA and BMC after adjustments for current weight and height. No interaction was observed between variables measuring prenatal growth and adult body size. Conclusion: Birth weight and postnatal growth are independent determinants of adult bone mass in a sample of Brazilian adults. This effect is already evident in early adulthood. (C) 2010 Elsevier Inc. All rights reserved.