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.

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.

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.

Application of thermal sums concept to estimate the time to harvest new banana hybrids for export

Application of the thermal sum concept was developed to determine the optimal harvesting stage of new banana hybrids to be grown for export. It was tested on two triploid hybrid bananas, FlhorBan 916 (F916) and FlhorBan 918 (F918), created by CIRAD`s banana breeding programme, using two different approaches. The first approach was used with F916 and involved calculating the base temperature of bunches sampled at two sites at the ripening stage, and then determining the thermal sum at which the stage of maturity would be identical to that of the control Cavendish export banana. The second approach was used to assess the harvest stage of F918 and involved calculating the two thermal parameters directly, but using more plants and a longer period. Using the linear regression model, the estimated thermal parameters were a thermal sum of 680 degree-days (dd) at a base temperature of 17.0 degrees C for cv. F916, and 970 dd at 13.9 degrees C for cv. F918. This easy-to-use method provides quick and reliable calculations of the two thermal parameters required at a specific harvesting stage for a given banana variety in tropical climate conditions. Determining these two values is an essential step for gaining insight into the agronomic features of a new variety and its potential for export. (C) 2011 Elsevier B.V. All rights reserved.

The Drop Technique: a Method to Control the Amount of Fluoride Dentifrice Used by Young Children

Purpose: The purpose of this study was to evaluate the amount of dentifrice applied to the toothbrush by school children using a liquid dentifrice (drop technique), when compared to toothpaste. Materials and Methods: A total of 178 school children (4-8 years old) from two cities in Brazil (Bauru and Bariri) participated in the present two-part crossover study. Children from Bauru received training regarding tooth-brushing techniques and use of dentifrice before data collection. In each phase, the amount of toothpaste or liquid dentifrice applied by the children to the toothbrush was measured, using a portable analytical balance (+/- 0.01 g). Data were tested by analysis of covariance (Ancova) and linear regression (p < 0.05). Results: The mean (+/- standard deviation) amounts of toothpaste and liquid dentifrice applied to the toothbrushes for children from Bauru were 0.41 +/- 0.20 g and 0.15 +/- 0.06 g, respectively. For children from Bariri, the amounts applied were and 0.48 +/- 0.24 g and 0.14 +/- 0.05 g, respectively. The amount of toothpaste applied was significantly larger than the amount of liquid dentifrice for both cities. Children from Bariri applied a significantly larger amount of toothpaste, when compared to those from Bauru. However, for the liquid dentifrice, there was no statistically significant difference between the cities. A significant correlation between the amount of toothpaste applied and the age of the children was verified, but the same was not found for the liquid dentifrice. Conclusion: The use of the drop technique reduced and standardised the amount of dentifrice applied to the toothbrush, which could reduce the risk of dental fluorosis for young children.

Differences in responses to the Oral Health Impact Profile (OHIP14) used as a questionnaire or in an interview

The objective of this study was to compare the completion rates and performance of the Brazilian version of the Oral Health Impact Profile (OHIP14) when applied as an interview or in its original self-reported form. A convenience sample of 74 adult patients was selected in a Dental Clinic (University of Araras, Brazil). One examiner administered the instrument in both formats to participants with an interval of 2 weeks between each administration. Data about dental health condition and socioeconomic status were collected and associated with total OHIP14 scores in both formats using linear regression analyses. No differences were found in the total scores and in each subscale of the OHIP14 according to the form of administration. Higher values of completion were found in the interview format. More severe impacts were recorded in the interview format than in the questionnaire format. Higher values of total OHIP-14 scores in both formats were related to the presence of dental caries. Total OHIP14 scores were not influenced by the method of administration. However, the use of the OHIP14 in the questionnaire format may result in lower completion rates and loss of data.

Presença de mosquitos (Diptera: Culicidae) em piscinões na zona leste de São Paulo

INTRODUÇÃO: Alterações no ambiente vêm contribuindo com mudanças climáticas, como o aumento do volume de chuvas, que acarreta as inundações. Medidas estão sendo tomadas no enfrentamento das inundações, como a implantação dos reservatórios de contenção de cheias (piscinões). Neste trabalho, foi avaliada a fauna de culicídeos, de importância epidemiológica, nos piscinões Caguaçu e Inhumas. MÉTODOS: Foram realizadas coletas mensais nos piscinões Caguaçu e Inhumas, situados na região leste de São Paulo, de março de 2006 a fevereiro de 2007, empregando-se os métodos de concha entomológica e aspirador. Para análise dos dados, foram realizadas análises estatísticas descritivas e a regressão linear simples. RESULTADOS: Foram coletados 8.917 culicídeos, destacando-se Culex (Culex) quinquefasciatus, que representou 98,9% dos espécimes no Inhumas e 95,2% no Caguaçu. No Caguaçu, a maior frequência de imaturos foi observada no vertedouro (61%) e no Inhumas na canaleta (42,6%). A precipitação prediz 87% da abundância numérica de larvas de terceiro e de quarto estágio no Caguaçu e 60% do número de pupas coletadas. No Inhumas, a precipitação explicou 36% da abundância numérica de larvas e 18% do número de pupas. CONCLUSÕES: Culex quinquefasciatus, vetor de agentes da filariose, arboviroses e fator de incômodo à população, foi a espécie mais frequente nos dois ambientes. Medidas de controle da espécie nos piscinões estudados se fazem necessárias tendo em vista seu potencial epidemiológico.

Influência do consumo alimentar na gestação sobre a retenção de peso pós-parto

OBJETIVO: Avaliar a influência da alimentação durante a gestação sobre a retenção de peso pós-parto. MÉTODOS: Foram acompanhadas 82 gestantes adultas e saudáveis que iniciaram o pré-natal em serviço público de saúde no Município de São Paulo, SP, entre abril e junho de 2005. As medidas de peso e estatura foram aferidas na primeira entrevista (até 16 semanas de gestação) e a medida de peso foi repetida em visita domiciliar 15 dias após o parto. O Recordatório de 24 horas foi usado para avaliar o consumo alimentar e foi aplicado nos três trimestres da gestação. Foi calculado o consumo médio de gordura saturada, fibras, açúcar adicionado, refrigerantes, alimentos processados, frutas, verduras e legumes, e a densidade energética da dieta. A retenção de peso foi obtida pela diferença entre a medida de peso pós-parto e a primeira medida realizada. A influência da alimentação sobre a retenção de peso pós-parto foi avaliada por meio de análise de regressão linear múltipla e foi realizado o teste para tendência linear. As variáveis utilizadas para ajuste do modelo foram: índice de massa corporal no início da gestação, estatura, renda familiar per capita, tabagismo, idade e escolaridade. RESULTADOS: O índice de massa corporal inicial médio foi de 24 kg/m² e a retenção média de peso foi de 1,9 kg. O aumento do consumo de gordura saturada (p = 0,005) e alimentos processados (p = 0,014) elevou de forma significativa a retenção de peso pós-parto, após ajuste pelas variáveis de controle. As demais variáveis de consumo alimentar não apresentaram relação significativa com a variável desfecho. CONCLUSÕES: O maior consumo de alimentos não saudáveis, como alimentos processados, e de gordura saturada influencia a elevação da retenção de peso pós-parto.

Dietary calcium intake and overweight: an epidemiologic view

OBJECTIVE: We evaluated the relation between overweight and calcium intake in adults living in the municipality of São Paulo, Brazil. METHODS: This was a cross-sectional population-based study on a sample of 1459 adults that was obtained by multistage cluster sampling. Dietary intake was measured by the 24-h recall method. Poisson's and linear regression analyses were performed to evaluate the relation between overweight and quartiles of calcium intake adjusted for energy. RESULTS: The prevalence of overweight was 43.1% and the average adjusted calcium intake was 448.6 mg. In the linear regression analyses, the regression coefficient for adjusted calcium was significant and negative (P = 0.019, beta(1) = -0.0001). Although evaluated by quartiles, the prevalence ratio for overweight in the first quartile of calcium intake was 1.24 (95% confidence interval 1.00-1.54) and that in the second quartile was 1.24 (95% confidence interval 1.03-1.49). CONCLUSION: In the present study, calcium intake showed a significant negative association with body mass index

Relationship between birthweight and arterial elasticity in childhood

There is a considerable debate about the potential influence of fetal programming on cardiovascular diseases in adulthood. In the present prospective epidemiological cohort study, the relationship between birthweight and arterial elasticity in 472 children between 5 and 8 years of age was assessed. LAEI (large artery elasticity index), SAEI (small artery elasticity index) and BP (blood pressure) were assessed using the HDI/PulseWave CR-2000 CardioVascular Profiling System. Blood concentrations of glucose, total cholesterol and its fractions [LDL (low-density lipoprotein)-cholesterol and HDL (high-density lipoprotein)-cholesterol] and triacylglycerols (triglycerides) were determined by automated enzymatic methods. Insulin was assessed by a chemiluminescent method, insulin resistance by HOMA (homoeostasis model assessment) and CRP (C-reactive protein) by immunonephelometry. Two linear regression models were applied to investigate the relationship between the outcomes, LAEI and SAEI, and the following variables: birthweight, gestational age, glucose, LDL-cholesterol, HDL-cholesterol, triacylglycerols, insulin, CRP, HOMA, age, gender, waist circumference, per capita income, SBP (systolic BP) and DBP (diastolic BP). LAEI was positively associated with birthweight (P=0.036), waist circumference (P<0.001) and age (P<0.001), and negatively associated with CRP (P=0.024) and SBP (P<0.001). SAEI was positively associated with birthweight (P=0.04), waist circumference (P=0.001) and age (P<0.001), and negatively associated with DBP (P<0.001). Arterial elasticity was decreased in apparently healthy children who had lower birthweights, indicating an earlier atherogenetic susceptibility to cardiovascular diseases in adolescence and adult life. Possible explanations for the results include changes in angiogenesis during critical phases of intrauterine life caused by periods of fetal growth inhibition and local haemodynamic anomalies

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.

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.

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.

Definition of priority areas for forest conservation through the ordered weighted averaging method

The general objective of this study was to evaluate the ordered weighted averaging (OWA) method, integrated to a geographic information systems (GIS), in the definition of priority areas for forest conservation in a Brazilian river basin, aiming at to increase the regional biodiversity. We demonstrated how one could obtain a range of alternatives by applying OWA, including the one obtained by the weighted linear combination method and, also the use of the analytic hierarchy process (AHP) to structure the decision problem and to assign the importance to each criterion. The criteria considered important to this study were: proximity to forest patches; proximity among forest patches with larger core area; proximity to surface water; distance from roads: distance from urban areas; and vulnerability to erosion. OWA requires two sets of criteria weights: the weights of relative criterion importance and the order weights. Thus, Participatory Technique was used to define the criteria set and the criterion importance (based in AHP). In order to obtain the second set of weights we considered the influence of each criterion, as well as the importance of each one, on this decision-making process. The sensitivity analysis indicated coherence among the criterion importance weights, the order weights, and the solution. According to this analysis, only the proximity to surface water criterion is not important to identify priority areas for forest conservation. Finally, we can highlight that the OWA method is flexible, easy to be implemented and, mainly, it facilitates a better understanding of the alternative land-use suitability patterns. (C) 2008 Elsevier B.V. All rights reserved.

Endophytic Colonization of Potato (Solanum tuberosum L.) by a Novel Competent Bacterial Endophyte, Pseudomonas putida Strain P9, and Its Effect on Associated Bacterial Communities

Pseudomonas putida strain P9 is a novel competent endophyte from potato. P9 causes cultivar-dependent suppression of Phytophthora infestans. Colonization of the rhizoplane and endosphere of potato plants by P9 and its rifampin-resistant derivative P9R was studied. The purposes of this work were to follow the fate of P9 inside growing potato plants and to establish its effect on associated microbial communities. The effects of P9 and P9R inoculation were studied in two separate experiments. The roots of transplants of three different cultivars of potato were dipped in suspensions of P9 or P9R cells, and the plants were planted in soil. The fate of both strains was followed by examining colony growth and by performing PCR-denaturing gradient gel electrophoresis (PCR-DGGE). Colonies of both strains were recovered from rhizoplane and endosphere samples of all three cultivars at two growth stages. A conspicuous band, representing P9 and P9R, was found in all Pseudomonas PCR-DGGE fingerprints for treated plants. The numbers of P9R CFU and the P9R-specific band intensities for the different replicate samples were positively correlated, as determined by linear regression analysis. The effects of plant growth stage, genotype, and the presence of P9R on associated microbial communities were examined by multivariate and unweighted-pair group method with arithmetic mean cluster analyses of PCR-DGGE fingerprints. The presence of strain P9R had an effect on bacterial groups identified as Pseudomonas azotoformans, Pseudomonas veronii, and Pseudomonas syringae. In conclusion, strain P9 is an avid colonizer of potato plants, competing with microbial populations indigenous to the potato phytosphere. Bacterization with a biocontrol agent has an important and previously unexplored effect on plant-associated communities.