Local influence in estimating equations

Local influence diagnostics based on estimating equations as the role of a gradient vector derived from any fit function are developed for repeated measures regression analysis. Our proposal generalizes tools used in other studies (Cook, 1986: Cadigan and Farrell, 2002), considering herein local influence diagnostics for a statistical model where estimation involves an estimating equation in which all observations are not necessarily independent of each other. Moreover, the measures of local influence are illustrated with some simulated data sets to assess influential observations. Applications using real data are presented. (C) 2010 Elsevier B.V. All rights reserved.

Small-Sample Corrections for Score Tests in Birnbaum-Saunders Regressions

In this article, we deal with the issue of performing accurate small-sample inference in the Birnbaum-Saunders regression model, which can be useful for modeling lifetime or reliability data. We derive a Bartlett-type correction for the score test and numerically compare the corrected test with the usual score test and some other competitors.

Local Influence Under Parameter Constraints

Calculations of local influence curvatures and leverage have been well developed when the parameters are unrestricted. In this article, we discuss the assessment of local influence and leverage under linear equality parameter constraints with extensions to inequality constraints. Using a penalized quadratic function we express the normal curvature of local influence for arbitrary perturbation schemes and the generalized leverage matrix in interpretable forms, which depend on restricted and unrestricted components. The results are quite general and can be applied in various statistical models. In particular, we derive the normal curvature under three useful perturbation schemes for generalized linear models. Four illustrative examples are analyzed by the methodology developed in the article.

Transformed symmetric models

For the first time, we introduce a class of transformed symmetric models to extend the Box and Cox models to more general symmetric models. The new class of models includes all symmetric continuous distributions with a possible non-linear structure for the mean and enables the fitting of a wide range of models to several data types. The proposed methods offer more flexible alternatives to Box-Cox or other existing procedures. We derive a very simple iterative process for fitting these models by maximum likelihood, whereas a direct unconditional maximization would be more difficult. We give simple formulae to estimate the parameter that indexes the transformation of the response variable and the moments of the original dependent variable which generalize previous published results. We discuss inference on the model parameters. The usefulness of the new class of models is illustrated in one application to a real dataset.

Cutpoint selection for discretizing a continuous covariate for generalized estimating equations

We consider consider the problem of dichotomizing a continuous covariate when performing a regression analysis based on a generalized estimation approach. The problem involves estimation of the cutpoint for the covariate and testing the hypothesis that the binary covariate constructed from the continuous covariate has a significant impact on the outcome. Due to the multiple testing used to find the optimal cutpoint, we need to make an adjustment to the usual significance test to preserve the type-I error rates. We illustrate the techniques on one data set of patients given unrelated hematopoietic stem cell transplantation. Here the question is whether the CD34 cell dose given to patient affects the outcome of the transplant and what is the smallest cell dose which is needed for good outcomes. (C) 2010 Elsevier BM. All rights reserved.

A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

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.

Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. in this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Systematic risk estimation in symmetric models

The aim of this article is to discuss the estimation of the systematic risk in capital asset pricing models with heavy-tailed error distributions to explain the asset returns. Diagnostic methods for assessing departures from the model assumptions as well as the influence of observations on the parameter estimates are also presented. It may be shown that outlying observations are down weighted in the maximum likelihood equations of linear models with heavy-tailed error distributions, such as Student-t, power exponential, logistic II, so on. This robustness aspect may also be extended to influential observations. An application in which the systematic risk estimate of Microsoft is compared under normal and heavy-tailed errors is presented for illustration.

Prevalência de hipertensão arterial em militares jovens e fatores associados

OBJETIVO: Estimar a prevalência de hipertensão arterial entre militares jovens e fatores associados. MÉTODOS: Estudo transversal realizado com amostra de 380 militares do sexo masculino de 19 e 35 anos de idade em uma unidade da Força Aérea Brasileira em São Paulo, SP, entre 2000 e 2001. Os pontos de corte para hipertensão foram: >140mmHg para pressão sistólica e > 90mmHg para pressão diastólica. As variáveis estudadas incluíram fatores de risco e de proteção para hipertensão, como características comportamentais e nutricionais. Para análise das associações, utilizou-se regressão linear generalizada múltipla, com família binomial e ligação logarítmica, obtendo-se razões de prevalências com intervalo de 90% de confiança e seleção hierarquizada das variáveis. RESULTADOS: A prevalência de hipertensão arterial foi de 22% (IC 90%: 21;29). No modelo final da regressão múltipla verificou-se prevalência de hipertensão 68% maior entre os ex-fumantes em relação aos não fumantes (IC 90%: 1,13;2,50). Entre os indivíduos com sobrepeso (índice de massa corporal - IMC de 25 a 29kg/m2) e com obesidade (IMC>29kg/m2) as prevalências foram, respectivamente, 75% (IC 90%: 1,23;2,50) e 178% (IC 90%: 1,82;4,25) maiores do que entre os eutróficos. Entre os que praticavam atividade física regular, comparado aos que não praticavam, a prevalência foi 52% menor (IC 90%: 0,30;0,90). CONCLUSÕES: Ser ex-fumante e ter sobrepeso ou obesidade foram situações de risco para hipertensão, enquanto que a prática regular de atividade física foi fator de proteção em militares jovens.

Gender and schooling inequalities in risk and protective factors for chronic diseases among Brazilian adults, through telephone survey

OBJECTIVES: To assess risk and protective factors for chronic noncommunicable diseases (CNCD) and to identify social inequalities in their distribution among Brazilian adults. METHODS: The data used were collected in 2007 through VIGITEL, an ongoing population-based telephone survey. This surveillance system was implemented in all of the Brazilian State capitals, over 54,000 interviews were analyzed. Age-adjusted prevalence ratios for trends at different schooling levels were calculated using Poisson regression with linear models. RESULTS: These analyses have shown differences in the prevalence of risk and protective factors for CNCD by gender and schooling. Among men, the prevalence ratios of overweight, consumption of meat with visible fat, and dyslipidemia were higher among men with more schooling, while tobacco use, sedentary lifestyle, and high-blood pressure were lower. Among women, tobacco use, overweight, obesity, high-blood pressure and diabetes were lower among men with more schooling, and consumption of meat with visible fat and sedentary lifestyles were higher. As for protective factors, fruit and vegetables intake and physical activity were higher in both men and women with more schooling. CONCLUSION: Gender and schooling influence on risk and protective factors for CNCD, being the values less favorable for men. vigitel is a useful tool for monitoring these factors amongst the Brazilian population.

Prevalence and social distribution of risk factors for chronic noncommunicable diseases in Brazil

OBJETIVOS: Evaluar los factores de riesgo de enfermedades crónicas no transmisibles (ECNT) e identificar las desigualdades sociales relacionadas con su distribución en la población adulta brasileña.MÉTODOS: Se estudiaron los factores de riesgo de ECNT (entre ellos el consumo de tabaco, el sobrepeso y la obesidad, el bajo consumo de frutas y vegetales [BCFV], la insuficiente actividad física en el tiempo de ocio [IAFTO], el estilo de vida sedentario y el consumo excesivo de alcohol) en una muestra probabilística de 54369 adultos de 26 capitales estatales de Brasil y el Distrito Federal en 2006. Se utilizó el Sistema de Vigilancia de los Factores Protectores y de Riesgo para Enfermedades Crónicas No Transmisibles por Entrevistas Telefónicas (VIGITEL), un sistema de encuestas telefónicas asistido por computadora, y se calcularon las prevalencias ajustadas por la edad para las tendencias en cuanto al nivel educacional mediante la regresión de Poisson con modelos lineales. RESULTADOS: Los hombres informaron mayor consumo de tabaco, sobrepeso, BCFV, estilo de vida sedentario y consumo excesivo de alcohol que las mujeres, pero menos IAFTO. En los hombres, la educación se asoció con un mayor sobrepeso y un estilo de vida sedentario, pero con un menor consumo de tabaco, BCFV e IAFTO. En las mujeres, la educación se asoció con un menor consumo de tabaco, sobrepeso, obesidad, BCFV e IAFTO, pero aumentó el estilo de vida sedentario CONCLUSIONES: En Brasil, la prevalencia de factores de riesgo para ECNT (excepto IAFTO) es mayor en los hombres que en las mujeres. En ambos sexos, el nivel de educación influye en la prevalencia de los factores de riesgo para ECNT

Inequalities in mortality of men by oral and pharyngeal cancer in Barcelona, Spain and Sao Paulo, Brazil, 1995-2003

Background: Large inequalities of mortality by most cancers in general, by mouth and pharynx cancer in particular, have been associated to behaviour and geopolitical factors. The assessment of socioeconomic covariates of cancer mortality may be relevant to a full comprehension of distal determinants of the disease, and to appraise opportune interventions. The objective of this study was to compare socioeconomic inequalities in male mortality by oral and pharyngeal cancer in two major cities of Europe and South America. Methods: The official system of information on mortality provided data on deaths in each city; general censuses informed population data. Age-adjusted death rates by oral and pharyngeal cancer for men were independently assessed for neighbourhoods of Barcelona, Spain, and Sao Paulo, Brazil, from 1995 to 2003. Uniform methodological criteria instructed the comparative assessment of magnitude, trends and spatial distribution of mortality. General linear models assessed ecologic correlations between death rates and socioeconomic indices (unemployment, schooling levels and the human development index) at the inner-city area level. Results obtained for each city were subsequently compared. Results: Mortality of men by oral and pharyngeal cancer ranked higher in Barcelona (9.45 yearly deaths per 100,000 male inhabitants) than in Spain and Europe as a whole; rates were on decrease. Sao Paulo presented a poorer profile, with higher magnitude (11.86) and stationary trend. The appraisal of ecologic correlations indicated an unequal and inequitably distributed burden of disease in both cities, with poorer areas tending to present higher mortality. Barcelona had a larger gradient of mortality than Sao Paulo, indicating a higher inequality of cancer deaths across its neighbourhoods. Conclusion: The quantitative monitoring of inequalities in health may contribute to the formulation of redistributive policies aimed at the concurrent promotion of wellbeing and social justice. The assessment of groups experiencing a higher burden of disease can instruct health services to provide additional resources for expanding preventive actions and facilities aimed at early diagnosis, standardized treatments and rehabilitation.

Performance of different immobilized lipases in palm oil biodiesel synthesis

Performance of different immobilized lipases in palm oil biodiesel synthesis. Optimized conditions for palm oil and ethanol enzymatic biodiesel synthesis were determined with different immobilized lipases SiO(2)-PVA-immobilized lipase from Pseudomonas fluorescens and acrylic resin-immobilized lipase, Novozym (R) 435, from Candida antartica, in solvent-free medium. A full factorial design assessed the influence of temperature (42 - 58 degrees C) and ethanol: palm oil (6:1 - 18:1) molar ratio on the transesterification yield. Main effects were adjusted by multiple regression analysis to linear models and the maximum transesterification yield was obtained at 42 degrees C and 18:1 ethanol: palm oil molar ratio. Mathematical models featuring total yield for each immobilized lipase were suitable to describe the experimental results.