Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

Clinical risk factors for osteoporotic fractures in Brazilian women and men: the Brazilian Osteoporosis Study (BRAZOS)

The Brazilian Osteoporosis Study (BRAZOS) is the first epidemiological study carried out in a representative sample of Brazilian men and women aged 40 years or older. The prevalence of fragility fractures is about 15.1% in the women and 12.8% in the men. Moreover, advanced age, sedentarism, family history of hip fracture, current smoking, recurrent falls, diabetes mellitus and poor quality of life are the main clinical risk factors associated with fragility fractures. The Brazilian Osteoporosis Study (BRAZOS) is the first epidemiological study carried out in a representative sample of Brazilian men and women aged 40 years or older with the purpose of identifying the prevalence and the main clinical risk factors (CRF) associated with osteoporotic fracture in our population. A total of 2,420 individuals (women, 70%) from 150 different cities in the five geographic regions in Brazil, and all different socio-economical classes were selected to participate in the present survey. Anthropometrical data as well as life habits, fracture history, food intake, physical activity, falls and quality of life were determined by individual quantitative interviews. The representative sampling was based on Brazilian National data provided by the 2000 and 2003 census. Low trauma fracture was defined as that resulting of a fall from standing height or less in individuals 50 years or older at specific skeletal sites: forearm, femur, ribs, vertebra and humerus. Sampling error was 2.2% with 95% confidence intervals. Logistic regression analysis models were designed having the fragility fracture as the dependent variable and all other parameters as the independent variable. Significance level was set as p < 0.05. The average of age, height and weight for men and women were 58.4 +/- 12.8 and 60.1 +/- 13.7 years, 1.67 +/- 0.08 and 1.56 +/- 0.07 m and 73.3 +/- 14.7 and 64.7 +/- 13.7 kg, respectively. About 15.1% of the women and 12.8% of the men reported fragility fractures. In the women, the main CRF associated with fractures were advanced age (OR = 1.6; 95% CI 1.06-2.4), family history of hip fracture (OR = 1.7; 95% CI 1.1-2.8), early menopause (OR = 1.7; 95% CI 1.02-2.9), sedentary lifestyle (OR = 1.6; 95% CI 1.02-2.7), poor quality of life (OR = 1.9; 95% CI 1.2-2.9), higher intake of phosphorus (OR = 1.9; 95% CI 1.2-2.9), diabetes mellitus (OR = 2.8; 95% CI 1.01-8.2), use of benzodiazepine drugs (OR = 2.0; 95% CI 1.1-3.6) and recurrent falls (OR = 2.4; 95% CI 1.2-5.0). In the men, the main CRF were poor quality of life (OR = 3.2; 95% CI 1.7-6.1), current smoking (OR = 3.5; 95% CI 1.28-9.77), diabetes mellitus (OR = 4.2; 95% CI 1.27-13.7) and sedentary lifestyle (OR = 6.3; 95% CI 1.1-36.1). Our findings suggest that CRF may contribute as an important tool to identify men and women with higher risk of osteoporotic fractures and that interventions aiming at specific risk factors (quit smoking, regular physical activity, prevention of falls) may help to manage patients to reduce their risk of fracture.

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.

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.

Asymptotic skewness in Birnbaum-Saunders nonlinear regression models

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum-Saunders nonlinear regression models, recently introduced by Lemonte and Cordeiro (2009). The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors, in order to obtain closed-form skewness in a wide range of nonlinear regression models. Empirical and real applications are analyzed and discussed. (C) 2010 Elsevier B.V. All rights reserved.