Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients

In this paper, we present different ofrailtyo models to analyze longitudinal data in the presence of covariates. These models incorporate the extra-Poisson variability and the possible correlation among the repeated counting data for each individual. Assuming a CD4 counting data set in HIV-infected patients, we develop a hierarchical Bayesian analysis considering the different proposed models and using Markov Chain Monte Carlo methods. We also discuss some Bayesian discrimination aspects for the choice of the best model.

Caries, gender and socio-economic change in the Xavante Indians from Central Brazil

Background: The oral health conditions of indigenous peoples in Amazonia are closely associated with ecological and dietary changes related to interaction with non-Indians. Aim: The study investigated the incidence of caries in an indigenous community from Central Brazil focusing on gender differences. Subjects and methods: The research was conducted among the Xavante Indians and was based on longitudinal data collected in two surveys (1999 and 2004). The study included 128 individuals, 63 (49.2%) males and 65 (50.8%) females, divided in four age brackets (6-12, 13-19, 20-34, 35-60 years of age). The DMFT (decayed, missing and filled teeth) index and incidences (difference between 1999 and 2004) were calculated for each individual. The proportion of incidence was also calculated. Differences in caries risk between gender and age brackets were compared by parametric and non-parametric tests. Results: There were statistically significant differences in relation to caries incidence between age brackets and gender. The greatest incidence was observed in the 20-34 age bracket, which presented 3.30 new decayed teeth, twice the risk of the 6-12 age bracket (p0.01), chosen as reference. While females in most age groups did not show higher risk for caries when compared to males, there was a 4.04-fold risk in the 20-34 age bracket (p0.01). Conclusion: It is concluded that factors related to the social functions of each sex (gender issues) and differential access to information, health services, and education may help to understand the differences observed in the incidence of caries.

A Bayesian model for estimating the malaria transition probabilities considering individuals lost to follow-up

It is known that patients may cease participating in a longitudinal study and become lost to follow-up. The objective of this article is to present a Bayesian model to estimate the malaria transition probabilities considering individuals lost to follow-up. We consider a homogeneous population, and it is assumed that the considered period of time is small enough to avoid two or more transitions from one state of health to another. The proposed model is based on a Gibbs sampling algorithm that uses information of lost to follow-up at the end of the longitudinal study. To simulate the unknown number of individuals with positive and negative states of malaria at the end of the study and lost to follow-up, two latent variables were introduced in the model. We used a real data set and a simulated data to illustrate the application of the methodology. The proposed model showed a good fit to these data sets, and the algorithm did not show problems of convergence or lack of identifiability. We conclude that the proposed model is a good alternative to estimate probabilities of transitions from one state of health to the other in studies with low adherence to follow-up.

Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective

Linear mixed models were developed to handle clustered data and have been a topic of increasing interest in statistics for the past 50 years. Generally. the normality (or symmetry) of the random effects is a common assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize skew-normal/independent distributions as a tool for robust modeling of linear mixed models under a Bayesian paradigm. The skew-normal/independent distributions is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal distribution, skew-t, skew-slash and the skew-contaminated normal distributions as special cases, providing an appealing robust alternative to the routine use of symmetric distributions in this type of models. The methods developed are illustrated using a real data set from Framingham cholesterol study. (C) 2009 Elsevier B.V. All rights reserved.

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.

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.

Local influence for Student-t partially linear models

In this paper we extend partial linear models with normal errors to Student-t errors Penalized likelihood equations are applied to derive the maximum likelihood estimates which appear to be robust against outlying observations in the sense of the Mahalanobis distance In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data the local influence curvatures are derived and some diagnostic graphics are proposed A motivating example preliminary analyzed under normal errors is reanalyzed under Student-t errors The local influence approach is used to compare the sensitivity of the model estimates (C) 2010 Elsevier B V All rights reserved

Leverage analysis for linear mixed models

We consider a generalized leverage matrix useful for the identification of influential units and observations in linear mixed models and show how a decomposition of this matrix may be employed to identify high leverage points for both the marginal fitted values and the random effect component of the conditional fitted values. We illustrate the different uses of the two components of the decomposition with a simulated example as well as with a real data set.

Copula-based regression models: A survey

In this review paper we collect several results about copula-based models, especially concerning regression models, by focusing on some insurance applications. (C) 2009 Elsevier B.V. All rights reserved.

Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Beta-binomial/Poisson regression models for repeated bivariate counts

We analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of Parkinson`s disease patients. Maximum likelihood methods were used to fit beta-binomial/Poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods, controlling for disease stage and use of the preferred hand. We extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data. The results suggest that the expected number of attempts and successes increase with training, except for patients with advanced stages of the disease using the non-preferred hand. Copyright (c) 2008 John Wiley & Sons, Ltd.

Metabolic acidosis in patients with severe sepsis and septic shock: A longitudinal quantitative study

Objective: To describe the composition of metabolic acidosis in patients with severe sepsis and septic shock at intensive care unit admission and throughout the first 5 days of intensive care unit stay. Design: Prospective, observational study. Setting: Twelve-bed intensive care unit. Patients: Sixty patients with either severe sepsis or septic shock. Interventions: None. Measurements and Main Results: Data were collected until 5 days after intensive care unit admission. We studied the contribution of inorganic ion difference, lactate, albumin, phosphate, and strong ion gap to metabolic acidosis. At admission, standard base excess was -6.69 +/- 4.19 mEq/L in survivors vs. -11.63 +/- 4.87 mEq/L in nonsurvivors (p < .05); inorganic ion difference (mainly resulting from hyperchloremia) was responsible for a decrease in standard base excess by 5.64 +/- 4.96 mEq/L in survivors vs. 8.94 +/- 7.06 mEq/L in nonsurvivors (p < .05); strong ion gap was responsible for a decrease in standard base excess by 4.07 +/- 3.57 mEq/L in survivors vs. 4.92 +/- 5.55 mEq/L in nonsurvivors with a nonsignificant probability value; and lactate was responsible for a decrease in standard base excess to 1.34 +/- 2.07 mEq/L in survivors vs. 1.61 +/- 2.25 mEq/L in nonsurvivors with a nonsignificant probability value. Albumin had an important alkalinizing effect in both groups; phosphate had a minimal acid-base effect. Acidosis in survivors was corrected during the study period as a result of a decrease in lactate and strong ion gap levels, whereas nonsurvivors did not correct their metabolic acidosis. In addition to Acute Physiology and Chronic Health Evaluation 11 score and serum creatinine level, inorganic ion difference acidosis magnitude at intensive care unit admission was independently associated with a worse outcome. Conclusions: Patients with severe sepsis and septic shock exhibit a complex metabolic acidosis at intensive care unit admission, caused predominantly by hyperchloremic acidosis, which was more pronounced in nonsurvivors. Acidosis resolution in survivors was attributable to a decrease in strong ion gap and lactate levels. (Crit Care Med 2009; 37:2733-2739)