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.

Heteroscedastic Nonlinear Regression Models

In this article, we present a generalization of the Bayesian methodology introduced by Cepeda and Gamerman (2001) for modeling variance heterogeneity in normal regression models where we have orthogonality between mean and variance parameters to the general case considering both linear and highly nonlinear regression models. Under the Bayesian paradigm, we use MCMC methods to simulate samples for the joint posterior distribution. We illustrate this algorithm considering a simulated data set and also considering a real data set related to school attendance rate for children in Colombia. Finally, we present some extensions of the proposed MCMC algorithm.

Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics

The purpose of this paper is to develop a Bayesian analysis for nonlinear regression models under scale mixtures of skew-normal distributions. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the error distributions cover both skewness and heavy-tailed distributions such as the skew-t, skew-slash and the skew-contaminated normal distributions. The main advantage of these class of distributions is that they have a nice hierarchical representation that allows the implementation of Markov chain Monte Carlo (MCMC) methods to simulate samples from the joint posterior distribution. In order to examine the robust aspects of this flexible class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. Further, some discussions on the model selection criteria are given. The newly developed procedures are illustrated considering two simulations study, and a real data previously analyzed under normal and skew-normal nonlinear regression models. (C) 2010 Elsevier B.V. All rights reserved.

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.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Exploratory Approach to the use of Techniques of Regression Analysis and Pooled Analysis in Studies of Consumer Behavior

This paper is part of a large study to assess the adequacy of the use of multivariate statistical techniques in theses and dissertations of some higher education institutions in the area of marketing with theme of consumer behavior from 1997 to 2006. The regression and conjoint analysis are focused on in this paper, two techniques with great potential of use in marketing studies. The objective of this study was to analyze whether the employement of these techniques suits the needs of the research problem presented in as well as to evaluate the level of success in meeting their premisses. Overall, the results suggest the need for more involvement of researchers in the verification of all the theoretical precepts of application of the techniques classified in the category of investigation of dependence among variables.

A nonlinear regression model with skew-normal errors

In this paper we have discussed inference aspects of the skew-normal nonlinear regression models following both, a classical and Bayesian approach, extending the usual normal nonlinear regression models. The univariate skew-normal distribution that will be used in this work was introduced by Sahu et al. (Can J Stat 29:129-150, 2003), which is attractive because estimation of the skewness parameter does not present the same degree of difficulty as in the case with Azzalini (Scand J Stat 12:171-178, 1985) one and, moreover, it allows easy implementation of the EM-algorithm. As illustration of the proposed methodology, we consider a data set previously analyzed in the literature under normality.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Regression analysis of mean quality-adjusted survival time based on pseudo-observations

Regression models for the mean quality-adjusted survival time are specified from hazard functions of transitions between two states and the mean quality-adjusted survival time may be a complex function of covariates. We discuss a regression model for the mean quality-adjusted survival (QAS) time based on pseudo-observations, which has the advantage of directly modeling the effect of covariates in the QAS time. Both Monte Carlo Simulations and a real data set are studied. Copyright (C) 2009 John Wiley & Sons, Ltd.

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.

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.

Discontinuation of continuous renal replacement therapy: A post hoc analysis of a prospective multicenter observational study

Objectives: To describe current practice for the discontinuation of continuous renal replacement therapy in a multinational setting and to identify variables associated with successful discontinuation. The approach to discontinue continuous renal replacement therapy may affect patient outcomes. However, there is lack of information on how and under what conditions continuous renal replacement therapy is discontinued. Design: Post hoc analysis of a prospective observational study. Setting. Fifty-four intensive care units in 23 countries. Patients: Five hundred twenty-nine patients (52.6%) who survived initial therapy among 1006 patients treated with continuous renal replacement therapy. Interventions: None. Measurements and Main Results., Three hundred thirteen patients were removed successfully from continuous renal replacement therapy and did not require any renal replacement therapy for at least 7 days and were classified as the ""success"" group and the rest (216 patients) were classified as the ""repeat-RRT"" (renal replacement therapy) group. Patients in the ""success"" group had lower hospital mortality (28.5% vs. 42.7%, p < .0001) compared with patients in the ""repeat-RRT"" group. They also had lower creatinine and urea concentrations and a higher urine output at the time of stopping continuous renal replacement therapy. Multivariate logistic regression analysis for successful discontinuation of continuous renal replacement therapy identified urine output (during the 24 hrs before stopping continuous renal replacement therapy: odds ratio, 1.078 per 100 mL/day increase) and creatinine (odds ratio, 0.996 per mu mol/L increase) as significant predictors of successful cessation. The area under the receiver operating characteristic curve to predict successful discontinuation of continuous renal replacement therapy was 0.808 for urine output and 0.635 for creatinine. The predictive ability of urine output was negatively affected by the use of diuretics (area under the receiver operating characteristic curve, 0.671 with diuretics and 0.845 without diuretics). Conclusions. We report on the current practice of discontinuing continuous renal replacement therapy in a multinational setting. Urine output at the time of initial cessation (if continuous renal replacement therapy was the most important predictor of successful discontinuation, especially if occurring without the administration of diuretics. (Crit Care Med 2009; 37:2576-2582)

Mucosal leishmaniasis: description of case management approaches and analysis of risk factors for treatment failure in a cohort of 140 patients in Brazil

Background Mucosal leishmaniasis is caused mainly by Leishmania braziliensis and it occurs months or years after cutaneous lesions. This progressive disease destroys cartilages and osseous structures from face, pharynx and larynx. Objective and methods The aim of this study was to analyse the significance of clinical and epidemiological findings, diagnosis and treatment with the outcome and recurrence of mucosal leishmaniasis through binary logistic regression model from 140 patients with mucosal leishmaniasis from a Brazilian centre. Results The median age of patients was 57.5 and systemic arterial hypertension was the most prevalent secondary disease found in patients with mucosal leishmaniasis (43%). Diabetes, chronic nephropathy and viral hepatitis, allergy and coagulopathy were found in less than 10% of patients. Human immunodeficiency virus (HIV) infection was found in 7 of 140 patients (5%). Rhinorrhea (47%) and epistaxis (75%) were the most common symptoms. N-methyl-glucamine showed a cure rate of 91% and recurrence of 22%. Pentamidine showed a similar rate of cure (91%) and recurrence (25%). Fifteen patients received itraconazole with a cure rate of 73% and recurrence of 18%. Amphotericin B was the drug used in 30 patients with 82% of response with a recurrence rate of 7%. The binary logistic regression analysis demonstrated that systemic arterial hypertension and HIV infection were associated with failure of the treatment (P < 0.05). Conclusion The current first-line mucosal leishmaniasis therapy shows an adequate cure but later recurrence. HIV infection and systemic arterial hypertension should be investigated before start the treatment of mucosal leishmaniasis. Conflicts of interest The authors are not part of any associations or commercial relationships that might represent conflicts of interest in the writing of this study (e.g. pharmaceutical stock ownership, consultancy, advisory board membership, relevant patents, or research funding).

Oral mucositis in acute lymphoblastic leukaemia: analysis of 169 paediatric patients

Chemotherapy-induced oral mucositis is a frequent therapeutic challenge in cancer patients. The purpose of this retrospective study was to estimate the prevalence and risk factors of oral mucositis in 169 acute lymphoblastic leukaemia (ALL) patients treated according to different chemotherapeutic trials at the Darcy Vargas Children`s Hospital from 1994 to 2005. Demographic data, clinical history, chemotherapeutic treatment and patients` follow-up were recorded. The association of oral mucositis with age, gender, leucocyte counts at diagnosis and treatment was assessed by the chi-squared test and multivariate regression analysis. Seventy-seven ALL patients (46%) developed oral mucositis during the treatment. Patient age (P = 0.33), gender (P = 0.08) and leucocyte counts at diagnosis (P = 0.34) showed no correlation with the occurrence of oral mucositis. Multivariate regression analysis showed a significant risk for oral mucositis (P = 0.009) for ALL patients treated according to the ALL-BFM-95 protocol. These results strongly suggest the greater stomatotoxic effect of the ALL-BFM-95 trial when compared with Brazilian trials. We concluded that chemotherapy-induced oral mucositis should be systematically analysed prospectively in specialized centres for ALL treatment to establish the degree of toxicity of chemotherapeutic drugs and to improve the quality of life of patients based on more effective therapeutic and prophylactic approaches for prevention of its occurrence. Oral Diseases (2008) 14, 761-766

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.