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.

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

A Model for comparing reduced impact logging with conventional logging for an Eastern Amazonian Forest

Using data from a logging experiment in the eastern Brazilian Amazon region, we develop a matrix growth and yield model that captures the dynamic effects of harvest system choice on forest structure and composition. Multinomial logistic regression is used to estimate the growth transition parameters for a 10-year time step, while a Poisson regression model is used to estimate recruitment parameters. The model is designed to be easily integrated with an economic model of decisionmaking to perform tropical forest policy analysis. The model is used to compare the long-run structure and composition of a stand arising from the choice of implementing either conventional logging techniques or more carefully planned and executed reduced-impact logging (RIL) techniques, contrasted against a baseline projection of an unlogged forest. Results from log and leave scenarios show that a stand logged according to Brazilian management requirements will require well over 120 years to recover its initial commercial volume, regardless of logging technique employed. Implementing RIL, however, accelerates this recovery. Scenarios imposing a 40-year cutting cycle raise the possibility of sustainable harvest volumes, although at significantly lower levels than is implied by current regulations. Meeting current Brazilian forest policy goals may require an increase in the planned total area of permanent production forest or the widespread adoption of silvicultural practices that increase stand recovery and volume accumulation rates after RIL harvests. Published by Elsevier B.V.

Worse renal outcome of lupus nephritis in male patients: a case-control study

Background: Progression and long-term renal outcome of lupus nephritis (LN) in male patients is a controversial subject in the literature. The aim of this study was to evaluate the influence of male gender on the renal outcome of LN. Methods: All male (M) LN patients who fulfilled American College of Rheumatology lupus criteria and who were referred for a kidney biopsy from 1999 to 2009 were enrolled in the study. Subjects with end-stage renal disease at baseline, or follow-up time below 6 months, were excluded. Cases were randomly matched to female (F) patients according to the class of LN, baseline estimated glomerular filtration rate (eGFR, Modification of Diet in Renal Disease simplified formula) and follow-up time. Treatment was decided by the clinical staff based on usual literature protocols. The primary endpoint was doubling of serum creatinine and/or end-stage renal disease. The secondary endpoint was defined as a variation of glomerular filtration rate (GFR) per year (Delta GFR/y index), calculated as the difference between final and initial eGFR adjusted by follow-up time for each patient. Results: We included 93 patients (31 M : 62 F). At baseline, M and F patients were not statistically different regarding WHO LN class (II 9.7%, IV 71%, V 19.3%), eGFR (M 62.4 +/- 36.4 ml/min/1.73 m(2) versus F 59.9 +/- 32.7 ml/min/1.73 m(2)), follow-up time (M 44.2 +/- 27.3 months versus F 39.9 +/- 27.9 months), and 24-hour proteinuria (M 5.3 +/- 4.6 g/day versus F 5.2 +/- 3.0 g/day), as well as age, albumin, C3, antinuclear antibody, anti-DNA antibody and haematuria. There was no difference in the primary outcome (M 19% versus F 13%, log-rank p = 0.62). However, male gender was significantly associated with a worse renal function progression, as measured by Delta GFR/y index (beta coefficient for male gender -12.4, 95% confidence interval -22.8 to -2.1, p = 0.02). The multivariate linear regression model showed that male gender remained statistically associated with a worse renal outcome even after adjustment for eGFR, proteinuria, albumin and C3 complement at baseline. Conclusion: In our study, male gender presented a worse evolution of LN (measured by an under GFR recovering) when compared with female patients with similar baseline features and treatment. Factors that influence the progression of LN in men and sex-specific treatment protocols should be further addressed in new studies. Lupus (2011) 20, 561-567.

The relationship between body mass index and the variation in plasma levels of triglycerides after short-term red wine consumption

BACKGROUND: Alcoholic beverages may have protective cardiovascular effects but are known to increase the plasma levels of triglycerides (TG). Both TG and the ratio of TO to high-density lipoprotein cholesterol (TG/HDL-cholesterol) are associated with increased cardiovascular risk. OBJECTIVES: To determine the predictive factors for variations in plasma levels of TO and the TG/HDL-cholesterol ratio in patients after they had consumed red wine for 14 days. METHODS: Forty-two subjects (64% men, 46 +/- 9 years, baseline body mass index [BMI] 25.13 +/- 2.76 kg/m(2)) were given red wine (12% or 12.2% alc/vol, 250 mL/day with meals). Plasma concentration of lipids and glucose were measured before and after red wine consumption. Blood was collected after 12 hours of fast and alcohol abstention. RESULTS: Red wine increased plasma levels of TO from 105 +/- 42 mg/dL to 120 +/- 56 mg/dL (P = .001) and the TG/HDL-cholesterol ratio from 2.16 +/- 1.10 to 2.50 +/- 1.66 (P = .014). In a multivariate linear regression model that included age, baseline BMI, blood pressure, lipids, and glucose, only BMI was independently predictive of the variation in plasma TO after red wine (beta coefficient 0.592, P < .001). BMI also predicted the variation in TG/HDL-cholesterol ratio (beta coefficient 0.505, P = .001, adjusted model). When individuals were divided into three categories, according to their BMI, the average percentage variation in TG after red wine was -4%, 17%, and 33% in the lower (19.60-24.45 kg/m(2)), intermediate, and greater (26.30-30.44 kg/m(2)) tertiles, respectively (P = .001). CONCLUSIONS: Individuals with higher BMI, although nonobese, might be at greater risk for elevation in plasma TO levels and the TG/HDL-cholesterol ratio after short-term red wine consumption. (C) 2011 National Lipid Association. All rights reserved.

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.

Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

Hypotheses Testing on a Multivariate Null Intercept Errors-in-Variables Model

Considering the Wald, score, and likelihood ratio asymptotic test statistics, we analyze a multivariate null intercept errors-in-variables regression model, where the explanatory and the response variables are subject to measurement errors, and a possible structure of dependency between the measurements taken within the same individual are incorporated, representing a longitudinal structure. This model was proposed by Aoki et al. (2003b) and analyzed under the bayesian approach. In this article, considering the classical approach, we analyze asymptotic test statistics and present a simulation study to compare the behavior of the three test statistics for different sample sizes, parameter values and nominal levels of the test. Also, closed form expressions for the score function and the Fisher information matrix are presented. We consider two real numerical illustrations, the odontological data set from Hadgu and Koch (1999), and a quality control data set.

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.

Evolutionary model trees for handling continuous classes in machine learning

Model trees are a particular case of decision trees employed to solve regression problems. They have the advantage of presenting an interpretable output, helping the end-user to get more confidence in the prediction and providing the basis for the end-user to have new insight about the data, confirming or rejecting hypotheses previously formed. Moreover, model trees present an acceptable level of predictive performance in comparison to most techniques used for solving regression problems. Since generating the optimal model tree is an NP-Complete problem, traditional model tree induction algorithms make use of a greedy top-down divide-and-conquer strategy, which may not converge to the global optimal solution. In this paper, we propose a novel algorithm based on the use of the evolutionary algorithms paradigm as an alternate heuristic to generate model trees in order to improve the convergence to globally near-optimal solutions. We call our new approach evolutionary model tree induction (E-Motion). We test its predictive performance using public UCI data sets, and we compare the results to traditional greedy regression/model trees induction algorithms, as well as to other evolutionary approaches. Results show that our method presents a good trade-off between predictive performance and model comprehensibility, which may be crucial in many machine learning applications. (C) 2010 Elsevier Inc. All rights reserved.

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

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.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

NONHOMOGENEOUS RANDOM WALKS SYSTEMS ON Z

We consider a random walks system on Z in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on Z, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to I but not fast enough.