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.

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.

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.

An Analysis of the Telecommunications Business in China by Linear Regression

In this paper, we study the influence of the National Telecom Business Volume by the data in 2008 that have been published in China Statistical Yearbook of Statistics. We illustrate the procedure of modeling “National Telecom Business Volume” on the following eight variables, GDP, Consumption Levels, Retail Sales of Social Consumer Goods Total Renovation Investment, the Local Telephone Exchange Capacity, Mobile Telephone Exchange Capacity, Mobile Phone End Users, and the Local Telephone End Users. The testing of heteroscedasticity and multicollinearity for model evaluation is included. We also consider AIC and BIC criterion to select independent variables, and conclude the result of the factors which are the optimal regression model for the amount of telecommunications business and the relation between independent variables and dependent variable. Based on the final results, we propose several recommendations about how to improve telecommunication services and promote the economic development.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Logistic regression analysis of potential prognostic factors for pulmonary thromboembolism

Objective: To identify potential prognostic factors for pulmonary thromboembolism (PTE), establishing a mathematical model to predict the risk for fatal PTE and nonfatal PTE.Method: the reports on 4,813 consecutive autopsies performed from 1979 to 1998 in a Brazilian tertiary referral medical school were reviewed for a retrospective study. From the medical records and autopsy reports of the 512 patients found with macroscopically and/or microscopically,documented PTE, data on demographics, underlying diseases, and probable PTE site of origin were gathered and studied by multiple logistic regression. Thereafter, the jackknife method, a statistical cross-validation technique that uses the original study patients to validate a clinical prediction rule, was performed.Results: the autopsy rate was 50.2%, and PTE prevalence was 10.6%. In 212 cases, PTE was the main cause of death (fatal PTE). The independent variables selected by the regression significance criteria that were more likely to be associated with fatal PTE were age (odds ratio [OR], 1.02; 95% confidence interval [CI], 1.00 to 1.03), trauma (OR, 8.5; 95% CI, 2.20 to 32.81), right-sided cardiac thrombi (OR, 1.96; 95% CI, 1.02 to 3.77), pelvic vein thrombi (OR, 3.46; 95% CI, 1.19 to 10.05); those most likely to be associated with nonfatal PTE were systemic arterial hypertension (OR, 0.51; 95% CI, 0.33 to 0.80), pneumonia (OR, 0.46; 95% CI, 0.30 to 0.71), and sepsis (OR, 0.16; 95% CI, 0.06 to 0.40). The results obtained from the application of the equation in the 512 cases studied using logistic regression analysis suggest the range in which logit p > 0.336 favors the occurrence of fatal PTE, logit p < - 1.142 favors nonfatal PTE, and logit P with intermediate values is not conclusive. The cross-validation prediction misclassification rate was 25.6%, meaning that the prediction equation correctly classified the majority of the cases (74.4%).Conclusions: Although the usefulness of this method in everyday medical practice needs to be confirmed by a prospective study, for the time being our results suggest that concerning prevention, diagnosis, and treatment of PTE, strict attention should be given to those patients presenting the variables that are significant in the logistic regression model.

Some practical advice on polynomial regression analysis from blocked response surface designs

It is often necessary to run response surface designs in blocks. In this paper the analysis of data from such experiments, using polynomial regression models, is discussed. The definition and estimation of pure error in blocked designs are considered. It is recommended that pure error is estimated by assuming additive block and treatment effects, as this is more consistent with designs without blocking. The recovery of inter-block information using REML analysis is discussed, although it is shown that it has very little impact if thc design is nearly orthogonally blocked. Finally prediction from blocked designs is considered and it is shown that prediction of many quantities of interest is much simpler than prediction of the response itself.

Buffalos milk yield analysis using random regression models

Data comprising 1,719 milk yield records from 357 females (predominantly Murrah breed), daughters of 110 sires, with births from 1974 to 2004, obtained from the Programa de Melhoramento Genetic de Bubalinos (PROMEBUL) and from records of EMBRAPA Amazonia Oriental - EAO herd, located in Belem, Para, Brazil, were used to compare random regression models for estimating variance components and predicting breeding values of the sires. The data were analyzed by different models using the Legendre's polynomial functions from second to fourth orders. The random regression models included the effects of herd-year, month of parity date of the control; regression coefficients for age of females (in order to describe the fixed part of the lactation curve) and random regression coefficients related to the direct genetic and permanent environment effects. The comparisons among the models were based on the Akaike Infromation Criterion. The random effects regression model using third order Legendre's polynomials with four classes of the environmental effect were the one that best described the additive genetic variation in milk yield. The heritability estimates varied from 0.08 to 0.40. The genetic correlation between milk yields in younger ages was close to the unit, but in older ages it was low.

Bayesian outlier analysis in binary regression

We propose alternative approaches to analyze residuals in binary regression models based on random effect components. Our preferred model does not depend upon any tuning parameter, being completely automatic. Although the focus is mainly on accommodation of outliers, the proposed methodology is also able to detect them. Our approach consists of evaluating the posterior distribution of random effects included in the linear predictor. The evaluation of the posterior distributions of interest involves cumbersome integration, which is easily dealt with through stochastic simulation methods. We also discuss different specifications of prior distributions for the random effects. The potential of these strategies is compared in a real data set. The main finding is that the inclusion of extra variability accommodates the outliers, improving the adjustment of the model substantially, besides correctly indicating the possible outliers.

Prevalence of Treponema Species Detected in Endodontic Infections: Systematic Review and Meta-regression Analysis

Introduction: This systematic review and meta-regression analysis aimed to calculate a combined prevalence estimate and evaluate the prevalence of different Treponema species in primary and secondary endodontic infections, including symptomatic and asymptomatic eases. Methods: The MEDLINE/PubMed, Embase, Scielo, Web of Knowledge, and Scopus data-bases were searched without starting date restriction up to and including March 2014. Only reports in English were included. The selected literature was reviewed by 2 authors and classified as suitable or not to be included in this review. Lists were compared, and, in case of disagreements, decisions were made after a discussion based on inclusion and exclusion criteria. A pooled prevalence of Treponema species in endodontic infections was estimated. Additionally, a meta-regression analysis was performed. Results: Among the 265 articles identified in the initial search, only 51 were included in the final analysis. The studies were classified into 2 different groups according to the type of endodontic infection and whether it was an exclusively primary/secondary study (n = 36) or a primary/secondary comparison (n = 15). The pooled prevalence of Treponema species was 41.5% (95% confidence interval, 35.9-47.0). In the multivariate model of meta-regression analysis, primary endodontic infections (P < .001), acute apical abscess, symptomatic apical periodontitis (P < .001), and concomitant presence of 2 or more species (P = .028) explained the heterogeneity regarding the prevalence rates of Treponema species. Conclusions: Our findings suggest that Treponema species are important pathogens involved in endodontic infections, particularly in cases of primary and acute infections.

Anesthesia-related and perioperative cardiac arrest in low- and high-income countries: a systematic review with meta-regression and proportional meta-analysis

The anesthesia-related cardiac arrest (CA) rate is a quality indicator to improve patient safety in the perioperative period. A systematic review with meta-analysis of the worldwide literature related to anesthesia-related CA rate has not yet been performed.This study aimed to analyze global data on anesthesia-related and perioperative CA rates according to country's Human Development Index (HDI) and by time. In addition, we compared the anesthesia-related and perioperative CA rates in low- and high-income countries in 2 time periods.A systematic review was performed using electronic databases to identify studies in which patients underwent anesthesia with anesthesia-related and/or perioperative CA rates. Meta-regression and proportional meta-analysis were performed with 95% confidence intervals (CIs) to evaluate global data on anesthesia-related and perioperative CA rates according to country's HDI and by time, and to compare the anesthesia-related and perioperative CA rates by country's HDI status (low HDI vs high HDI) and by time period (pre-1990s vs 1990s-2010s), respectively.Fifty-three studies from 21 countries assessing 11.9 million anesthetic administrations were included. Meta-regression showed that anesthesia-related (slope: -3.5729; 95% CI: -6.6306 to -0.5152; P = 0.024) and perioperative (slope: -2.4071; 95% CI: -4.0482 to -0.7659; P = 0.005) CA rates decreased with increasing HDI, but not with time. Meta-analysis showed per 10,000 anesthetics that anesthesia-related and perioperative CA rates declined in high HDI (2.3 [95% CI: 1.2-3.7] before the 1990s to 0.7 [95% CI: 0.5-1.0] in the 1990s-2010s, P < 0.001; and 8.1 [95% CI: 5.1-11.9] before the 1990s to 6.2 [95% CI: 5.1-7.4] in the 1990s-2010s, P < 0.001, respectively). In low-HDI countries, anesthesia-related CA rates did not alter significantly (9.2 [95% CI: 2.0-21.7] before the 1990s to 4.5 [95% CI: 2.4-7.2] in the 1990s-2010s, P = 0.14), whereas perioperative CA rates increased significantly (16.4 [95% CI: 1.5-47.1] before the 1990s to 19.9 [95% CI: 10.9-31.7] in the 1990s-2010s, P = 0.03).Both anesthesia-related and perioperative CA rates decrease with increasing HDI but not with time. There is a clear and consistent reduction in anesthesia-related and perioperative CA rates in high-HDI countries, but an increase in perioperative CA rates without significant alteration in the anesthesia-related CA rates in low-HDI countries comparing the 2 time periods.

Latent residual analysis in binary regression with skewed link

Model diagnostics is an integral part of model determination and an important part of the model diagnostics is residual analysis. We adapt and implement residuals considered in the literature for the probit, logistic and skew-probit links under binary regression. New latent residuals for the skew-probit link are proposed here. We have detected the presence of outliers using the residuals proposed here for different models in a simulated dataset and a real medical dataset.