Bayesian Approach to Zero-Inflated Bivariate Ordered Probit Regression Model, with an Application to Tobacco Use

This paper presents a Bayesian analysis of bivariate ordered probit regression model with excess of zeros. Specifically, in the context of joint modeling of two ordered outcomes, we develop zero-inflated bivariate ordered probit model and carry out estimation using Markov Chain Monte Carlo techniques. Using household tobacco survey data with substantial proportion of zeros, we analyze the socioeconomic determinants of individual problem of smoking and chewing tobacco. In our illustration, we find strong evidence that accounting for excess zeros provides good fit to the data. The example shows that the use of a model that ignores zero-inflation masks differential effects of covariates on nonusers and users

Bayesian Inference for Skew-Normal Mixture Models With Left-Censoring

Assays to measure concentration of antibody after vaccination are often subject to left-censoring due to a lower detection limit (LDL), leading to a high proportion of observations below the detection limit. Not accounting for such left-censoring appropriately can lead to biased parameter estimates. To properly adjust for left-censoring and a high proportion of observations at LDL, this article proposes a mixture model combining a point mass below LDL and a Tobit model with skew-elliptical error distribution. We show that skew-elliptical distributions, where the skew-normal and skew-t are special cases, have great flexibility for simultaneously handling left-censoring, skewness, and heaviness in the tails of a distribution of a response variable with left-censored data. A Bayesian procedure is used to estimate model parameters. Two real data sets from a study of the measles vaccine and an HIV/AIDS study are used to illustrate the proposed models

Bayesian Semiparametric Mixture Tobit Models with Left Censoring, Skewness, and Covariate Measurement Errors

Common problems to many longitudinal HIV/AIDS, cancer, vaccine, and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time-varying covariates with measurement errors. There has been relatively little work published simultaneously dealing with these features of longitudinal data. In particular, left-censored data falling below a limit of detection may sometimes have a proportion larger than expected under a usually assumed log-normal distribution. In such cases, alternative models, which can account for a high proportion of censored data, should be considered. In this article, we present an extension of the Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for an outcome with possible left censoring and skewness, and covariates with substantial measurement error. To quantify the covariate process, we offer a flexible nonparametric mixed-effects model within the Tobit framework. A Bayesian modeling approach is used to assess the simultaneous impact of left censoring, skewness, and measurement error in covariates on inference. The proposed methods are illustrated using real data from an AIDS clinical study. Copyright © 2013 John Wiley & Sons, Ltd

Bayesian Approach to Zero-Inflated Bivariate Ordered Probit Regression Model, with an Application to Tobacco Use

This paper presents a Bayesian analysis of bivariate ordered probit regression model with excess of zeros. Specifically, in the context of joint modeling of two ordered outcomes, we develop zero-inflated bivariate ordered probit model and carry out estimation using Markov Chain Monte Carlo techniques. Using household tobacco survey data with substantial proportion of zeros, we analyze the socioeconomic determinants of individual problem of smoking and chewing tobacco. In our illustration, we find strong evidence that accounting for excess zeros provides good fit to the data. The example shows that the use of a model that ignores zero-inflation masks differential effects of covariates on nonusers and users

Mixed-Effects Tobit Joint Models for Longitudinal Data with Skewness, Detection Limits, and Measurement Errors

Complex longitudinal data are commonly analyzed using nonlinear mixed-effects (NLME) models with a normal distribution. However, a departure from normality may lead to invalid inference and unreasonable parameter estimates. Some covariates may be measured with substantial errors, and the response observations may also be subjected to left-censoring due to a detection limit. Inferential procedures can be complicated dramatically when such data with asymmetric characteristics, left censoring, and measurement errors are analyzed. There is relatively little work concerning all of the three features simultaneously. In this paper, we jointly investigate a skew-t NLME Tobit model for response (with left censoring) process and a skew-t nonparametric mixed-effects model for covariate (with measurement errors) process under a Bayesian framework. A real data example is used to illustrate the proposed methods

Mixed-Effects Tobit Joint Models for Longitudinal Data with Skewness, Detection Limits, and Measurement Errors

Complex longitudinal data are commonly analyzed using nonlinear mixed-effects (NLME) models with a normal distribution. However, a departure from normality may lead to invalid inference and unreasonable parameter estimates. Some covariates may be measured with substantial errors, and the response observations may also be subjected to left-censoring due to a detection limit. Inferential procedures can be complicated dramatically when such data with asymmetric characteristics, left censoring, and measurement errors are analyzed. There is relatively little work concerning all of the three features simultaneously. In this paper, we jointly investigate a skew-t NLME Tobit model for response (with left censoring) process and a skew-t nonparametric mixed-effects model for covariate (with measurement errors) process under a Bayesian framework. A real data example is used to illustrate the proposed methods

Hierarchical Modeling of Sequential Behavioral Data Examining Complex Association Patterns in Mediation Models

This article presents new methods for modeling the strength of association between multiple behaviors in a behavioral sequence, particularly those involving substantively important interaction patterns. Modeling and identifying such interaction patterns becomes more complex when behaviors are assigned to more than two categories, as is the case for most observational research. The authors propose multilevel empirical Bayes methods to overcome the challenges inherent in such data. Furthermore, these methods allow the study of how variation in interaction patterns can mediate the effects of antecedents or intervention on distal outcomes. New procedures are developed to compare alternative mediation models and pinpoint which random effects operate as mediators. These models are then applied to observational data taken from a study of the behavioral interactions of 254 couples

Mixture Joint Models for Event Time and Longitudinal Data With Multiple Features

<p>It often happens in longitudinal studies that repeated measurements of markers are observed with various data features of a heterogeneous population comprising of several subclasses, left-censoring due to a limit of detection (LOD) and covariates measured with error. Moreover, repeatedly measured markers in time may be associated with a time-to-event of interest. Inferential procedures may become very complicated when one analyzes data with these features together. This article explores a finite mixture of hierarchical joint models of event times and longitudinal measures with an attempt to alleviate departures from homogeneous characteristics, tailor observations below LOD as missing values, mediate accuracy from measurement error in covariate and overcome shortages of confidence in specifying a parametric time-to-event model with a nonparametric distribution. The Bayesian joint modeling is employed to not only estimate all parameters in mixture of joint models, but also evaluate probabilities of class membership. A real data example is analyzed to demonstrate the methodology by jointly modeling the viral dynamics and the time to decrease in CD4/CD8 ratio in the presence of CD4 cell counts with measurement error and the analytic results are reported by comparing potential models for various scenarios. Supplementary materials for this article are available online.</p

Morphological diversity of northeastern fat-tailed and northwestern thin-tailed indigenous sheep breeds of Ethiopia

Characterization of indigenous sheep breeds using morphological traits is essential for designing rational conservation and improvement strategies. This study was conducted to check the morphological diversity of three fat-tailed and three thin-tailed indigenous sheep breeds of Ethiopia. The phenotypic traits such as live body weight and linear body measurements (body length, wither height, chest girth, chest depth, rump height, rump length, ear length, tail length, and pelvic width) were measured and used for analysis. The statistical analysis was done using different procedures of SAS 9.4. Analysis of variance showed significant variation between breeds. Multivariate analyses clearly assigned the studied sheep breeds into distinct populations. Mahalanobis distance showed significant (p < 0.01) difference between breeds. The present morphometric information obtained could support future decision-making on the management, conservation, and improvement of the studied sheep genetic resources

Hierarchical modeling of sequential behavioral data: an empirical Bayesian approach

The authors review the common methods for measuring strength of contingency between 2 behaviors in a behavioral sequence, the binomial z score and the adjusted cell residual, and point out a number of limitations of these approaches. They present a new approach using log odds ratios and empirical Bayes estimation in the context of hierarchical modeling, an approach not constrained by these limitations. A series of hierarchical models is presented to test the stationarity of behavioral sequences, the homogeneity of sequences across a sample of episodes, and whether covariates can account for variation in sequences across the sample. These models are applied to observational data taken from a study of the behavioral interactions of 254 couples to illustrate their use