Bayesian Analysis of Doubly Inflated Poisson Regression for Correlated Count Data: Application to DMFT Data

Outcome variables in clinical studies sometimes include count data with inflation in two points (usually zero and k (k>0)). Doubly inflated models can be adopted for modeling these types of data. In statistical modeling, the association among subjects due to longitudinal or cluster study designs is considered by random effects models. In this article, we proposed a doubly inflated random effects model using the Bayesian approach for correlated count data with inflation in two values, and compared this model with Bayesian zero-inflated Poisson and Bayesian Poisson models. The parameters’ estimates by these models were obtained by Markov Chain Monte Carlo method using OpenBUGS software. Bayesian models were compared using the deviance information criterion. To this end, we utilized the total number of decayed, missed, and filled teeth of 12-year-old children and also conducted a simulation study.  Results of real data and the simulation study revealed that the proposed model is fitted better than previous models.&nbsp

Bayesian Variable Selection for Multivariate Spatially Varying Coefficient Regression

Physical activity has many well-documented health benefits for cardiovascular fitness and weight control. For pregnant women, the American College of Obstetricians and Gynecologists currently recommends 30 minutes of moderate exercise on most, if not all, days; however, very few pregnant women achieve this level of activity. Traditionally, studies have focused on examining individual or interpersonal factors to identify predictors of physical activity. There is a renewed interest in whether characteristics of the physical environment in which we live and work may also influence physical activity levels. We consider one of the first studies of pregnant women that examines the impact of characteristics of the built environment on physical activity levels. Using a socioecologic framework, we study the associations between physical activity and several factors including personal characteristics, meteorological/air quality variables, and neighborhood characteristics for pregnant women in four counties of North Carolina. We simultaneously analyze six types of physical activity and investigate cross-dependencies between these activity types. Exploratory analysis suggests that the associations are different in different regions. Therefore we use a multivariate regression model with spatially-varying regression coefficients. This model includes a regression parameter for each covariate at each spatial location. For our data with many predictors, some form of dimension reduction is clearly needed. We introduce a Bayesian variable selection procedure to identify subsets of important variables. Our stochastic search algorithm determines the probabilities that each covariate’s effect is null, non-null but constant across space, and spatially-varying. We found that individual level covariates had a greater influence on women’s activity levels than neighborhood environmental characteristics, and some individual level covariates had spatially-varying associations with the activity levels of pregnant women

Marginalized two-part models for semicontinuous data with application to medical costs

In health services research, it is common to encounter semicontinuous data characterized by a point mass at zero followed by a right-skewed continuous distribution with positive support. Examples include health expenditures, in which the zeros represent a subpopulation of patients who do not use health services, while the continuous distribution describes the level of expenditures among health services users. Semicontinuous data are typically analyzed using two-part mixture models that separately model the probability of health services use and the distribution of positive expenditures among users. However, because the second part conditions on a nonzero response, conventional two-part models do not provide a marginal interpretation of covariate effects on the overall population of health service users and non-users, even though this is often of greatest interest to investigators. Here, we propose a marginalized two-part model that yields more interpretable effect estimates in two-part models by parameterizing the model in terms of the marginal mean. This model maintains many of the important features of conventional two-part models, such as capturing zero-inflation and skewness, but allows investigators to examine covariate effects on the overall marginal mean, a target of primary interest in many applications. Using a simulation study, we examine properties of the maximum likelihood estimators from this model. We illustrate the approach by evaluating the effect of a behavioral weight loss intervention on health care expenditures in the Veterans Affairs (VA) health care system. We then extend this marginalized two-part model to clustered or longitudinal data structures by incorporating random effects. This longitudinal marginalized two-part model is fit following a fully Bayesian approach with non-informative or weakly informative prior distributions, and we illustrate it by analyzing the effect of a copayment increase in the VA health system. Finally, using simulation studies, we compare the performance of the marginalized two-part model to commonly used one-part generalized linear models (GLMs) fit via quasi-likelihood estimation over a range of simulated data scenarios with varying percentages of zero-valued observations.Doctor of Public Healt

Statistical Modelling of Breastfeeding Data

This thesis addresses some key methodological problems in statistical modelling of breastfeeding data. Meta-analysis techniques were used to analyse aggregated breastfeeding data. Generalised linear mixed model and an extended Cox model were used with time-varying exposures to analyse longitudinal and time-to-event breastfeeding data, respectively. Shared frailty models were applied to correlated breastfeeding duration data controlling for heterogeneity. A novel two-part mixed-effects model was proposed for modelling clustered time-to-event breastfeeding data with clumping at zero

Augmented Mixed Beta Regression Models For Periodontal Proportion Data

Continuous (clustered) proportion data often arise in various domains of medicine and public health where the response variable of interest is a proportion (or percentage) quantifying disease status for the cluster units, ranging between zero and one. However, because of the presence of relatively disease-free as well as heavily diseased subjects in any study, the proportion values can lie in the interval [0,1]. While beta regression can be adapted to assess covariate effects in these situations, its versatility is often challenged because of the presence/excess of zeros and ones because the beta support lies in the interval (0,1). To circumvent this, we augment the probabilities of zero and one with the beta density, controlling for the clustering effect. Our approach is Bayesian with the ability to borrow information across various stages of the complex model hierarchy and produces a computationally convenient framework amenable to available freeware. 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