Analyzing longitudinal clustered count data with zero inflation: Marginal modeling using the Conway–Maxwell–Poisson distribution

Kang, Tong; Levy, Steven M.; Datta, Somnath

doi:10.1002/bimj.202000061

Cited by 5 publications

(6 citation statements)

References 35 publications

(53 reference statements)

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“…It provides a novel development to the cross‐sectional analysis in Choo‐Wosoba et al, 20 which did not take the temporal information of IFS data across multiple dental visits into consideration. Our approach also has three major advantages over our previous longitudinal zero‐inflated GEE approach 25 . First, a hurdle model provides more straightforward interpretation for risk and protective factors than a zero‐inflated model in the dental example, as there is only one source of zero scores (ie, healthy teeth).…”

Section: Discussionmentioning

confidence: 99%

“…With regard to marginal regression modeling, Choo‐Wosoba et al 24 developed a clustered zero‐inflated CMP approach to analyze the IFS data at a single time point. In a previous work, we proposed a novel extension of their GEE approach to multiple time points 25 . In the present article, we use a Bayesian GLMM approach to analyze the longitudinal data using a more structured correlation matrix, which can be physically interpreted.…”

Section: Introductionmentioning

confidence: 99%

“…In a previous work, we proposed a novel extension of their GEE approach to multiple time points. 25 In the present article, we use a Bayesian GLMM approach to analyze the longitudinal data using a more structured correlation matrix, which can be physically interpreted. For example, teeth belonging to the same individual exhibit certain correlation due to shared environmental factors.…”

Section: Introductionmentioning

confidence: 99%

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A longitudinal Bayesian mixed effects model with hurdle Conway‐Maxwell‐Poisson distribution

Kang

Gaskins

Levy

et al. 2020

Statistics in Medicine

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Dental caries (i.e., cavities) is one of the most common chronic childhood diseases and may continue to progress throughout a person's lifetime. The Iowa Fluoride Study (IFS) was designed to investigate the effects of various fluoride, dietary and nondietary factors on the progression of dental caries among a cohort of Iowa school children. We develop a mixed effects model to perform a comprehensive analysis of the longitudinal clustered data of IFS at ages 5, 9, 13, and 17. We combine a Bayesian hurdle framework with the Conway‐Maxwell‐Poisson regression model, which can account for both excessive zeros and various levels of dispersion. A hierarchical shrinkage prior distribution is used to share the temporal information for predictors in the fixed‐effects model. The dependence among teeth of each individual child is modeled through a sparse covariance structure of the random effects across time. Moreover, we obtain the parameter estimates and credible intervals from a Gibbs sampler. Simulation studies are conducted to assess the accuracy and effectiveness of our statistical methodology. The results of this article provide novel tools to statistical practitioners and offer fresh insights to dental researchers on effects of various risk and protective factors on caries progression.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A longitudinal Bayesian mixed effects model with hurdle Conway‐Maxwell‐Poisson distribution

Kang

Gaskins

Levy

et al. 2020

Statistics in Medicine

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“…The goal of the IFS was to study the associations between various dietary and non-dietary factors and two outcomes of interest: dental fluorosis (spots on teeth) and dental caries (cavities) for a cohort of Iowa school children. Previous studies have focused on the dental caries outcome, [14][15][16][17] and here, we focus on methodology for the fluorosis outcome. The fluorisis data are a longitudinal and multilevel clustered ordinal outcome.…”

Section: Introductionmentioning

confidence: 99%

Analyzing dental fluorosis data using a novel Bayesian model for clustered longitudinal ordinal outcomes with an inflated category

Kang

Gaskins

Levy

et al. 2022

Statistics in Medicine

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We propose a Bayesian hurdle mixed‐effects model to analyze longitudinal ordinal data under a complex multilevel structure. This research was motivated by the dataset gathered from the Iowa Fluoride Study (IFS) in order to establish the relationships between fluorosis status and potential risk/protective factors. Dental fluorosis is characterized by spots on tooth enamel and is due to ingestion of excessive fluoride intake during enamel formation. Observations are collected from multiple surface zones on each tooth and on all available teeth of children from the studied cohort, which are longitudinally observed at ages 9, 13, and 17. The data not only exhibit a complex hierarchical structure, but also have a large proportion of zero values that are likely to follow different statistical patterns from non‐zero categories. Therefore, we develop a hurdle model to consider the zero category separately, while a proportional odds model is used for the positive categories. The estimated parameters are obtained from a Gibbs sampler implemented by the OpenBUGS software. Our model is compared with two popular methods for ordinal data: the proportional odds model and the partial proportional odds model. We perform a comprehensive analysis of the IFS data and evaluate the accuracy and effectiveness of our methodology through simulation studies. Our discoveries provide novel insights to statisticians and dental practitioners about the associations between patient and clinical characteristics and dental fluorosis.

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“…The model was used to analyze the number of seizures experienced by epileptic patients and to study the freshwater invertebrate offspring born counts in an aquatic toxicology experiment. Recent contributions on the analysis of clustered count data are due to Choo-Wosoba et al (2016, and Kang et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Poisson-Birnbaum-Saunders Regression Model for Clustered Count Data

Gonçalves¹,

Barreto‐Souza²,

Ombao³

2022

Preprint

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The premise of independence among subjects in the same cluster/group often fails in practice, and models that rely on such untenable assumption can produce misleading results. To overcome this severe deficiency, we introduce a new regression model to handle overdispersed and correlated clustered counts. To account for correlation within clusters, we propose a Poisson regression model where the observations within the same cluster are driven by the same latent random effect that follows the Birnbaum-Saunders distribution with a parameter that controls the strength of dependence among the individuals. This novel multivariate count model is called Clustered Poisson Birnbaum-Saunders (CPBS) regression. As illustrated in this paper, the CPBS model is analytically tractable, and its moment structure can be explicitly obtained. Estimation of parameters is performed through the maximum likelihood method, and an Expectation-Maximization (EM) algorithm is also developed. Simulation results to evaluate the finite-sample performance of our proposed estimators are presented. We also discuss diagnostic tools for checking model adequacy. An empirical application concerning the number of inpatient admissions by individuals to hospital emergency rooms, from the Medical Expenditure Panel Survey (MEPS) conducted by the United States Agency for Health Research and Quality, illustrates the usefulness of our proposed methodology.

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Analyzing longitudinal clustered count data with zero inflation: Marginal modeling using the Conway–Maxwell–Poisson distribution

Cited by 5 publications

References 35 publications

A longitudinal Bayesian mixed effects model with hurdle Conway‐Maxwell‐Poisson distribution

A longitudinal Bayesian mixed effects model with hurdle Conway‐Maxwell‐Poisson distribution

Analyzing dental fluorosis data using a novel Bayesian model for clustered longitudinal ordinal outcomes with an inflated category

Poisson-Birnbaum-Saunders Regression Model for Clustered Count Data

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