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Bayesian Zero-Inflated Negative Binomial Regression Based on Polya-Gamma Mixtures.

ABSTRACT: Motivated by a study examining spatiotemporal patterns in inpatient hospitalizations, we propose an efficient Bayesian approach for fitting zero-inflated negative binomial models. To facilitate posterior sampling, we introduce a set of latent variables that are represented as scale mixtures of normals, where the precision terms follow independent Pólya-Gamma distributions. Conditional on the latent variables, inference proceeds via straightforward Gibbs sampling. For fixed-effects models, our approach is comparable to existing methods. However, our model can accommodate more complex data structures, including multivariate and spatiotemporal data, settings in which current approaches often fail due to computational challenges. Using simulation studies, we highlight key features of the method and compare its performance to other estimation procedures. We apply the approach to a spatiotemporal analysis examining the number of annual inpatient admissions among United States veterans with type 2 diabetes.

SUBMITTER: Neelon B

PROVIDER: S-EPMC7880198 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature

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Bayesian Zero-Inflated Negative Binomial Regression Based on Pólya-Gamma Mixtures.

Neelon Brian B

Bayesian analysis 20190611 3

Motivated by a study examining spatiotemporal patterns in inpatient hospitalizations, we propose an efficient Bayesian approach for fitting zero-inflated negative binomial models. To facilitate posterior sampling, we introduce a set of latent variables that are represented as scale mixtures of normals, where the precision terms follow independent Pólya-Gamma distributions. Conditional on the latent variables, inference proceeds via straightforward Gibbs sampling. For fixed-effects models, our ap ...[more]

PMID: 33584949

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Project description:The Research Center for Human Development in Dakar (CRDH) with the technical assistance of ICF Macro and the National Malaria Control Programme (NMCP) conducted in 2008/2009 the Senegal Malaria Indicator Survey (SMIS), the first nationally representative household survey collecting parasitological data and malaria-related indicators. In this paper, we present spatially explicit parasitaemia risk estimates and number of infected children below 5 years. Geostatistical Zero-Inflated Binomial models (ZIB) were developed to take into account the large number of zero-prevalence survey locations (70%) in the data. Bayesian variable selection methods were incorporated within a geostatistical framework in order to choose the best set of environmental and climatic covariates associated with the parasitaemia risk. Model validation confirmed that the ZIB model had a better predictive ability than the standard Binomial analogue. Markov chain Monte Carlo (MCMC) methods were used for inference. Several insecticide treated nets (ITN) coverage indicators were calculated to assess the effectiveness of interventions. After adjusting for climatic and socio-economic factors, the presence of at least one ITN per every two household members and living in urban areas reduced the odds of parasitaemia by 86% and 81% respectively. Posterior estimates of the ORs related to the wealth index show a decreasing trend with the quintiles. Infection odds appear to be increasing with age. The population-adjusted prevalence ranges from 0.12% in Thillé-Boubacar to 13.1% in Dabo. Tambacounda has the highest population-adjusted predicted prevalence (8.08%) whereas the region with the highest estimated number of infected children under the age of 5 years is Kolda (13940). The contemporary map and estimates of malaria burden identify the priority areas for future control interventions and provide baseline information for monitoring and evaluation. Zero-Inflated formulations are more appropriate in modeling sparse geostatistical survey data, expected to arise more frequently as malaria research is focused on elimination.

Project description:BACKGROUND:Combined with the increasing life expectancy, chronic medical conditions have gradually become the dominant cause of death and disability, and multimorbidity became an increasingly serious public health challenge. However, most existing studies have focused on the coexistence of specific diseases or relatively few diseases. Given one person may have multiple diseases at the same time, we applied Charlson Comorbidity Index (CCI) to systematically evaluate one's 10-year mortality. In this study, we explored the effects of nutrients and physical activity on CCI using National Health and Nutrition Examination Survey (NHANES) 2013-2014 data. METHODS:The study sample consists of one continuous cycle (2013-2014) of NHANES, and 4386 subjects were included in the study. Nutrients intake was measured by dietary recall, and physical activity was evaluated by the Global Physical Activity Questionnaire respectively. Besides, CCI was the sum of the scores assigned for each medical condition. We utilized zero-inflated negative binomial (ZINB) model to investigate the effects in nutrients intake and physical activity on CCI by adjusting for seven sociodemographic characteristics, smoking and drinking. RESULTS:Among the 4386 participants, 2018 (68.7%) are Non-Hispanic White, over half participants (78.6%) drink. In count part (CCI???0), holding other variables constant, the expected change in CCI for a one-unit increase in niacin is 1.621(RR?=?1.621, p?=?0.016), in lutein + zeaxanthin is 0.974 (RR?=?0.974, p?=?0.031), and in sedentary time is 1.035 (RR?=?1.035, p?=?0.005). Moreover, those who do not have vigorous work activity would be more likely to have higher CCI than those who have (RR?=?1.275, P?=?0.045). In logit part (CCI?=?0), the log odds of having CCI equals zero would increase by 0.541 and 0.708 for every additional vigorous recreational activity (OR?=?0.541, p?=?0.004) and moderate recreational activity (OR?=?0.708, p?=?0.017) respectively. CONCLUSIONS:Lutein and zeaxanthin intake, vigorous work activity, vigorous recreational activity and moderate recreational activity may be good for one's health. Rather, increasing niacin intake and sedentary activity may be likely to raise 10-year mortality. Our findings may be significant for preventing diseases and improving health, furthermore, reducing people's financial burden on healthcare.

Dataset Information

Bayesian Zero-Inflated Negative Binomial Regression Based on Polya-Gamma Mixtures.

Publications

Bayesian Zero-Inflated Negative Binomial Regression Based on Pólya-Gamma Mixtures.

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