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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.

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.

Similar Datasets

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