Abstract
Malaria is a parasitic infectious tropical disease that causes high mortality rates in the tropical belt. In Venezuela, Sucre state is considered the third state with most disease prevalence. This paper presents a hierarchical regression log-Poisson space-time model within a Bayesian approach to represent the incidence of malaria in Sucre state, Venezuela, during the period 1990–2002 in 15 municipalities of the state. Several additive models for the logarithm of the relative risk of the disease for each district were considered. These models differ in their structure by including different combinations of social-economic and climatic covariates in a multiple regression term. A random effect that captures the spatial heterogeneity in the study region, and a CAR (Conditionally Autoregressive) component that recognizes the effect of nearby municipalities in the transmission of the disease each year, are also included in the model. A simpler version without including the CAR component was also fitted to the data. Model estimation and predictive inference was carried out through the implementation of a computer code in the WinBUGS software, which makes use of Markov Chain Monte Carlo (MCMC) methods. For model selection the criterion of minimum posterior predictive loss (D) was used. The Moran I statistic was calculated to test the independence of the residuals of the resulting model. Finally, we verify the model fit by using the Bayesian p-value, and in most cases the selected model captures the spatial structure of the relative risks among the neighboring municipalities each year. For years with a poor model fit, the t-Student distribution is used as an alternative model for the spatial local random effect with better fit to the tail behavior of the data probability distribution.
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http://portal.unesco.org/education/es/ev.php-URL_ID=36655&URL_DO=DO_TOPIC&URL_SECTION=201.html (2008). Accessed 20 November 2008
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Acknowledgements
Authors would like to acknowledge the National Fund of Scientific and Technological Research (FONACIT) for partially funding this research under the project. No. 2005-000184. We are also thankful to two anonymous referees for their thoughtful comments and suggestions in considerably improving an earlier version of this manuscript.
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Appendix
Appendix
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Posterior conditional distribution for α t
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Posterior conditional distribution for β t
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Posterior conditional distributions for each CAR effect b it
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Posterior conditional distribution for each random effect v it
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Posterior conditional distribution for τ bt
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Posterior conditional distribution for τ ht
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Villalta, D., Guenni, L., Rubio-Palis, Y. et al. Bayesian space-time modeling of malaria incidence in Sucre state, Venezuela. AStA Adv Stat Anal 97, 151–171 (2013). https://doi.org/10.1007/s10182-012-0190-9
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DOI: https://doi.org/10.1007/s10182-012-0190-9