Modeling of the Deaths Due to Ebola Virus Disease Outbreak in Western Africa
DOI:
https://doi.org/10.6000/1929-6029.2015.04.04.1Keywords:
Ebola Virus Disease, Conditional Autoregressive Model, Bayesian Analysis, Change-Point ModelAbstract
Problem: The recent 2014 Ebola virus outbreak in Western Africa is the worst in history. It is imperative that appropriate statistical and mathematical models are used to identify risk factors and to monitor the development and spread of the disease.
Method: Deaths data due to Ebola virus disease (EVD) in Guinea, Liberia, and Sierra Leone from October 10, 2014 to March 24, 2015 were collected via Situation Reports published by the World Health Organization [1]. Conditional autoregressive (CAR) models were applied to account for the spatial dependency in the countries along with the temporal dimension of the disease. Bayesian change-point models were used to identify key changes in growth and drop time points in the spatial distribution of deaths due to EVD within each country. Country-specific Poisson and negative binomial mixed models of covariate effects were applied to understand the between-country variability in deaths due to EVD.
Results: Both CAR models and generalized linear mixed models identified statistically significant covariate effects; however, the CAR models depended on the interval of data analyzed, whereas the mixed models depended on the underlying distribution assumed. Bayesian change-point models identified one significant change-point in the distribution of deaths due to EVD within each country.
Practical Application: CAR models, Bayesian change-point models, and generalized linear mixed models demonstrate useful techniques in modeling the incidence of deaths due to EVD.
References
World Health Organization [homepage on the Internet]. Ebola virus disease 2015. Available from: http://www.who.int/ mediacentre/factsheets/fs103/en/.
Dallatomasina S, Crestani R, Squire SS, Sylvester SJ, et al. Ebola outbreak in rural West Africa: epidemiology, clinical features and outcomes. Trop Med Int Health 2015; 20: 448-54. http://dx.doi.org/10.1111/tmi.12454 DOI: https://doi.org/10.1111/tmi.12454
McKinley T, Cook AR, Deardon R. Inference in epidemic models without likelihoods. The International Journal of Biostatistics 2009; 5(1): 1-40. http://dx.doi.org/10.2202/1557-4679.1171 DOI: https://doi.org/10.2202/1557-4679.1171
Lekone PE, Finkenstadt BF. Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 2006; 62: 1170-77. http://dx.doi.org/10.1111/j.1541-0420.2006.00609.x DOI: https://doi.org/10.1111/j.1541-0420.2006.00609.x
Millar RB. Comparison of hierarchical Bayesian models for overdispersed count data using DIC and Bayes’s factors. Biometrics 2009; 65: 962-69. http://dx.doi.org/10.1111/j.1541-0420.2008.01162.x DOI: https://doi.org/10.1111/j.1541-0420.2008.01162.x
Hossain MM, Lawson AB, Cai B, Choi J, Liu J, Kirby RS. Space-time areal mixture modeling: Relabeling algorithm and model selection issues. Environmetrics 2014; 25: 84-96. http://dx.doi.org/10.1002/env.2265 DOI: https://doi.org/10.1002/env.2265
Gardner W, Mulvey EP, Shaw EC. Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models. Psych Bulletin 1995; 118: 392-404. http://dx.doi.org/10.1037/0033-2909.118.3.392 DOI: https://doi.org/10.1037/0033-2909.118.3.392
Navarro A, Utzet F, Puig P, Caminal J, Martin M. Negative binomial distribution versus Poisson in the analysis of recurrent phenomena. Gaceta Sanitaria 2001; 15: 447-52. http://dx.doi.org/10.1016/S0213-9111(01)71599-3 DOI: https://doi.org/10.1016/S0213-9111(01)71599-3
Ng S, Basta NE, Cowling BJ. Association between temperature, humidity and ebolavirus disease outbreaks in Africa, 1976 to 2014. Euro Surveill 2014; 19: 1-11. http://dx.doi.org/10.2807/1560-7917.es2014.19.35.20892 DOI: https://doi.org/10.2807/1560-7917.ES2014.19.35.20892
Carlin BP, Louis TA. Bayesian methods for data analysis. 3rd ed. Boca Raton, FL: CRC Press 2009.
Lawson AB. Bayesian disease mapping: Hierarchical modeling in spatial epidemiology. 2nd ed. Boca Raton, FL: CRC Press 2013. DOI: https://doi.org/10.1201/b14073
Gelman A, Carlin J, Stern H, Rubin DB. Bayesian data analysis.3rd ed. London: Chapman & Hall 2013. DOI: https://doi.org/10.1201/b16018
Raudenbush SW, Bryk AS. Hierarchical linear models. 2nd ed. Thousand Oaks: Sage Publications 2002.
Lunn DJ, Thomas A, Best N, Spiegelhalter D. WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility. Stats Comp 2000; 10: 325-37. http://dx.doi.org/10.1023/A:1008929526011 DOI: https://doi.org/10.1023/A:1008929526011
Hawkins DM. Fitting multiple change-point models to data. Comp Stats Data Analysis 2001; 37: 323-41. http://dx.doi.org/10.1016/S0167-9473(00)00068-2 DOI: https://doi.org/10.1016/S0167-9473(00)00068-2
SAS Institute Inc. Base SAS® 9.3 Procedures Guide. Cary, NC: SAS Institute Inc., 2011.
Kiernan K, Tao J, Gibbs P. Tips and strategies for mixed modelling with SAS/STAT procedures. SAS 2012 Global Forum: Orlando, FL 2012.
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Copyright (c) 2015 Robert J. Milletich, Norou Diawara, Anna Jeng
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