Improved Spatial-Temporal CAR Models for Dengue Fever Incidence: Evidence from Banyumas

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Jajang, Mashuri, Novita Eka Chandra, Budi Pratikno

Abstract

In the last six years, dengue fever cases in Banyumas Regency in 2024 were very high.  The relative risk (RR) of dengue hemorrhagic fever (DHF) is of interest. In this paper, we proposed the Spatial Temporal-Conditional Autoregressive (ST-CAR) model to analyze the association of DHF with related factors. In addition, we improve the model with offset modification on ST-CAR.  The results of research showed that the best ST-CAR model was the interaction of intrinsic CAR and independent identically distributed temporal effects.  In addition, the offset modification in the ST-CAR model resulted in the smallest Watanabe-Akaike Information Criterion (WAIC).  Based on the study's findings, the two highest RR from year to year are located not far from the city center (North Purwokerto) and the tourist attraction (Baturaden). Both locations are often associated with higher risk factors such as population density and greater social interaction, which facilitate transmission.

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References

  1. D. Lee, A. Rushworth, S.K. Sahu, A Bayesian Localized Conditional Autoregressive Model for Estimating the Health Effects of Air Pollution, Biometrics 70 (2014), 419-429. https://doi.org/10.1111/biom.12156.
  2. A. Aswi, S. Cramb, E. Duncan, K. Mengersen, Evaluating the Impact of a Small Number of Areas on Spatial Estimation, Int. J. Health Geogr. 19 (2020), 39. https://doi.org/10.1186/s12942-020-00233-1.
  3. M.R. Desjardins, M.D. Eastin, R. Paul, I. Casas, E.M. Delmelle, Space–Time Conditional Autoregressive Modeling to Estimate Neighborhood-Level Risks for Dengue Fever in Cali, Colombia, Am. J. Trop. Med. Hyg. 103 (2020), 2040-2053. https://doi.org/10.4269/ajtmh.20-0080.
  4. A. Wubuli, F. Xue, D. Jiang, X. Yao, H. Upur, et al., Socio-Demographic Predictors and Distribution of Pulmonary Tuberculosis (TB) in Xinjiang, China: A Spatial Analysis, PLOS ONE 10 (2015), e0144010. https://doi.org/10.1371/journal.pone.0144010.
  5. S. Mclafferty, Disease Cluster Detection Methods: Recent Developments and Public Health Implications, Ann. GIS 21 (2015), 127-133. https://doi.org/10.1080/19475683.2015.1008572.
  6. T.A. Nelson, B. Boots, Detecting Spatial Hot Spots in Landscape Ecology, Ecography 31 (2008), 556-566. https://doi.org/10.1111/j.0906-7590.2008.05548.x.
  7. S. Ahmed, A. Hussein, M. Al-Momani, Efficient Estimation for the Conditional Autoregressive Model, J. Stat. Comput. Simul. 85 (2014), 2569-2581. https://doi.org/10.1080/00949655.2014.893346.
  8. Q. Zeng, H. Wen, S. Wong, H. Huang, Q. Guo, et al., Spatial Joint Analysis for Zonal Daytime and Nighttime Crash Frequencies Using a Bayesian Bivariate Conditional Autoregressive Model, J. Transp. Saf. Secur. 12 (2018), 566-585. https://doi.org/10.1080/19439962.2018.1516259.
  9. X. Han, L. Lee, Bayesian Estimation and Model Selection for Spatial Durbin Error Model with Finite Distributed Lags, Reg. Sci. Urban Econ. 43 (2013), 816-837. https://doi.org/10.1016/j.regsciurbeco.2013.04.006.
  10. J. Hendricks, C. Neumann, A Bayesian Approach for the Analysis of Error Rate Studies in Forensic Science, Forensic Sci. Int. 306 (2020), 110047. https://doi.org/10.1016/j.forsciint.2019.110047.
  11. Y. Cheng, J. Norris, C. Bao, Q. Liang, J. Hu, et al., Geographical Information Systems-Based Spatial Analysis and Implications for Syphilis Interventions in Jiangsu Province, People’s Republic of China, Geospat. Health 7 (2012), 63. https://doi.org/10.4081/gh.2012.105.
  12. Z. Peng, Y. Cheng, K.H. Reilly, L. Wang, et al., Spatial Distribution of HIV/AIDS in Yunnan Province, People’s Republic of China, Geospat. Health 5 (2011), 177. https://doi.org/10.4081/gh.2011.169.
  13. J. Aldstadt, A. Getis, Using AMOEBA to Create a Spatial Weights Matrix and Identify Spatial Clusters, Geogr. Anal. 38 (2006), 327-343. https://doi.org/10.1111/j.1538-4632.2006.00689.x.
  14. Jajang, B. Pratikno, M. Nusrang, Analysis of the W-Amoeba Getis and Moran on Spatial Dynamic Panel Models, Far East J. Math. Sci. 102 (2017), 655-667. https://doi.org/10.17654/ms102040655.
  15. A. Adin, T. Goicoa, M.D. Ugarte, Online Relative Risks/rates Estimation in Spatial and Spatio-Temporal Disease Mapping, Comput. Methods Programs Biomed. 172 (2019), 103-116. https://doi.org/10.1016/j.cmpb.2019.02.014.
  16. N. Cressie, Statistics for Spatial Data, John Wiley & Sons, 2015.
  17. S. Banerjee, B.P. Carlin, A.E. Gelfand, S. Banerjee, Hierarchical Modeling and Analysis for Spatial Data, Chapman and Hall/CRC, 2003. https://doi.org/10.1201/9780203487808.
  18. K. Ben-Ahmed, A. Bouratbine, M. El-Aroui, Generalized Linear Spatial Models in Epidemiology: A Case Study of Zoonotic Cutaneous Leishmaniasis in Tunisia, J. Appl. Stat. 37 (2009), 159-170. https://doi.org/10.1080/02664760802684169.
  19. Y. Wang, X. Chen, F. Xue, A Review of Bayesian Spatiotemporal Models in Spatial Epidemiology, ISPRS Int. J. Geo-Inf. 13 (2024), 97. https://doi.org/10.3390/ijgi13030097.
  20. P. McCullagh, Generalized Linear Models, Routledge, 2019.
  21. J. Besag, Spatial Interaction and the Statistical Analysis of Lattice Systems, J. R. Stat. Soc. Ser. B: Stat. Methodol. 36 (1974), 192-225. https://doi.org/10.1111/j.2517-6161.1974.tb00999.x.
  22. D. De Witte, A.A. Abad, G. Molenberghs, G. Verbeke, L. Sanchez, et al., A Multivariate Spatio-Temporal Model for the Incidence of Imported COVID-19 Cases and COVID-19 Deaths in Cuba, Spat. Spatio-temporal Epidemiol. 45 (2023), 100588. https://doi.org/10.1016/j.sste.2023.100588.
  23. M. Morris, K. Wheeler-Martin, D. Simpson, S.J. Mooney, A. Gelman, et al., Bayesian Hierarchical Spatial Models: Implementing the Besag York Mollié Model in Stan, Spat. Spatio-temporal Epidemiol. 31 (2019), 100301. https://doi.org/10.1016/j.sste.2019.100301.
  24. J. Jajang, B. Pratikno, M. Mashuri, I.E. Cahyarini, The Dengue Hemorrhagic Fever Modeling in Banyumas Regency by Using Car-Bym, Generalized Poisson, and Negative Binomial, in: Advances in Physics Research, Atlantis Press, Paris, France, 2022. https://doi.org/10.2991/apr.k.220503.007.
  25. A. Mozdzen, A. Cremaschi, A. Cadonna, A. Guglielmi, G. Kastner, Bayesian Modeling and Clustering for Spatio-Temporal Areal Data: An Application to Italian Unemployment, Spat. Stat. 52 (2022), 100715. https://doi.org/10.1016/j.spasta.2022.100715.
  26. L. Mariella, M. Tarantino, Spatial Temporal Conditional Auto-Regressive Model: A New Autoregressive Matrix, Austrian J. Stat. 39 (2016), 223-244. https://doi.org/10.17713/ajs.v39i3.246.
  27. A. Aswi, S. Rahardiantoro, A. Kurnia, B. Sartono, D. Handayani, et al., Bayesian Spatio-Temporal Conditional Autoregressive Localized Modeling Techniques for Socioeconomic Factors and Stunting in Indonesia, MethodsX 15 (2025), 103464. https://doi.org/10.1016/j.mex.2025.103464.
  28. A. Adin, T. Goicoa, M.D. Ugarte, Online Relative Risks/rates Estimation in Spatial and Spatio-Temporal Disease Mapping, Comput. Methods Programs Biomed. 172 (2019), 103-116. https://doi.org/10.1016/j.cmpb.2019.02.014.
  29. S.K. Sahu, D. Böhning, Bayesian Spatio-Temporal Joint Disease Mapping of COVID-19 Cases and Deaths in Local Authorities of England, Spat. Stat. 49 (2022), 100519. https://doi.org/10.1016/j.spasta.2021.100519.
  30. A. Urdangarin, T. Goicoa, P. Congdon, M. Ugarte, A Fast Approach for Analyzing Spatio-Temporal Patterns in Ischemic Heart Disease Mortality Across US Counties (1999–2021), Spat. Spatio-Temp. Epidemiol. 52 (2025), 100700. https://doi.org/10.1016/j.sste.2024.100700.
  31. L. Knorr‐Held, Bayesian Modelling of Inseparable Space‐Time Variation in Disease Risk, Stat. Med. 19 (2000), 2555-2567. https://doi.org/10.1002/1097-0258(20000915/30)19:17/18<2555::aid-sim587>3.0.co;2-#.
  32. M. Blangiardo, M. Cameletti, G. Baio, H. Rue, Spatial and Spatio-Temporal Models with R-Inla, Spat. Spatio-Temp. Epidemiol. 4 (2013), 33-49. https://doi.org/10.1016/j.sste.2012.12.001.