{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T09:37:09Z","timestamp":1787564229960,"version":"build-2736575974"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2015,8,28]],"date-time":"2015-08-28T00:00:00Z","timestamp":1440720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJERPH"],"abstract":"<jats:p>Epidemiological data often include excess zeros. This is particularly the case for data on rare conditions, diseases that are not common in specific areas or specific time periods, and conditions and diseases that are hard to detect or on the rise. In this paper, we provide a review of methods for modeling data with excess zeros with focus on count data, namely hurdle and zero-inflated models, and discuss extensions of these models to data with spatial and spatio-temporal dependence structures. We consider a Bayesian hierarchical framework to implement spatial and spatio-temporal models for data with excess zeros. We further review current implementation methods and computational tools. Finally, we provide a case study on five-year counts of confirmed cases of Lyme disease in Illinois at the county level.<\/jats:p>","DOI":"10.3390\/ijerph120910536","type":"journal-article","created":{"date-parts":[[2015,9,1]],"date-time":"2015-09-01T10:55:58Z","timestamp":1441104958000},"page":"10536-10548","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":58,"title":["Spatial and Spatio-Temporal Models for Modeling Epidemiological Data with Excess Zeros"],"prefix":"10.3390","volume":"12","author":[{"given":"Ali","family":"Arab","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Georgetown University, 37th and O streets, Washington, DC 20057, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,8,28]]},"reference":[{"key":"ref_1","unstructured":"Lawson, A.B. (2013). Statistical Methods in Spatial Epidemiology, John Wiley & Sons."},{"key":"ref_2","unstructured":"Cohen, A. Estimation in mixtures of discrete distributions. Proceedings of the International Symposium on Discrete Distributions, Montreal, QC, Canada."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1269547","article-title":"Zero-inflated Poisson regression with an application to defects in manufacturing","volume":"34","author":"Lambert","year":"1992","journal-title":"Technometrics"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hilbe, J.M. (2014). Modeling Count Data, Cambridge University Press.","DOI":"10.1017\/CBO9781139236065"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"829","DOI":"10.2307\/1909582","article-title":"Some statistical models for limited dependent variables with application to the demand for durable goods","volume":"39","author":"Cragg","year":"1971","journal-title":"Econometrica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/0304-4076(86)90002-3","article-title":"Specification and testing of some modified count data models","volume":"33","author":"Mullahy","year":"1986","journal-title":"J. Econom."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cameron, A.C., and Trivedi, P.K. (1998). Regression Analysis of Count Data, Cambridge University Press.","DOI":"10.1017\/CBO9780511814365"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1289\/ehp.6735","article-title":"Spatial epidemiology: Current approaches and future challenges","volume":"112","author":"Elliott","year":"2004","journal-title":"Environ. Health Perspect."},{"key":"ref_9","unstructured":"Berliner, L.M. (1996). Maximum Entropy and Bayesian Methods, Kluwer Academic Publishers."},{"key":"ref_10","unstructured":"Arab, A., Hooten, M.B., and Wikle, C.K. (2008). Encyclopedia of GIS, Springer Science & Business Media."},{"key":"ref_11","unstructured":"Cressie, N., and Wikle, C.K. (2011). Statistics for Spatio-temporal Data, John Wiley & Sons."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Banerjee, S., Carlin, B.P., and Gelfand, A.E. (2015). Hierarchical Modeling and Analysis for Spatial Data, CRC Press. [2nd ed.].","DOI":"10.1201\/b17115"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wikle, C.K., and Anderson, C.J. (2003). Climatological analysis of tornado report counts using a hierarchical Bayesian spatiotemporal model. J. Geophys. Res. Atmos., 108.","DOI":"10.1029\/2002JD002806"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1020910605990","article-title":"Zero-inflated models with application to spatial count data","volume":"9","author":"Agarwal","year":"2002","journal-title":"Environ. Ecol. Stat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1111\/j.1467-985X.2012.01039.x","article-title":"A spatial Poisson hurdle model for exploring geographic variation in emergency department visits","volume":"176","author":"Neelon","year":"2013","journal-title":"J. Roy. Stat. Soc. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1080\/02664763.2012.750286","article-title":"Predicting infectious disease outbreak risk via migratory waterfowl vectors","volume":"40","author":"Oleson","year":"2013","journal-title":"J. Appl. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.sste.2011.08.001","article-title":"Spatio-temporal modeling of sparse geostatistical malaria sporozoite rate data using a zero inflated binomial model","volume":"2","author":"Amek","year":"2011","journal-title":"Spat. Spatiotemporal Epidemiol."},{"key":"ref_18","first-page":"86","article-title":"Bayesian analysis of zero inflated spatiotemporal HIV\/TB child mortality data through the INLA and SPDE approaches: Applied to data observed between 1992 and 2010 in rural North East South Africa","volume":"22","author":"Musenge","year":"2013","journal-title":"Int. J. Appl. Earth Obs."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Cressie, N. (1993). Statistics for Spatial Data: Wiley Series in Probability and Statistics, John Wiley & Sons.","DOI":"10.1002\/9781119115151"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1002\/env.1142","article-title":"Semiparametric bivariate zero-inflated Poisson models with application to studies of abundance for multiple species","volume":"23","author":"Arab","year":"2012","journal-title":"Environmetrics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1111\/j.1467-9868.2008.00700.x","article-title":"Approximate Bayesian inference for latent Gaussian models by using integratednested Laplace approximations","volume":"71","author":"Rue","year":"2009","journal-title":"J. Roy. Stat. Soc. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.sste.2013.07.003","article-title":"Spatial and spatio-temporal models with R-INLA","volume":"7","author":"Blangiardo","year":"2013","journal-title":"Spat. Spatiotemporal Epidemiol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1111\/biom.12227","article-title":"A Bayesian approach to estimate the biomass of anchovies off the coast of Per\u00fa","volume":"71","author":"Quiroz","year":"2015","journal-title":"Biometrics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1111\/1467-9868.00353","article-title":"Bayesian measures of model complexity and fit","volume":"64","author":"Spiegelhalter","year":"2002","journal-title":"J. Roy. Stat. Soc. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1038\/nrmicro2714","article-title":"Of ticks, mice and men: understanding the dual-host lifestyle of Lyme disease spirochaetes","volume":"10","author":"Radolf","year":"2012","journal-title":"Nat. Rev. Microbial."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.idc.2015.02.010","article-title":"Epidemiology of Lyme disease","volume":"29","author":"Mead","year":"2015","journal-title":"Infect. Dis. Clin. North Am."},{"key":"ref_27","unstructured":"Center for Disease Control and Prevention: Reported Cases of Lyme Disease by State or Locality, 2004\u20132013, Available online: http:\/\/www.cdc.gov\/lyme\/stats\/chartstables\/reportedcases_statelocality.html."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.envres.2014.08.041","article-title":"Variability in results from negative binomial models for lyme disease measured at different spatial scales","volume":"136","author":"Tran","year":"2015","journal-title":"Environ. Res."},{"key":"ref_29","unstructured":"Lindgren, F., and Rue, H. Bayesian Spatial and Spatiotemporal Modelling with R-INLA. Available online: http:\/\/inla.googlecode.com\/hg-history\/5cba347753615e2bfdab62141acd4d6e858136bd\/r-inla.org\/papers\/jss\/lindgren.pdf."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"320","DOI":"10.4269\/ajtmh.2012.11-0395","article-title":"Human risk of infection with Borrelia burgdorferi, the Lyme disease agent, in Eastern United States","volume":"86","author":"Hoen","year":"2012","journal-title":"Am. J. Trop. Med. 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