Underestimating the effects of spatial heterogeneity due to individual movement and spatial scale: infectious disease as an example
- 528 Downloads
Many ecological and epidemiological studies occur in systems with mobile individuals and heterogeneous landscapes. Using a simulation model, we show that the accuracy of inferring an underlying biological process from observational data depends on movement and spatial scale of the analysis. As an example, we focused on estimating the relationship between host density and pathogen transmission. Observational data can result in highly biased inference about the underlying process when individuals move among sampling areas. Even without sampling error, the effect of host density on disease transmission is underestimated by approximately 50 % when one in ten hosts move among sampling areas per lifetime. Aggregating data across larger regions causes minimal bias when host movement is low, and results in less biased inference when movement rates are high. However, increasing data aggregation reduces the observed spatial variation, which would lead to the misperception that a spatially targeted control effort may not be very effective. In addition, averaging over the local heterogeneity will result in underestimating the importance of spatial covariates. Minimizing the bias due to movement is not just about choosing the best spatial scale for analysis, but also about reducing the error associated with using the sampling location as a proxy for an individual’s spatial history. This error associated with the exposure covariate can be reduced by choosing sampling regions with less movement, including longitudinal information of individuals’ movements, or reducing the window of exposure by using repeated sampling or younger individuals.
KeywordsSource-sink metapopulation Epidemiological model Observational bias Disease transmission Host density Modifiable areal unit problem
We thank M. Ebinger for help with the figures. PCC’s work was supported by U.S. Geological Survey, the NSF/NIH Ecology of Infectious Disease program DEB-1067129 and some ideas stem from working groups sponsored by the NIH/DHS funded RAPIDD program. DC’s work was supported by NSF Grant DEB-0749097 to L.A. Meyers. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.
- Anderson RM, May RM (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, OxfordGoogle Scholar
- Ferrari MJ, Perkins SE, Pomeroy LW, Bjørnstad ON (2011) Pathogens, social networks, and the paradox of transmission scaling. Interdiscip Perspect Infect Dis 267049Google Scholar
- Gehlke CE, Biehl K (1934) Certain effects of grouping upon the size of the correlation coefficient in census tract material. J Am Stat Assoc 24:169–170Google Scholar
- Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, CambridgeGoogle Scholar
- Greig-Smith P (1952) Use of random and contiguous quadrats in the study of the structure of plant communities. Ann Bot 16:293–316Google Scholar
- Halloran ME, Ferguson NM, Eubank S, Longini IM, Cummings DA, Lewis B, Xu S, Fraser C, Vullikanti A, Germann TC, Wagener D, Beckman R, Kadau K, Barrett C, Macken CA, Burke DS, Cooley P (2008) Modeling targeted layered containment of an influenza pandemic in the United States. Proc Natl Acad Sci USA 105(12):4639–4644PubMedCrossRefGoogle Scholar
- Openshaw S (1984) The modifiable areal unit problem. Concepts and techniques in modern geography 38. GeoBooks, NorwichGoogle Scholar
- R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
- Soetaert K, Petzoldt T, Setzer RW (2010) Solving differential equations in R: package deSolve. J Stat Softw 33(9):1–25Google Scholar
- Woodroffe R, Donnelly CA, Wei G, Cox DR, Bourne FJ, Burke T, Butlin RK, Cheeseman CL, Gettinby G, Gilks P, Hedges S, Jenkins HE, Johnston WT, McInerney JP, Morrison WI, Pope LC (2009) Social group size affects Mycobacterium bovis infection in European badgers (Meles meles). J Anim Ecol 78(4):818–827PubMedCrossRefGoogle Scholar