Statistics and Its Interface

Volume 5 (2012)

Number 2

Likelihood-based estimation of spatial intensity and variation in disease risk from locations observed with error

Pages: 207 – 219



Xiangming Fang (Department of Biostatistics, East Carolina University, Greenville, N.C., U.S.A.)

Peng Sun (Merck Research Laboratories, Merck and Co., North Wales, Pennsylvania, U.S.A.)

Dale L. Zimmerman (Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Ia., U.S.A.)


The accurate assignment of geocodes to the residences of subjects in a study population is an important component of the data acquisition/assimilation stage of many spatial epidemiological investigations. Unfortunately, however, when residential address geocoding is performed by the most common method of street-segment matching to a georeferenced road file and subsequent interpolation, positional errors of hundreds of meters are commonplace, especially in rural locations. Ignoring these errors in a statistical analysis may lead to biased estimators, a reduction in power, and incorrect conclusions. This article develops modifications to existing likelihood-based procedures for estimating the intensity of a Poisson spatial point process and the relative risk function relating two such processes, from locations ascertained without error, so as to permit valid inferences to be made from locations observed with error. The performance of the modified methods relative to methods that ignore positional errors is investigated by simulation. The methodology is applied to respiratory disease data from an Iowa county. Our investigation indicates that the magnitude of the positional error standard deviation relative to the rate of change in intensity or relative risk across the study area determines whether an analysis that accounts for positional errors will improve upon an analysis that does not; errors must be sufficiently large for an improvement to be realized.


case-control data, geocode, location uncertainty, Poisson process, positional accuracy, spatial epidemiology

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