Abstract
BackgroundA common, important problem in spatial epidemiology is measuring and identifying variation in disease risk across a study region. In application of statistical methods, the problem has two parts. First, spatial variation in risk must be detected across the study region and, second, areas of increased or decreased risk must be correctly identified. The location of such areas may give clues to environmental sources of exposure and disease etiology. One statistical method applicable in spatial epidemiologic settings is a generalized additive model (GAM) which can be applied with a bivariate LOESS smoother to account for geographic location as a possible predictor of disease status. A natural hypothesis when applying this method is whether residential location of subjects is associated with the outcome, i.e. is the smoothing term necessary? Permutation tests are a reasonable hypothesis testing method and provide adequate power under a simple alternative hypothesis. These tests have yet to be compared to other spatial statistics.ResultsThis research uses simulated point data generated under three alternative hypotheses to evaluate the properties of the permutation methods and compare them to the popular spatial scan statistic in a case-control setting. Case 1 was a single circular cluster centered in a circular study region. The spatial scan statistic had the highest power though the GAM method estimates did not fall far behind. Case 2 was a single point source located at the center of a circular cluster and Case 3 was a line source at the center of the horizontal axis of a square study region. Each had linearly decreasing logodds with distance from the point. The GAM methods outperformed the scan statistic in Cases 2 and 3. Comparing sensitivity, measured as the proportion of the exposure source correctly identified as high or low risk, the GAM methods outperformed the scan statistic in all three Cases.ConclusionsThe GAM permutation testing methods provide a regression-based alternative to the spatial scan statistic. Across all hypotheses examined in this research, the GAM methods had competing or greater power estimates and sensitivities exceeding that of the spatial scan statistic.
Highlights
A common, important problem in spatial epidemiology is measuring and identifying variation in disease risk across a study region
We evaluated four permutation tests applied with generalized additive model (GAM) to determine type I error rates and power estimates under simple hypotheses (Young, Weinberg, Vieira, Ozonoff, Webster: The Power of Hypothesis Testing Using Generalized Additive Models with Bivariate Smoothers, submitted) [11]
Detecting Exposure Source Locations We aimed to evaluate the ability of the GAM permutation tests and the spatial scan statistic to correctly identify the exposure source as high or low risk, i.e. the sensitivity of the methods
Summary
A common, important problem in spatial epidemiology is measuring and identifying variation in disease risk across a study region. Spatial variation in risk must be detected across the study region and, second, areas of increased or decreased risk must be correctly identified. The location of such areas may give clues to environmental sources of exposure and disease etiology. Webster et al (2006) used GAMs in spatial settings with a bivariate locally weighted regression (LOESS) smooth [5] and performed hypothesis tests using permutation techniques to determine whether there was spatial variation in disease risk and to locate statistically significant areas of increased or decreased risk [6]. Similar methods have been applied by other authors using tests based on permutation, bootstrap, and Monte Carlo techniques [7,8,9,10]
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