Relationships between several quadrat-based statistical measures used to characterize spatial aspects of disease incidence data

This article investigates the relationships between various statistical mea sures that are used to summarize spatial aspects of disease incidence data. The focus is on quadrat data in which each plant in a quadrat is classifie d as diseased or healthy. We show that spatial autocorrelation plays a cent ral role via the mean intraclass correlation, p, which is defined as the av erage correlation of the disease status of all pairs of plants within the q uadrat. The value of p determines the variance of the number of infected pl ants in the quadrat and, if this variable follows a beta-binomial distribut ion, the heterogeneity parameter of the beta-binomial distribution is direc tly related to the mean intraclass correlation. We consider in detail a mod el in which the spatial autocorrelation depends only on the distance betwee n the plants. For illustration, we consider a specific autocorrelation mode l that was derived from simulated data. We show that this model leads, appr oximately, to the binary form of the power law relating the variance of the number of infected plants per quadrat to the mean. Using an approximation technique, we then show how the index of dispersion is related to quadrat s ize and shape. The index of dispersion increases with quadrat size. The rat e of increase is dependent on quadrat shape, but the effect of quadrat shap e is small in comparison to the effect of quadrat size. Finally, we note th at if the spatial autocorrelation depends on the relative orientation of th e plants, as well as the distance between them, there are connections with distance class methods.