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A Generalized Linear Modeling Approach for Characterizing Disease Incidence in a Spatial Hierarchy

Several statistical models are introduced to quantify the effect of heterogeneity on disease incidence relationships in a three-scale spatial hierarchy: the sampling unit level (highest), the leaf scale (intermediate), and the leaflet scale (lowest). The models are an extension of the theory previously developed for a two-scale hierarchy and were tested using data collected from strawberry leaf blight epidemics. Disease incidence at the sampling-unit scale (proportion of sampling units with one or more diseased leaflets) increased as a saturation-type curve with increasing leaflet or leaf disease incidence (proportion of leaflets or leaves diseased) as predicted by the good fit of the beta-binomial distribution to the leaflet and leaf data. The relationship could be accurately described, without curve fitting, by several simple nonlinear models, in which the aggregation of disease was represented by a modified binomial function incorporating an effective sample size that was either constant or dependent on mean incidence. The relationship between incidence at the leaflet and leaf scales could be modeled based on the combined sampling-unit models for leaflets and leaves. By taking the complementary log-log (CLL) transformation of incidence, the equations could be expressed as generalized linear models, and curve fitting used to estimate the parameters. Generally, curve fitting gave slight to no improvement in the accuracy of the predictions of incidence. These models have broad applicability in sampling for disease incidence, and results can be used to interpret how diseased individuals at the lowest level in a hierarchy are arranged within sampling units.