Impact of misspecifying spatial exposures in a generalized additive modeling framework: With application to the study of the dynamics of Comandra blister rust in British Columbia

In environmental and epidemiological studies, the nearest distance between the susceptible subject and the exposure source is a commonly used exposure measure, principally because this measure is easy to collect; more recently, the density of the exposure has been considered as a measure of exposure. However, no study has ever quantitatively compared nearest distance and density of exposures in any field. In particular, in the field of forestry, few studies have accounted for density-based exposure measures to disease pathogen, mostly due to the difficulty of measuring the spatial locations of disease host plants. Misspecification of exposure measures may result in inaccurate determinations of the link between exposure and the response of interest. Such considerations are motivated by the study of the disease dynamics of Comandra blister rust (Cronartium comandrae) on lodgepole pine. This disease spreads to pine trees through alternate host plants near the trees. We aim at understanding the relationship between the alternate host plant presence and the disease, as well as effects relating to genetic variation in the trees. We contrast the use of nearest distance to the alternate host plant, with host plant densities at different orders of neighborhood, as exposure measures, in the framework of a flexible semi-parametric generalized additive model, while adjusting for a spatially smooth surface. We demonstrate that if exposure is inaccurately modeled, then bias in estimating genetic effects may manifest themselves and larger predictive error may be induced.