A spatiotemporal case‐crossover model of asthma exacerbation in the City of Houston

Case‐crossover design is a popular construction for analyzing the impact of a transient effect, such as ambient pollution levels, on an acute outcome, such as an asthma exacerbation. Case‐crossover design avoids the need to model individual, time‐varying risk factors for cases by using cases as their own ‘controls’, chosen to be time periods for which individual risk factors can be assumed constant and need not be modelled. Many studies have examined the complex effects of the control period structure on model performance, but these discussions were simplified when case‐crossover design was shown to be equivalent to various specifications of Poisson regression when exposure is considered constant across study participants. While reasonable for some applications, there are cases where such an assumption does not apply due to spatial variability in exposure, which may affect parameter estimation. This work presents a spatiotemporal model, which has temporal case‐crossover and a geometrically aware spatial random effect based on the Hausdorff distance. The model construction incorporates a residual spatial structure in cases when the constant assumption exposure is not reasonable and when spatial regions are irregular.