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.

中文翻译：

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休斯顿市哮喘加重的时空病例交叉模型

病例交叉设计是一种流行的结构，用于分析瞬时效应（如环境污染水平）对急性结果（如哮喘发作）的影响。案例交叉设计通过使用案例作为他们自己的“控制”来避免对案例的个体、随时间变化的风险因素进行建模，选择作为个体风险因素可以假设为恒定且无需建模的时间段。许多研究已经检查了控制期结构对模型性能的复杂影响，但是当研究参与者的暴露被认为是恒定的时，当案例交叉设计被证明等同于泊松回归的各种规格时，这些讨论被简化了。虽然对于某些应用来说是合理的，在某些情况下，由于暴露的空间可变性，这种假设不适用，这可能会影响参数估计。这项工作提出了一个时空模型，该模型具有时间案例交叉和基于 Hausdorff 距离的几何感知空间随机效应。在恒定假设暴露不合理和空间区域不规则的情况下，模型构建包含剩余空间结构。