Over the last three decades, case-crossover designs have found many applications in health sciences, especially in air pollution epidemiology. They are typically used, in combination with partial likelihood techniques, to define a conditional logistic model for the responses, usually health outcomes, conditional on the exposures. Despite the fact that conditional logistic models have been shown equivalent, in typical air pollution epidemiology setups, to specific instances of the well-known Poisson time series model, it is often claimed that they cannot allow for overdispersion. This paper clarifies the relationship between case-crossover designs, the models that ensue from their use, and overdispersion. In particular, we propose to relax the assumption of independence between individuals traditionally made in case-crossover analyses, in order to explicitly introduce overdispersion in the conditional logistic model. As we show, the resulting overdispersed conditional logistic model coincides with the overdispersed, conditional Poisson model, in the sense that their likelihoods are simple re-expressions of one another. We further provide the technical details of a Bayesian implementation of the proposed case-crossover model, which we use to demonstrate, by means of a large simulation study, that standard case-crossover models can lead to dramatically underestimated coverage probabilities, while the proposed models do not. We also perform an illustrative analysis of the association between air pollution and morbidity in Toronto, Canada, which shows that the proposed models are more robust than standard ones to outliers such as those associated with public holidays.

翻译：过去三十年间，病例交叉设计在健康科学领域（尤其是空气污染流行病学）得到了广泛应用。这类设计通常与偏似然技术相结合，用以构建以暴露为条件的条件逻辑模型，用于刻画健康结局等响应变量。尽管在典型空气污染流行病学设定中，条件逻辑模型已被证明等价于著名泊松时间序列模型的特定形式，但常有人声称其无法处理过度离散性。本文厘清了病例交叉设计、由其推导的模型与过度离散性之间的关系。具体而言，我们建议放宽病例交叉分析中个体间相互独立的传统假设，从而在条件逻辑模型中显式引入过度离散性。研究显示，由此得到的过度离散条件逻辑模型与过度离散条件泊松模型在似然函数互为简单重表达的意义上具有一致性。我们进一步提供了所提出病例交叉模型的贝叶斯实现技术细节，并通过大规模模拟研究证明：标准病例交叉模型可能导致覆盖率概率严重低估，而本模型则无此问题。此外，我们以加拿大多伦多市空气污染与发病率的关联分析为例证，表明所提模型对节假日等异常值的鲁棒性优于标准模型。