Case-crossover analyses of air pollution exposure data - Referent selection strategies and their implications for bias

The case-crossover design has been widely used to study the association between short-term air pollution exposure and the risk of an acute adverse health event. The design uses cases only; for each individual case, exposure just before the event is compared with exposure at other control (or "referent") times. Time-invariant confounders are controlled by making within-subject comparisons. Even more important in the air pollution setting is that time-varying confounders can also be controlled by design by matching referents to the index time. The referent selection strategy is important for reasons in addition to control of confounding. The case-crossover design makes the implicit assumption that there is no trend in exposure across the referent times. In addition, the statistical method that is used-conditional logistic regression-is unbiased only with certain referent strategies. We review here the case-crossover literature in the air pollution context, focusing on key issues regarding referent selection. We conclude with a set of recommendations for choosing a referent strategy with air pollution exposure data. Specifically, we advocate the time-stratified approach to referent selection because it ensures unbiased conditional logistic regression estimates, avoids bias resulting from time trend in the exposure series, and can be tailored to match on specific time-varying confounders.