Discussion on "A formal causal interpretation of the case-crossover design" by Zach Shahn, Miguel A. Hernán, and James M. Robins.

It has always been clear that the case-crossover design works, for some definition of "works," but some of the details have been surprisingly elusive, and it is good to see more of them nailed down by Shahn et al. My interest in case-crossover analyses has mostly been in the context of air pollution epidemiology mentioned at the end of the paper. The air pollution setting is distinctive for several reasons: as the exposure variable is plausibly exogenous, it is possible to use control times after the case time, the effects of interest are quite small, and the same measured exposure series is shared over many-perhaps all-of the cohort.