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

Shahn, Hernan, and Robins give conditions under which estimates from a case-crossover analysis converge to the desired causal relative risk times a bias factor, and they discuss conditions needed to have small bias. To simplify the problem, we discuss only two exposure times and rely on randomized exposure assignments, thereby avoiding the need for potential outcome notation. We identify many, but not all, of the conditions discussed by Shahn et al. in this simple analysis.