Bias in the Case--Crossover Design: Implications for Studies of Air Pollution

The case{crossover study design in principle allows testing for an acute health e ect of an exposure such as air pollution with restriction in time to remove seasonal confounding. We argue that much thinking about this design has been based on false analogies with matched case{control studies, and show that the usual design and analysis of case{crossover studies introduce a previously unrecognised bias by not conditioning correctly on the sampling scheme. We show that the usual conditional logistic regression analysis is a valid maximum likelihood method for a simple modi cation of the case{crossover design that divides time into strata. However, the bias from standard case{crossover designs will typically be small.