Self-controlled case series studies: Just how rare does a rare non-recurrent outcome need to be?

The self-controlled case series method assumes that adverse outcomes arise according to a non-homogeneous Poisson process. This implies that it is applicable to independent recurrent outcomes. However, the self-controlled case series method may also be applied to unique, non-recurrent outcomes or first outcomes only, in the limit where these become rare. We investigate this rare outcome assumption when the self-controlled case series method is applied to non-recurrent outcomes. We study this requirement analytically and by simulation, and quantify what is meant by 'rare' in this context. In simulations we also apply the self-controlled risk interval design, a special case of the self-controlled case series design. To illustrate, we extract data on the incidence rate of some recurrent and non-recurrent outcomes within a defined study population to check whether outcomes are sufficiently rare for the rare outcome assumption to hold when applying the self-controlled case series method to first or unique outcomes. The main findings are that the relative bias should be no more than 5% when the cumulative incidence over total time observed is less than 0.1 per individual. Inclusion of age (or calendar time) effects will further reduce bias. Designs that begin observation with exposure maximise bias, whereas little or no bias will be apparent when there is no time trend in the distribution of exposures, or when exposure is central within time observed.