Flexible modelling of vaccine effect in self-controlled case series models

The self-controlled case series (SCCS) method, commonly used to investigate the safety of vaccines, requires information on cases only and automatically controls all age-independent multiplicative confounders, while allowing for an age-dependent baseline incidence. Currently, the SCCS method represents the time-varying exposures using step functions with pre-determined cut points. A less prescriptive approach may be beneficial when the shape of the relative risk function associated with exposure is not known a priori, especially when exposure effects can be long-lasting. We therefore propose to model exposure effects using flexible smooth functions. Specifically, we used a linear combination of cubic M-splines which, in addition to giving plausible shapes, avoids the integral in the log-likelihood function of the SCCS model. The methods, though developed specifically for vaccines, are applicable more widely. Simulations showed that the new approach generally performs better than the step function method. We applied the new method to two data sets, on febrile convulsion and exposure to MMR vaccine, and on fractures and thiazolidinedione use.