Self-controlled case series method with smooth age effect

The self-controlled case series method, commonly used to investigate potential associations between vaccines and adverse events, requires information on cases only and automatically controls all age-independent multiplicative confounders while allowing for an age-dependent baseline incidence. In the parametric version of the method, we modelled the age-specific relative incidence by using a piecewise constant function, whereas in the semiparametric version, we left it unspecified. However, mis-specification of age groups in the parametric version can lead to biassed estimates of exposure effect, and the semiparametric approach runs into computational problems when the number of cases in the study is moderately large. We, thus, propose to use a penalized likelihood approach where the age effect is modelled using splines. We use a linear combination of cubic M-splines to approximate the age-specific relative incidence and integrated splines for the cumulative relative incidence. We conducted a simulation study to evaluate the performance of the new approach and its efficiency relative to the parametric and semiparametric approaches. Results show that the new approach performs equivalently to the existing methods when the sample size is small and works well for large data sets. We applied the new spline-based approach to data on febrile convulsions and paediatric vaccines. Co