Smooth Risk Functions for Self-Controlled Case Series Models

Weldeselassie, Yonas Ghebremichael (2014). Smooth Risk Functions for Self-Controlled Case Series Models. PhD thesis The Open University.



The self-controlled case series (SCCS) method is commonly used to investigate associations between vaccine exposures and adverse events (side effects). It is an alternative to cohort and case control study designs. It requires information only on cases, individuals who have experienced the adverse event at least once, and automatically controls all fixed confounders that could modify the true association between exposure and adverse event. However, time-varying confounders (age, season) are not automatically controlled.

The SCCS method has parametric and semi-parametric versions in terms of controlling the age effect. The parametric method uses piecewise constant functions with a priori chosen age groups and the semi-parametric method leaves the age effect unspecified. Mis-specification of age groups in the parametric version may lead to biased estimates of the exposure effect, and the semi-parametric approach runs into computational problems when the sample size is moderately large. Moreover, both versions of SCCS represent 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.

This thesis focuses on extending the SCCS method to avoid the aforementioned limitations by modelling the age and exposure effects using flexible smooth functions. Specifically, we used penalised regression splines based on cubic M-splines, which are piecewise polynomials of degree 3. We developed three new extensions: a method that represents only the age effect with splines, a method that uses splines to model only the exposure effect and a non-parametric SCCS method that represents both effects by splines. Simulation studies showed that these new methods outperformed the parametric and semi-parametric methods. The new methods are illustrated using large data sets.

Review of SCCS vaccine studies and directions on how to use the method are also given.

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