Use of Fixed Effects Models to Analyze Self-Controlled Case Series Data in Vaccine Safety Studies

Conditional Poisson models have been used to analyze vaccine safety data from self-controlled case series (SCCS) design. In this paper, we derived the likelihood function of fixed effects models in analyzing SCCS data and showed that the likelihoods from fixed effects models and conditional Poisson models were proportional. Thus, the maximum likelihood estimates (MLEs) of time-varying variables including vaccination effect from fixed effects model and conditional Poisson model were equal. We performed a simulation study to compare empirical type I errors, means and standard errors of vaccination effect coefficient, and empirical powers among conditional Poisson models, fixed effects models, and generalized estimating equations (GEE), which has been commonly used for analyzing longitudinal data. Simulation study showed that both fixed effect models and conditional Poisson models generated the same estimates and standard errors for time-varying variables while GEE approach produced different results for some data sets. We also analyzed SCCS data from a vaccine safety study examining the association between measles mumps-rubella (MMR) vaccination and idiopathic thrombocytopenic purpura (ITP). In analyzing MMR-ITP data, likelihood-based statistical tests were employed to test the impact of time-invariant variable on vaccination effect. In addition a complex semi-parametric model was fitted by simply treating unique event days as indicator variables in the fixed effects model. We conclude that theoretically fixed effects models provide identical MLEs as conditional Poisson models. Because fixed effect models are likelihood based, they have potentials to address methodological issues in vaccine safety studies such as how to identify optimal risk window and how to analyze SCCS data with misclassification of adverse events.