Abstract
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.
Highlights
The association between particular adverse events following immunization (AEFI) and receipt of a specific vaccine has been studied using large electronically-linked health care utilization databases [1,2,3,4,5,6,7,8]
We demonstrate that the likelihoods from the fixed effects model and the conditional Poisson model are proportional when analyzing self-controlled case series (SCCS) data
We show that by simulation, fixed effects models and conditional Poisson models typically used for SCCS data analysis are equivalent in estimating vaccination effects
Summary
The association between particular adverse events following immunization (AEFI) and receipt of a specific vaccine has been studied using large electronically-linked health care utilization databases [1,2,3,4,5,6,7,8]. Since individuals in observational settings such as the VSD are not randomly chosen to be vaccinated, vaccinated and unvaccinated individuals may differ greatly and possibly in ways related to the outcome of interest This confounding bias, if not accounted for properly, may invalidate analytic results of cohort studies. Traditional study designs such as matched cohort and case-control designs may not even be feasible for studying vaccine safety because 1) the coverage of some vaccines is nearly 100%, so there are not enough unvaccinated individuals to use for the control group; and 2) data are not collected in safety surveillance system for those who did not experience/report an adverse event (eg, the Vaccine Adverse Event Reporting System) For these reasons, a method known as the selfcontrolled case series (SCCS) has been developed and widely used for vaccine safety studies [7,8,9,10,11]. By making within-person comparisons of incidence rates between vaccine exposed and unexposed time intervals, conditional Poisson models implicitly adjust for all time-invariant individual-level risk factors and potential confounders (measured and not measured)
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