Bias correction of risk estimates in vaccine safety studies with rare adverse events using a self-controlled case series design

Am J Epidemiol. 2013 Dec 15;178(12):1750-9. doi: 10.1093/aje/kwt211. Epub 2013 Sep 27.


The self-controlled case series (SCCS) method is often used to examine the temporal association between vaccination and adverse events using only data from patients who experienced such events. Conditional Poisson regression models are used to estimate incidence rate ratios, and these models perform well with large or medium-sized case samples. However, in some vaccine safety studies, the adverse events studied are rare and the maximum likelihood estimates may be biased. Several bias correction methods have been examined in case-control studies using conditional logistic regression, but none of these methods have been evaluated in studies using the SCCS design. In this study, we used simulations to evaluate 2 bias correction approaches-the Firth penalized maximum likelihood method and Cordeiro and McCullagh's bias reduction after maximum likelihood estimation-with small sample sizes in studies using the SCCS design. The simulations showed that the bias under the SCCS design with a small number of cases can be large and is also sensitive to a short risk period. The Firth correction method provides finite and less biased estimates than the maximum likelihood method and Cordeiro and McCullagh's method. However, limitations still exist when the risk period in the SCCS design is short relative to the entire observation period.

Keywords: bias correction; penalized maximum likelihood; rare events; self-controlled case series; simulation study; vaccine safety.

Publication types

  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Bias
  • Case-Control Studies
  • Computer Simulation*
  • Humans
  • Incidence
  • Models, Theoretical*
  • Research Design
  • Risk Assessment
  • Vaccines / adverse effects*


  • Vaccines