Estimation of the adjusted risk difference for very rare events, large samples, and extreme exposure frequency:...

The post-authorization safety study of a vaccine is an important public health task, and its results contribute to the decisions about whether to recommend a vaccination by estimating not only the risk ratio but also the risk difference. There are few reports of adjusted risk differences. We evaluated the statistical performance of the adjusted risk difference and its variance under a post-authorization safety study's settings (rare events, large sample, extreme exposure frequency).

Adjusted risk differences were estimated using ordinary least squares estimators in a linear regression model with a binary outcome, and their variances were estimated using the standard error from ordinary least squares and four types of robust variance. In a simulation, we evaluated the risk differences' performances using bias, coverage, and power and using data from the Vaccine Effectiveness, Networking, and Universal Safety study as an example of an actual post-authorization safety study.

The adjusted risk difference using ordinary least squares was not biased. Compared to the ordinary least squares' standard error, the robust variance achieved more appropriate coverage and higher power. With actual data, including 2 × 2 tables of exposure and outcome with zero, both the ordinary least squares and robust variance could be estimated.

In post-authorization safety study settings, the estimation of the risk difference using ordinary least squares and robust variance showed better performance than the typical ordinary least squares. These findings may prove beneficial for reporting risk difference in extreme settings such as post-authorization safety studies.