The association between multidose vaccinations and death: comparing case series methods when the first exposure changes the general risk of an event

Abstract

Many case-control studies have shown a protective effect of vaccinations on the risk of sudden unexplained death (SUD). In this paper we compare the properties of different statistical methods in this situation, when the first vaccination appears to reduce the overall risk of an event (SUD). The first method is the self controlled case series (SCCS) method, which considers only subjects with an event during the observation time. This method yields unbiased estimates in the situation of non-censoring events. We show by simulation studies that the second method considered, the adjusted SCCS method, underestimates the parameter of interest, the effect of the first dose, when the general risk of SUD is lower in control periods after the first vaccination than in the period before vaccination. This type of bias could be eliminated by considering only cases who had received at least one vaccination. Additionally, we compare the adjusted SCCS method with the Cox model as a third method. Cox regression can take into account the time before the first vaccination, and this method yields unbiased estimates at modest effect sizes and short risk periods. We applied the SCCS method and Cox regression to data from the German study on sudden infant death (GeSID) and to a case series study from Italy (the HERA study) examining sudden unexpected deaths and vaccinations during the first 2 years of life. We show that the adjusted SCCS analysis with all cases underestimates the vaccination effect, as expected from the simulation analyses. Using Cox regression, we examined the general risk reduction after vaccination, as was the focus of the above mentioned studies. With a relative incidence of 0.8, our results were less pronounced than in the case-control analysis of the GeSID study (adjusted odds ratio: 0.51). SCCS analyses of both the GeSID and HERA studies yielded very similar estimates for the first and second vaccine doses.

Appendix

1.1 Definition of age classes

We derived the age classes included in adjusted SCCS models from the empirical age distribution of 318 GeSID cases divided into 21 age groups. Age class $k$ has as its upper limit the $k \times 4.76$th percentile of the distribution. This ensures that each class has nearly the same number of cases. The definition of the second interval [30.00–37.19) is $30.00 \le age_i < 37.19$. The round bracket indicates that the 37.19 is not included in the interval (Table 7).

Table 7 Definition of age classes in days from the GeSID study