A Statistical Argument Against Vaccine Injury

Vaccine hesitancy is a major threat to public health. While the root causes of vaccine hesitancy are numerous, they largely revolve around some form of perceived risk to the self. In particular, the unknown long-term risks are amongst the most frequently cited concerns. In this work, we show that regardless of their peak onset following vaccination, the incidence of adverse outcomes will follow some distribution f ( x | µ, σ 2 ) of mean onset µ , and standard deviation σ , and variance σ 2 . Despite the small proportion of events at the tails of these distributions, the large-scale public deployment of vaccines would imply that any signal for a given adverse outcome would be observed soon after distribution begins, even in cases where t x < t µ− 3 σ . The absence of such an early signal, however low, would suggest that long term effects are unlikely and that vaccine safety is therefore likely. Indeed, when enough individuals have been exposed to a new therapy - even if the majority of adverse outcomes only manifest at a future time t µ , the number of adverse outcomes given by the cumulative density function (CDF) near t 0 + dt > 0. Otherwise stated: We evoke the theory behind normal (Gaussian) and skew-normal distributions and use Chebyshev’s Theorem to evaluate the COVID-19 vaccine data as an example. The findings of this study are not vaccine-specific and can be applied to assess the health effects of the mass distribution of any good, treatment or policy at large.