Technical note: The calculated real world BNT162b2 vaccine efficacy was 88% when accounting for asymptomatic cases

ABSTRACT

COVID-19 trials have relied on symptomatic subjects for judging the effectiveness of vaccine candidates, whereas asy–mptomatic subjects have been suspected as the main driver of the pandemic. An assumption of the same impact on symptomatic and asymptomatic breakthrough infections is shown to be flawed, resulting in an overestimate of the vaccines’ true effectiveness. Recent available data provide the first large-scale unbiased data on asymptomatic versus symptomatic infections postvaccination, providing a unique opportunity to reassess the true infection rates after vaccination. By this, the breakthrough of the BNT162b2 vaccine is seen to be 12% rather than 5% for a corrected overall efficiency (symptomatic + asymptomatic) of 88% with the original virus strain in a real-world setting.

Introduction

The article by Angel et al.¹ provided the first available unbiased data on asymptomatic versus symptomatic infections postvaccination by a real-world routine screening protocol in an observational cohort study. Because all vaccine trials have relied on symptomatic subjects for judging infections, these data provide a unique opportunity to reassess the true infection rates after vaccination. Whereas high-intensity exposure settings have shown greater susceptibility to vaccine breakthrough² that is further exacerbated by the high R0 of the delta variant that is currently prevalent,³ the principle of how to calculate a total infection rate from symptomatic incidence with asymptomatic ratio data is demonstrated. With new variants, the method for calculation is the same.

Methods

Ratios of symptomatic (S) to asymptomatic (A) cases in the Angel et al. study¹ are derived mathematically from the vaccinated and unvaccinated cohorts. Total infections are calculated as T = S + A. When applied to the Pfizer BNT162b2 data, these cohort ratios are employed to derive the relative infection rates for the vaccinated and unvaccinated in the registration trial to derive a new rate. Relevant formulas are displayed in text. These data were based primarily on the early variants while the delta variant was not yet abundant.

Results

Reexamination of the data of Angel et al.¹ reveals that vaccination reverses the ratio of infections from predominantly symptomatic (S) among the nonvaccinated (nv; S/A 38/17, R = 2.24) to predominantly asymptomatic (A) among the vaccinated (v; A/S 19/8, R = 2.38) (p < .001 by Fisher exact test).

In contrast, the registration trial for the Pfizer vaccine used in this study performed PCR solely on symptomatic subjects to estimate 5% breakthrough versus control (Sv/Snv) for a 95% efficiency.⁴ With recognition of asymptomatic infections (total, T = S + A), a total breakthrough rate (Tv/Tnv) is derived:

$\mathit{Tv}/\mathit{Tnv}=\left(\mathit{Sv}+\mathit{Av}\right)/\left(\mathit{Snv}+\mathit{Anv}\right)=\left(1+\mathit{Av}/\mathit{Sv}\right)/\left(1+\mathit{Anv}/\mathit{Snv}\right)\ast \mathit{Sv}/\mathit{Snv}=\left(1+2.38\right)/\left(1+1/2.24\right)\ast 5\mathrm{\%}=2.34\ast 5\mathrm{\%}$

This calculates to a net 12% post-vaccination infection rate versus control, increased by 234% versus the prior promulgated estimate of 5%, for a reduced overall efficiency of 1−Tv/Tnv = 88%. Put another way, whereas vaccine reduces symptomatic infections by 95% to 5% or 20-fold versus nonvaccinated (Sv/Snv), vaccine reduces asymptomatic infections to a lesser degree, by 73% to 27% or just 2.7-fold versus nonvaccinated (Av/Anv = (Tv/Tnv)*(1-Sv/Tv)/(1-Snv/Tnv)).^a

It is likely that A/S ratios for other vaccines will also flip based on the milder clinical profiles for infections postvaccination, for this and other viruses.⁵ By extension, therefore, for other vaccines with efficiencies based on symptomatic subjects (e.g., Sv/Snv of 5–30%),⁶ the total breakthrough adjusted for asymptomatic subjects (Tv/Tnv), increased by the same factor of 2.34, would be 12–70%, with corresponding efficiencies of 88% to 30% (1−Tv/Tnv).

Discussion

The key observation is that vaccination induces a striking reversal of the ratios of symptomatic to asymptomatic subjects for a net 5.3-fold shift, from 2.24 ratio in favor of symptomatic to 2.38 ratio in favor of asymptomatic after vaccination. While not surprising, as vaccine breakthroughs are typically less severe,⁵ and while these changing ratios were not the focus of the Angel et al. study,¹ these data do offer a unique opportunity to refine our perception of the vaccine’s true rate of protection.

For the period of January–April 2021, the CDC reported >7500 symptomatic breakthrough infections among 101 million fully vaccinated individuals,⁷ which would be >25,000 when accounting for asymptomatics (Tv = Sv*(1 + Av/Sv) = Sv*3.38). (These data predated the delta variant.) It is widely held that asymptomatic subjects have been the stealth driver of the pandemic, in some studies not differing from symptomatic by culture positivity or PCR cycle threshold (Ct), and by inference, with no lesser capacity to transmit infection,⁸ an adjustable model parameter that is intrinsic to the calculated group R0. Whether or not the same fully applies to vaccinated subjects in breakthrough, it remains highly probable that this large asymptomatic group with mucosal viral RNA is infectious at some level for which maintaining preventive measures remains relevant. By these calculations, therefore, it is a reasonable speculation that the high proportions of asymptomatic breakthroughs in combination with complacency among the vaccinated may be contributing to the current surges in cases in the United States and Europe, where vaccination is prevalent.

In conclusion, it is highly relevant to recognize the substantial breakthrough hidden in the expanded asymptomatic group for calculating postvaccination risk in pandemic models and for informing public policy.

Disclosure statement

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Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.

Notes

[a] This model predicts a vaccine-mediated absolute increase in actual numbers of asymptomatic cases versus control (Av/Anv > 1) for vaccines with symptomatic breakthroughs (Sv/Snv) significantly above 20% (calculations not shown). This prediction is corroborated generally by numerically more asymptomatic cases in vaccinated than unvaccinated in the two months postvaccination in the ChAdOx study where vaccine efficiency was lower (Supplementary Table 7 “Voysey, ChAdOx (22)” in ref.⁶).