When assessing quantitatively the benefit/risk (or risk/benefit) ratio for any therapeutic intervention, two simple numerical standards are employed: the number needed to treat (NNT) to prevent a single health outcome of interest, and the number needed to harm (NNH), or each adverse event caused by the same therapy, per the number to whom it is administered (1). Both NNT and NNH are dependent on absolute risk differences between the treated and untreated comparison groups. The NNT/NNH or NNH/NNT, provide quantitative estimates of the benefit/risk, or risk/benefit ratios, respectively.
The question of whether to mandate covid-19 vaccination of previously SARS-CoV-2 infected healthcare workers can be uniquely illuminated by calculating NNT and NNH from recently published data (2,3). Moreover, as I will demonstrate, the NNT/NNH calculations from these published findings (2,3) are independently validated by Rhode Island Department of Health July, 2021 data just released August 31, 2021 (4,5).
Data from the Israeli Maccabi Health Maintenance Organization (HMO) have revealed that prior SARS-CoV-2 infection among those unvaccinated against covid-19 conferred a 7.0-fold decreased risk for new clinical, symptomatic SARS-CoV-2 infection, and a 6.7-fold lower risk for covid-19 hospitalization, relative to those with no prior SARS-CoV-2 infection, but fully vaccinated against covid-19 (2). Although secondary analyses from this Israeli HMO cohort found, similarly, that covid-19 vaccination of previously SARS-CoV-2 infected persons did not reduce either symptomatic, clinical SARS-CoV-2 infections, or covid-19 hospitalizations, the occurrence of asymptomatic SARS-CoV-2 infections was reduced (2). This latter finding can be used to calculate the NNT for prevention of new, asymptomatic SARS-CoV-2 infections, afforded by covid-19 vaccinating those previously infected with SARS-CoV-2, and recovered from their infection.
The NNT for asymptomatic infection prevention, using the absolute risk reductions, is calculated as follows, from the formula, NNT=1/absolute risk reduction: 37/14,029=0.0026 in the unvaccinated, previously infected, vs. 20/14,029=0.0014, in the vaccinated, previously infected. The absolute risk difference is a mere 0.0012 so 1/ 0.0012 gives a NNT of 833 to prevent 1 asymptomatic infection. (Also, the absolute risk reduction is only 0.12%; another way of expressing this vanishingly small benefit)
NNH can be calculated from published United Kingdom Healthcare worker survey data comparing the reactions of those covid-19 vaccinated with and without prior SARS-CoV-2 infection (3). The proportion reporting one moderate to severe symptom was higher in the previous SARS-CoV-2 infected group (56% v 47%, OR=1.5 [95%CI, 1.1–2.0], p=.009), with fever, fatigue, myalgia-arthralgia and lymphadenopathy significantly more common. NNH is 56%-47%=9%, or 0.09, then 1/0.09=11.1. Thus, for each ~11 previously SARS-CoV-2 infected healthcare workers vaccinated, 1 developed a “moderate to severe symptom,” including “fever, fatigue, myalgia-arthralgia and lymphadenopathy (3).”
Comparing the NNT (from 2)/ NNH (from 3) ratio, 883/11, indicates that if you covid-19 vaccinated n=883 previously SARS-CoV-2 infected persons (for example, healthcare workers), ONE asymptomatic SARS-CoV-2 infection would be prevented, while EIGHTY persons vaccinated would experience “moderate to severe symptoms,” including “fever, fatigue, myalgia-arthralgia and lymphadenopathy.
Finally, July, 2021 SARS-CoV-2 (covid-19) infection data collected by the Rhode Island Department of Health, with presentation of the findings by both vaccination, and prior infection status, provide independent validation of these NNT/NNH results (4,5). While 30% of these total (n=2127) new SARS-CoV-2 infections occurred among persons fully covid-19 vaccinated (639/2127), only 3.4% of those with a prior infection, regardless of vaccination status, were infected in July (73/2127). Fully vaccinating those with a prior covid-19 infection did not lower this percentage at all (22/639=3.4% fully vaccinated; 51/1488=3.4% not fully vaccinated).
2) Gazit S, Shlezinger R, Perez G, Lotan R, Peretz A, Ben-Tov A, Cohen D, Muhsen K, Chodick G, Patalon T. “Comparing SARS-CoV-2 natural immunity to vaccine-induced immunity: reinfections versus breakthrough infections”. medRxiv August 24,2021. https://doi.org/10.1101/2021.08.24.21262415
3) “Self-reported real-world safety and reactogenicity of COVID-19 vaccines: An international vaccine-recipient survey”. Mathioudakis AG, Ghrew M, Ustianowski A, Ahmad S, Borrow R, Papavasileiou LP, Petrakis D, Bakerly ND medRxiv, February 26, 2021. https://doi.org/10.1101/2021.02.26.21252096
4) “Prior infection, vaccination status, and age-stratified Rhode Island Department of Health, July 2021 data on covid-19 infections, hospitalizations, and deaths sent to Sen. Delacruz and Rep. Chippendale, 8/31/21”. https://www.andrewbostom.org/2021/09/prior-infection-vaccination-status-and-age-stratified-rhode-island-department-of-health-july-2021-data-on-covid-19-infections-hospitalizations-and-deaths-sent-to-sen-delacruz-and-rep-chippendal/
5) “Rhode Island Department of Health, July 2021, Data Reveal Prior Covid-19 Infection in the Unvaccinated (Natural Immunity)~8.5-Fold More Protective Against New Covid-19 Infections, and ~1.5-Fold More Protective Against Covid-19 Hospitalizations, Vs. Full Vaccination, Without Prior Infection”. https://www.andrewbostom.org/2021/09/rhode-island-department-of-health-july-2021-data-reveal-prior-covid-19-infection-in-the-unvaccinated-natural-immunity8-5-fold-more-protective-against-new-covid-19-infections-and-1-5-fold-more-p/