key: cord-0854841-l4l1296e
authors: Guerriero, Vincenzo; Carriero, Flavia; Terrazzano, Giuseppe
title: Fast COVID-19 vaccine effectiveness estimation on the basis of recovered individual propensity to be vaccinated
date: 2021-11-09
journal: Public Health
DOI: 10.1016/j.puhe.2021.10.014
sha: 0d1afb4a9004bdb683904c435d3f42592a0a456e
doc_id: 854841
cord_uid: l4l1296e

nan

recovered individuals; Conditional probability of being vaccinated given recovery Since March 2020, the study of COVID-19 pandemic contagion data is perceived as relevant by a wide audience composed not only of epidemiologists and specialized personnel but also of press offices, independent agencies and ordinary people. There is therefore a strong need to provide clear information, understandable to a wide unspecialized public. Vaccine efficacy, in terms of risk reducing of infection/hospitalization/death, is usually estimated by the Government Centers for Disease Control (CDC) through multivariate analysis [e.g. 1, 2], however these statistical methods are often incomprehensible to the general public. In order to provide immediate information to the general (unqualified) public, the CDCs of different nations [e.g. 3, 4, 5] , as well as several prestigious press offices [e.g. 6], have published epidemiological data and statistics on dedicated web pages and dashboards.

The main purpose of this article is to point out to the CDCs of the various governments, as well as to independent agencies and press offices, the need and advantages of correcting incidence data of the infection, as well as to propose a practical equation to calculate vaccine effectiveness, based on the count of recovered subjects who have not yet been vaccinated. This equation can be used to accompany data on infection incidence aimed at the general public, as well as an "easy-to-access" formula to be used for the 

where R = Nv / Nn.

In the proposed equation, the contagion reduction risk (RRR in case of vaccine, EG in case of recovery) may be defined as the value, averaged over the population and a time interval, of the relative reduction in probability of contracting the infection at each contact or occasion of contagion.

The propensity of recovered individuals to undergo vaccination, is affected by technical time to vaccinate (of several months), as well as by postponing the decision or give up (propensity strictosensu). We suggest to CDCs to provide updated Pr values, in order to allow correcting effectiveness estimates according to Eq.

2, within the framework of a simplified analysis.

In order to illustrate the advantages related to the proposed correction, we have applied such method to simulated data whose solution is already known, according the scenario illustrated in Fig. 1A , where likely values have been assigned to vaccine and recovery efficacy: RRR = Eg = 0,8.

By way of example, biased RRR values (Eq. 1) and corrected ones, by means of Eq. 2, for each age class, have been compared (Fig. 1B) .

For the week 4-10 oct 2021, corrected and uncorrected SARS-CoV2 contagion incidence values have been compared in Fig.s 1C and 1D . This latter figure provides a valid example of diagram possibly aimed to a wide unspecialized audience, to be published in dedicated web pages or dashboards.

In summary, we point out to the CDCs of various nations the importance and the need of correcting contagion incidence data (e.g. tables, diagrams etc.), as well as risk reduction estimates by means of Eq. 2, on the basis of the propensity of recovered individuals to vaccination, in order to disseminate immediate and explanatory information regarding Covid-19 vaccine effectiveness.

Here we have assumed that recovered and never infected individuals, if vaccinated, exhibit the same degree of immunization.

As, when a population fraction is infected in a certain interval time, it results: NV / NN= SV / SN; therefore, after substitution of SV and SN with the terms in Eq.s A1 and A2, respectively and after simple manipulations, Eq.s 2 or 3 are derived. 

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