key: cord-0736490-fmywwil7
authors: Günther, Michael; Mörl, Falk; Rockenfeller, Robert
title: Where Have the Dead Gone?
date: 2022-03-16
journal: Front Med (Lausanne)
DOI: 10.3389/fmed.2022.837287
sha: 7443457c8d5bce4c2a63bf961dfcae12abf0e984
doc_id: 736490
cord_uid: fmywwil7

nan

Data published from pivotal clinical trials contain the key information on efficacy and safety of newly developed drugs. With the magnified public awareness focused around the world on the SARS-CoV-2 existence, the authors, albeit medical laymen though ardent scientists, could likewise not escape being prodded to research data published in the virological and epidemiological fields. This commentary is a consequence of our ruminating what the trials' published safety data tell us.

To Say It Outright: We do not understand why plain and important data informing of vaccination safety seem to be unpublished as a rule, namely, the plain count of how many persons had died in each trial group during the time interval from receiving the first dose of a vaccine (or placebo, respectively) until the end of the follow-up period (the monitoring interval). The high scientific value of such raw death counts comes, in particular, from not depending on any selection criterion applied to the collected data. The counts should be given for each randomized trial group, usually, the placebo-treated and the vaccinated one. These overall death counts, first of all for the placebo group, can then be compared with a number that is prognosticated from (i) the absolute number of persons within each age cohort the groups consist of, (ii) known annual mortality rates of the age cohorts, and (iii) the time interval between first dose reception and followup termination. In a second step, the prognosticated number of deaths and the dead counted in the placebo group can be compared with the dead counted in the vaccinated group. We here apply the prognosis method to the first three pivotal clinical trials on SARS-CoV-2 vaccines, BNT162b2 (1), mRNA-1273 (2), and Ad26.COV2.S (3), with the method certainly being applicable to any clinical fatality examination or safety trial as, e.g., most recent ones (4, 5) . The comparisons presented here are facilitated by the three trials probed having compared groups that all consist of nearly matching age cohorts.

Analysing (1) persons that were expected to die in the (1) placebo group during the monitored time interval of three (between first and second dose) plus eight weeks (follow-up after second dose). This is nearly an order of magnitude higher than the 4 dead given in (1, their Supplementary Table S3), whilst this Table apparently reflects "events" in a subset of only 2,638 persons. The number of just 2 dead in a subset of 5,770 vaccinated seems then even more inconsistent.

In the above calculation (prognosis), we have marked by under-bracing the study-specific overall annual mortality rate, which arises (see first row of the calculation) from the weighted sum of the three cohort-specific annual mortality rates (each the first factor in a summand), with their weights (each the second factor in a summand) being the study-specific fractions of the cohorts. Related to the trial study (1) investigated here, the prognosis method requires seven parameters to be known: the monitoring interval (eleven weeks) plus both the numbers of persons and the annual mortality rates for each age cohort taken into account (three). The uncertainty of the prognosticated number of deaths is calculated in the section "Estimating the uncertainty of the prognosticated number of deaths" appended to this communication. In short, assuming age cohort weighting in the trials to be uncertain among oldest and youngest by 10%, while knowing how the cohorts' mortality rates vary among the recruiting regions for the trial groups, we calculate the minimum estimate of the prognosticated number of deaths to be 25% lower than the 25 deaths calculated above on the basis of German annual mortality rate values, thus, 19 deaths in the trial study (1) just investigated.

In continuation of Polack et al. (1) , interestingly, the authors of (7) finally counted 15 (vaccinated) and 14 (placebo) dead during eleven weeks, then evidently giving numbers for complete trial groups (see their Supplementary Table S4 ; 21,920 persons). If our German-based estimate (25 deaths in 21,620 persons) is assumed to be the expected value of a binomial probability distribution then the corresponding standard deviation is quite exactly 5 . A corresponding binomial test reveals that the 14 dead in the placebo group are significantly different from prognosticated 25 deaths, at a p-value of 0.0012 . Hence, counting just 14 dead in Thomas et al. (7) is already utterly unlikely to be explainable by chance; and the 4 dead reported in Polack et al. (1) are an entirely impossible count, which can only reflect some preliminary data analysis. In stark disaccord, the data reported in Polack et al. (1) should without doubt stand on their own and not rely on additional publications, as this was a public dissemination of both safety and efficacy probed by a pivotal vaccine trial. Publishing another, later (6-month) safety data set as in Thomas et al. (7) , or even secondary reports like, e.g., by the USA's "Food and Drug Administration, " should not be required when disseminating a primary endpoint assessment of safety (mortality).

Due to the age cohort distributions nearly matching in the three pivotal clinical trial studies (1-3) investigated here (i.e., the overall annual mortality rate is assumed to have the same value 0.0054, within the uncertainty estimated below), the 25 deaths prognosticated for (1) can be easily scaled to the trial groups in (2, their Supplementary Table S8 ), which consist of each about 15,200 persons. As the monitored interval was four (between first and second dose) plus four weeks (follow-up after second dose), the prognosis becomes 25 · 15200 21620 · 8 w 11 w ≈ 13 deaths during eight weeks. Their data (2, their Supplementary Table S8) tell 3 dead in an apparent "event" subset of 3,277 persons within the placebo group, and 2 dead in 3,632 "event"-attributed vaccinated persons.

Further astonishing numbers can be found, if the prognosis is applied to the trial groups in Sadoff et al. (3): The prognosticated deaths can likewise be easily calculated by scaling, for a trial group now consisting of about 21,900 persons. We calculate 25 · 21900 21620 · 4 w 11 w ≈ 9 deaths, whereas 16 dead are documented in (3, their Supplementary Table S7) for the "event" subset of the placebo group, with half of them attributed to having died of CoViD-19. In the vaccinated group then again, only 3 died during the four weeks after the single dose treatment, which is again much lower a number then prognosticated. The "event" subsets seem to have consisted of 3,380 and 3,356 persons, respectively.

As our conclusion, in perfect line with a recent scientific request (8) for raw trial data, we urgently ask researchers carrying out pivotal clinical trials: Please, publish the entire number of deaths having occurred in each complete trial group during the monitoring interval! They are the most meaningful and reliable data recorded in these trials, as they lack any potential interpretative bias by conceivably applying selection criteria after recording. Accordingly, giving the full and raw number of fatalities within each the placebotreated and the vaccinated trial group during a monitoring interval (identical for all treated persons) after the first treatment is critical to assess the efficacy and safety of the vaccines.

Failing to properly measure and report mortality, a primary endpoint, is inexcusable. Unconditional opening of the scientific raw trial data (9) , which are claimed to be privately "owned" yet decisively shape public policy, is a remedy for such failure.

The formula given above enables calculating prognoses for any comparable study in the literature. Here, we provide information of how uncertain the prognosticated death values are, given empirically known uncertainties of the input parameters for the prognosis. More exactly, we provide an absolute minimum estimate of our prognosis and estimates of how much a prognosticated value goes up if US, Brazilian, or South-African mortality rates contribute, rather than German ones. We start with explaining how we distinguished, by inference from supplementary data, three age cohorts in Polack et al. (1) study, although only two are explicitly set out in their main paper. , respectively, i.e., the USA-based values are in general at least 20% higher than the German-based ones (0.15, 0.7, and 1.5%), which would accordingly increase the overall mortality rate from 0.0054 (German-based) to about 0.0065 (USA-based). In Brazil (11, 12) , we find 0.23, 0.98, and 2,45%, respectively, which are nearly 50% higher than in Germany. In South Africa (13, 14) , we find 0.55, 1.82, and 3,13%, respectively, which are all more than 100% higher than in Germany.

Thus, regarding mortality rates alone, using German values as a proxy minimizes the number of prognosticated deaths.

To identify an absolute minimum estimate of the number of prognosticated deaths, we first of all hypothesize as an extreme that the persons in the cohort [66-75]y of a trial group may only be half as many, i.e., we consider another source of uncertainty of the study-specific cohort distribution, namely, we assume a study-specific [66-75]y fraction value of 0.10 rather than 0.20, together with adding all these persons to the [16-55]y cohort. As a result, the number of prognosticated deaths would be 20% lower than any prognosis calculation based on German mortality data. Next, the number of persons in a trial group is well-defined, and the monitored interval is uncertain by less than half a week. Accordingly, in the above prognosis calculation, the whole multiplier (product of the number of persons in a group and the monitored weeks, divided by the weeks in a year) to the overall mortality rate is uncertain by maximally 1% ; correspondingly, this source of uncertainty is almost insignificant. Eventually, some further source of uncertainty is inherent to the parameter values assumed for the mortality rates. As the monitoring interval consists of the order of ten weeks, and reflects the epidemiological conditions at specific places and during a specific period in time, the natural fluctuations of the weekly mortality rates may be taken into account. In Germany, about 19,200 all-cause deaths currently occur per week, with an empirically determined longterm standard deviation of about 250 persons [combined (6) and (15)]. Thus, a weekly mortality rate is uncertain on the level of about 1.3% .

All in all, the absolute minimum estimate of the number of prognosticated deaths is 20% (cohort fraction uncertainty) plus 1% (monitoring interval uncertainty) plus 4% (approximately three times the uncertainty of weekly mortality rates), that is, 25% below the number of deaths that is prognosticated on the basis of German annual mortality rate values.

MG did the calculations. All three authors contributed to writing the words and revising the text.

Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine

Efficacy and safety of the mRNA-1273 SARS-CoV-2 vaccine

Safety and efficacy of single-dose Ad26.COV2.S vaccine against Covid-19

Efficacy and safety of the CVnCoV SARS-CoV-2 mRNA vaccine candidate in ten countries in Europe and Latin America (HERALD): a randomised, observer-blinded, placebo-controlled, phase 2b/3 trial

Efficacy, safety, and lot-to-lot immunogenicity of an inactivated SARS-CoV-2 vaccine (BBV152): interim results of a randomised, double-blind, controlled, phase 3 trial

Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine through 6 months

Covid-19 vaccines and treatments: we must have raw data, now

Instituto Brasileiro de Geografia e Estatística

Available online at

Mortality and Causes of Death in South Africa: Findings From Death Notification

EuroMOMO: A European mortality monitoring activity

The authors have not been funded while writing this commentary; publication costs were covered by the Open Access Fund of the University of Koblenz-Landau.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.Publisher's Note: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.Copyright © 2022 Günther, Mörl and Rockenfeller. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.