*Copyright 2020 Robert Clark*

Several studies have shown multiple different anti-inflammatories
such as steroids can be beneficial against COVID-19. It is simply unreasonable then to suppose HCQ as one of the most effective anti-inflammatories is not. It’s probably the reason so many HCQ studies,
including ones claiming “no benefit”, *did* show benefit.

An astonishing instance
of this last occurred in the RECOVERY trial. The RECOVERY trial was a
randomized-controlled trial (RCT), which are called the
"gold-standard" of medical studies. Because it was negative towards
HCQ, it was frequently cited as evidence of HCQ having no benefit.

RCT's aren't perfect of
course. There can be flaws in interpreting the data, there may not be
sufficient numbers of subjects to draw a strong conclusion. They can use the
wrong dosage, etc. And unfortunately there can also be cases where researchers
falsify data.

I did not consider this
last possibility to be likely with the RECOVERY trial. However, what I found did
happen in the RECOVERY trial was nearly as bad in regards to accurately evaluating the effectiveness of HCQ. While the data was presented correctly, the way it was presented obscured the HCQ effectiveness. *Note I am making no assertion on whether or not this was intentional.*

Here's the HCQ report from the RECOVERY trial:

Effect of Hydroxychloroquine in Hospitalized Patients with COVID-19: Preliminary results from a multi-centre, randomized, controlled trial. https://www.medrxiv.org/content/10.1101/2020.07.15.20151852v1.full.pdf

Here's the relevant table, from page 24:

You see instead of deaths on mechanical ventilation being given directly,
it is combined with all deaths into one category. So, we need to do the calculation to find the
proportion of the ventilated patients who died on HCQ and then calculate the
proportion for those not on HCQ who died, since these are not given directly. Use
the formula for counting the number of elements in the union of two sets with possible
overlap:

which simply means you add together the number in each set, then subtract off the number in the overlap.

First look at the cases on HCQ. Call A those
within the HCQ group on "Invasive mechanical ventilation", at a count
of 118. Call B those cases listed among the "Deaths", at a count of
308. Then the union of these two cases is listed in the "Receipt of
mechanical ventilation or death" category at a count of 388. Let x equal
the count of the cases that are in *both*
"Death" and "Invasive mechanical ventilation", i.e., the
intersection of the two sets. This is the number specifically in the ventilated
group who died. Then using the formula we see: 388 = 118 + 308 - x. So x = 38.
Then the proportion of the ventilated group who died on HCQ is 38/118 = .322,
or 32.2%

Now calculate it for the non-HCQ group, i.e., the
usual care group. The numbers appear in the "Usual care" column in
the table. Again let A be those on "Invasive mechanical ventilation",
at a count of 215, and B those cases listed among the "Deaths", at a
count of 572. Then the union of the two groups is the "Receipt of
mechanical ventilation or death" category at a count of 696.

Let x again be the number in the intersection
of the two sets, i.e., the number on mechanical ventilation who died. Then
using the formula again we get 696 = 215 + 572 - x. So x = 91. Then the
proportion of the ventilated group who died not taking HCQ is 91/215 = .423, or
42.3%.

* This difference between the number of
ventilated patients on HCQ who died of 32.2% and those not on HCQ who died of
42.3% is large enough that it should have been reported. *

The RECOVERY trial made headlines world-wide
when it sent out a news release on the "breakthrough" that the
steroid dexamethasone could cut mortality for ventilated patients by 30%.

Here is the published article on the discovery:

Dexamethasone in Hospitalized Patients with Covid-19 — Preliminary Report.

The RECOVERY Collaborative Group July 17, 2020

DOI: 10.1056/NEJMoa2021436

https://www.nejm.org/doi/full/10.1056/NEJMoa2021436

In the Results section the mortality for
ventilated patients on dexamethasone is given as 29.3%, while for those not on
dexamethasone it's given as 41.4%. Note these numbers are quite close to those
for HCQ. Yet the RECOVERY trial described HCQ as offering "no
benefit" while dexamethasone was described as a "breakthrough".

I want to reiterate I do not know if this obscuring of the HCQ effectiveness was intentional or not. However, there was another report which presented the data on ventilated patients in a similar way by combining the total number of deaths with the number on mechanical ventilation. That was the report by Geleris et. al. I discussed this report here:

About the article, “Observational Study of Hydroxychloroquine in Hospitalized Patients with Covid-19”. UPDATED, 6/26/2020

http://exoscientist.blogspot.com/2020/06/about-article-observational-study-of.html

In this case as well presenting the data in this way obscured the benefits for patients on mechanical ventilation. In this study, the mortality for ventilated patients was cut 50% on HCQ. Yet this was not apparent because of the way the data was presented.

This was particularly unfortunate because the study was from patients in New York and in New York at the time the mortality for ventilated patients was in the range of 80%:

A bridge between life and death: Most COVID-19 patients put on ventilators will not survive.

John Bacon

USA TODAY Updated April 10, 2020

https://www.usatoday.com/story/news/health/2020/04/08/coronavirus-cases-ventilators-covid-19/2950167001/

Again, I do not know if this was intentional or not. However, I have found there has been a pattern in which beneficial effects of HCQ were not included in the conclusions of papers that asserted that HCQ had "no benefit".

In an upcoming article I'll discuss these papers where the final conclusion on HCQ was "no benefit", yet in the data in the paper themselves, HCQ did show benefit such as for ventilated patients for example. I don't know if this was intentional or not but the effect was to remove HCQ for consideration for treatment of COVID-19 particularly when it would be most beneficial.

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Robert Clark

Department of Mathematics

Widener University

Chester, PA 19013 USA

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