Analysis of the hydroxychloroquine dosing regimen in RECOVERY and SOLIDARITY

The RECOVERY and SOLIDARITY trial is undoubtfully the two most influential papers on hydroxychloroquine. But concerns have been raised as to the dosing being too high. A pharmacokinetic modeling paper was then published as a response to justify the dosing regimen. But analyzing the pharmacokinetic modeling it becomes clear that the paper is flawed. The whole blood levels reached a grey zone.

The RECOVERY trial is an ongoing trial by Oxford University researchers testing different therapeutics against covid-19. One of those was hydroxychloroquine and their results were first published on the 5th of June 2020 and 10 days later as a preprint in MedRxiv. They found no effect of hydroxychloroquine but rather a trend towards harm as mortality rose by 9% in the hydroxychloroquine-arm. With a population of over 4700 patients, it is by far the biggest study on hydroxychloroquine and therefore carries the most weight.

In the Australian Covid-19 Clinical Evidence Taskforce’s metaanalysis, RECOVERY has 98% weight in their mortality estimate, basically producing the same result. The British drug agency MHRA is advising against hydroxychloroquine for inpatients solely on the basis of RECOVERY.

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RECOVERY is the first study in the NIH’s treatment panel’s review of the literature. The panel did not mention the dosing regimen as a limitation:

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The SOLIDARITY trial is an ongoing large randomized trial as well. Conducted by the WHO, it stopped its hydroxychloroquine arm (n=954) on the 4th of June because of a no observed effect. The results were published on the 15th of October showing increased mortality by 19% with hydroxychloroquine.

The two studies shared the same dosing protocol as the Oxford researchers guided the SOLIDARITY trial (“Nicholas J. White and colleagues provided unpublished data on the pharmacokinetic characteristics of hydroxychloroquine to help the WHO select the regimen”):

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This protocol shows the loading dose was 2400 mg in the first 24 hours. In 10 days a total of 9,6 g was given to the patients. But the pills only contained 77,5% base (155mg/200mg). This meant the loading dose was actually 1860 mg base hydroxychloroquine and the total dose was 7440 mg base.

Hydroxychloroquine is well known to cause gastrointestinal symptoms like diarrhea and nausea. However, the main concern about hydroxychloroquine relates to its ability to affect the heart.

Hydroxychloroquine at higher concentrations can block potassium ion channels in the heart causing potassium concentration inside the cells to accumulate. This can prolong the QT-interval which in turn can lead to torsades de pointes (heart arrhythmia) and cardiac death.

Here is Professor John Campbell from the Institute of Infections in Glasgow commenting on the dosing:

Here is the well known hydroxychloroquine supporter, Didier Raoult, commenting on the dose (he says that while the dosing was unprecedented no toxicity was described by the authors. While it wasn’t described, it was apparent in the supplementary appendix as we will see):

Even the Indian health authorities, the Indian Center for Medical Research (ICMR), wrote to the WHO concerned about the dosing regimen, which was 4 times higher than in India, where there is widespread use of the drug.

Comparisons to the Brazilian Borba study from April were made, that tested 12 g of chloroquine over 10 days against a normal low-dose regimen showing mortality almost triple with the high-dose. The dosing in this trial was so high that the authors are being investigated for negligent manslaughter. Chloroquine however is known to be more toxic than hydroxychloroquine which invalidates the comparison.

The preprint from RECOVERY did not contain any comments or justification of the dosing regimen. However, on their website, a document named “Hydroxychloroquine information sheet V3” contained information about the pharmacokinetic modeling but in its third update, they simply removed 22 pages including 12 pages of references containing this information.

As attention rose, FranceSoir tried finding out how the doses were chosen by interviewing lead author, Martin Landray:

He stated it was based on pharmacokinetic modeling (which was published later in November) and that the lethal dose (single dose toxicity) was 10 times the loading dose.

We know for a fact that the potentially lethal single dose of hydroxychloroquine is around 4000 mg. This means that the loading dose of 1860 mg base was almost half the potential lethal dose (46,5%). While “10 times that” is a gross hyperbole, it’s still below the potentially lethal dose.

Interestingly, Martin Landray states the dosing was in line with that used for amoebic dysentery when (hydroxy)chloroquine’s use for malaria would be a much more appropriate comparison. To my knowledge, the only description in the literature of chloroquine for amoebic dysentery is a case series from 1949 where the loading dose was 600 mg (this study is quoted in the later published pharmacokinetic modeling paper).

Also, the drug class “hydroxyquinolines” — and not “hydroxychloroquine” — is widely used to treat dysentery. Hydroquinolines are used at high doses “because they are not absorbed from the GI tract to any degree, their main use has been to treat intestinal infections”. Thus, for example, the hydroxyquinoline “iodoquinol” is used at 2 g per day (remember 1,86 g of hydroxychloroquine base was given the first day in RECOVERY and SOLIDARITY):

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Add to this, that in 177 academic articles about covid-19, hydroxychloroquine and -quinoline were mistaken (per February 10, 2021).

All this confusion put pressure on the Oxford researchers. In September they published a pharmacokinetic paper supporting their dosing regimen.

The paper took data from suicide attempts to determine toxic whole-blood concentrations. They found that safe whole blood concentrations of hydroxychloroquine occurred below 10 μM (micromolar). Then the authors computed a dosing regimen sufficient to reach the EC50 level (the concentration needed to inhibit 50% of the virus) but still under the “safe-cap”:

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As we can see, according to their calculations no more than 3 μM would be reached, well below the safe limit of 10 μM. Thus, their conclusion is:

Pharmacokinetic modeling in combination with information regarding blood levels and mortality from a case series involving 302 patients with chloroquine overdose predicts that a chloroquine regimen that was equivalent to the hydroxychloroquine regimen used in our trial should have an acceptable safety profile

How can we verify this curve? There is a lot of variables influencing this calculation — like bioavailability, volume of distribution, concentration ratio between whole blood and plasma, etc. And these variables are estimates and differ between sources. An example of this is the terminal half-life in blood ranging from 22.4 days, 40 days, or 54 days. It is important to remember that the curve is entirely hypothetical and easily manipulated using favorable variable estimates. Verifying the curve with a combination of all possible variable estimates would yield too many different results.

If only we had a way to simplify the calculation without lowering precision so we can test fewer combinations of variables. Wait, we can do that!

When we give a drug, not everything will be absorbed and the molecules that get absorbed will be so at different paces. Some of the molecules will get metabolized, some will get distributed back and forth between the first and second compartment, some will get excreted. All these factors influence the time and magnitude of the peak concentration in blood (the one we are interested in since it’s strictly correlated to toxicity).

It would be nice to know the exact values of all the factors leading to that peak concentration so we can calculate it. It would also be nice to know what exact concentrations constitute danger so we can compare them. But there is so much uncertainty related to those estimates. However, we can do something smart. We can take advantage of an estimate that is well described and use it to kill two birds with one stone.

The single-dose toxicity.

The single-dose toxicity of hydroxychloroquine is 20 mg/kg or 1400mg for a 70kg normal adult. Now, what does this actually mean? It means that after you ingest 1400 mg — after absorption, some distribution and elimination — the peak whole blood concentration, typically occurring after 3.26 hours, will reach dangerous levels.

That’s all we need to know. If the peak concentration of a 1400 mg intake reaches toxic levels, then a dose of 620 mg would proportionally reach 44% toxic levels. In the same way, a dose of 310 mg would result in 0.22 toxic levels. This is logical. Plus, it’s a precise estimate of the overall result from all the “unknown” variables influencing this peak concentration.

The only variable left is how these peak concentrations decay over time. Then we can project the magnitude of the concentrations (relative to the toxic concentration). Lastly, we can sum up these estimates for each dose to see how far from toxic levels we are at any given time.

Concentrations decay is best described exponentially (y=ba^x). But with a different slope according to different phases. When referring to drug concentration decay the classical exponential function of f(x)=b*a^x is rewritten to f(x)=b*e^-kx, where e is Eulers constant and k is the decay factor (which is proportional to the slope a).

The original paper used these measurements (where lambda is the old synonym for k):

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From Tett et al., 1989

This means that the first 88.7% (257 to 29) of the peak concentration decays by the k-factor 0.084. This is equivalent to 26 hours. Afterwards, the concentration decays by the k-factor 0.0031 until it drops a further 76.55% (29 to 6.8). This level is reached on the 20th day. For the remaining time, it decays by the k-factor 0.00058.

(This course is natural as hydroxychloroquine is very lipophilic (philic meaning “to like” and lipo meaning fat) which causes it to diffuse into body fats causing a huge distribution away from the blood. Thereafter, the elimination phases are much slower. Some might think that when we add another dose, then the new total concentration (and not just the added dose) would decay uniformly with the k-value from the distribution phase causing a bigger drop. However, this is not logical. Suppose we give a dose and later another one. The molecules from the first dose would not suddenly decay faster. The rate of decay (k-value) is determined by time, not by further dosing.)

Using these k-values for each dose and adding them up, this is the curve we get:

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Raw data and calculation here

Thus, the concentrations never reached toxic levels though they came close (70%). This is much closer than calculated by the original paper (around 30% or 3 μM against 10 μM).

However, the toxic level of 20 mg/kg is based on data from healthy adults. The observational suicide data used by the original paper to determine safe concentrations mainly consisted of young, healthy adults trying to commit suicide. For covid-19 patients under immense stress infected by a virus known to affect the heart, less hydroxychloroquine might cause harm. Thus, toxic whole blood levels of hydroxychloroquine might be lower for covid-19 patients (in severe disease).

Henceforth, the dosing regimen was placed in a grey zone. While blood levels did not quite reach “classically” toxic levels, it might have been the case for the patients in the study.

The k-values used for this calculation is not universal. I found a newer study from 2018 with the following decay rates:

Distribution phase: 0.06 h^-1
Elimination phase: 0.0107 h^-1
(This was a 2 compartment model, so I added the k-value 0.00058 h^-1 from day 20 and on representing the terminal half life).

Using these values this is the resulting curve:

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It looks much like the first curve however with a higher peak from the loading dose. Replicating our findings with variables from other observations increases our confidence in our findings.

One could stress that toxic hydroxychloroquine levels does not mean lethal levels. While there is some truth to that, for covid-patients it is contradicted by clinical data. The dosing in Borba et al. was undoubtfully lethal as the study showed a mortality OR of 2.8 in the high dose group. Using the same method and decay estimates, this is the calculated whole blood levels (relative to toxic levels) in Borba et al.:

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Raw data and calculations

Thus, the whole blood concentration surpassed toxic levels only by 20%. But the conventional lethal level is described as 260% bigger than the toxic level (4000 mg vs 1500 mg). This means, conventional lethal levels of hydroxychloroquine is much lower for severe covid-patients.

There is not much doubt that the pharmacokinetic paper is not independent as it is done by co-authors of the RECOVERY study. The lead author Peter Horby has done much research together with the lead author of the pharmacokinetic study Nicholas White suggesting they are “research buddies”. This can cause a bias.

One thing that suggests bias — other than calculating peak concentrations to be further from toxic levels (60%) than is the case (20-30%) — is the discourse in the paper and what is put emphasis on. Here is a worrying quote:

“There was a small absolute excess of cardiac mortality of 0.4 percentage points in the hydroxychloroquine group on the basis of very few events”

This is the data given by the authors in the supplementary appendix:

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They rounded down the absolute difference of 0.45 to 0.4 when in reality it should be rounded up to 0.5 (9/1561 minus 4/3155 is 0.4502).

Also, the devil is in the detail. Always be cautious when someone only gives you the absolute or relative difference. The relative difference is 455%, meaning the risk of cardiac death was 4.5x higher in the hydroxychloroquine group. This is highly significant:

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Now, 5 extra deaths didn’t cause the 9% extra mortality with HCQ. But there is a fine line between dying from covid-19 and your heart suddenly stopping — indeed to die from covid your heart must stop as well! There has been criticism towards the inclination of declaring covid as the cause of death if given the choice.

In the supplementary appendix, they provided data on arrhythmias showing the hydroxychloroquine group being 30% more at risk, however with a low base risk (8.2%).

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There is a risk of bias in this data. A curious remark is “major arrhythmia”. When is an arrhythmia major enough to be included (is some being neglected?)?

Concerns have been raised to the dosing regimen of the RECOVERY and SOLIDARITY study of hydroxychloroquine. Inspecting this it becomes clear that while the dosing regimen wasn’t as safe and fantastic as calculated in the pharmacokinetic paper, blood concentrations were still below toxic levels. Toxic levels, however, might be lower for severe covid-patients. Thus, the dosing regimen was in a grey zone and could have had a significant influence on the 9% (RECOVERY) and 19% (SOLIDARITY) excess deaths.

Interested in data, statistics, and evidence. 20 years old.

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