Hydroxychloroquine After Action Report

I was a vehement advocate of prescribing hydroxychloroquine (HCQ) off label while waiting for the results of clinical trials. I wasn’t all that much embarrassed to agree with Donald Trump for once. Now I feel obliged to note that my guess was totally wrong. I thought that the (uncertain) expected benefits were greater than the (relatively well known) costs.

The cost is that HCQ affects the heart beat prolonging the QT period (from when the atrium begins to contract to when the ventrical repolarizes and is read to go again). This can cause arrhythmia especially in people who already have heart problems. I understood that one might argue that all people with Covid 19 have heart problems but didn’t consider that argument decisive (I probably should have).

The positive expected value of the uncertain benefits was based on strong in vitro evidence that HCQ blocks SARS Cov2 infection of human cells in culture. (this is a publication in the world’s top general science journal).

Already in early May, there was evidence that any effect of HCQ on the rate of elimination of the virus must be small. In this controlled trial conducted in China, the null of no effect is not rejected. Much more importantly, the point estimates of the effects over time are all almost exactly zero. I considered the matter settled (although the painfully disappointed authors tried to argue for HCQ and that their study was not conclusive).

There are now four large retrospective studies all of which suggest no benefit from HCQ and two of which suggest it causes increased risk of death. I am going to discuss the two studies most recently reported.

One is a very large study (fairly big data goes to the hospital) published yesterday in The Lancet. In this study patients who received HCQ had a significantly higher death rate with a hazard of dying 1.335 times as high. The estimate comes from a proportional hazard model with a non parametric baseline probability and takes into account many risk factors including crucially initial disease severity. It is also important that only patients who were treated within 48 hours of diagnosis were considered.

I am, of course, dismayed by this result. I am also puzzled, because it is quite different from the result obtained in a smaller retrospective study published in JAMA

I think the practical lessons are that it seems unwise to give Covid 19 patients HCQ. Also maybe Robert Waldmann should be more humble. After the jump, I will discuss the two studies in some detail and propose an explanation of the difference in results.

To but my conclusion at the start, I think the difference in results occured because the JAMA paper used a more flexible specification to correct for differences in initial disease severity. The Lancet article reduced all information on severity to two indicator variables so patients were classified into one of 4 possible groups. This leaves out most of the data on disease severity. I think it likely that the gigantic data set could not have been assembled keeping track of more variables without the loss of many data points.

OK so Lancet massive study has an estimated increased hazard of dying a given day of 31% of the baseline hazard.
The New York specific JAMA study has an insignificant estimated change in the hazard of dying and point estimate close to one of the hazard ratio.

In the primary analysis, following adjustment for demographics, specific hospital, preexisting conditions, and illness severity, no significant differences in mortality were found between patients receiving hydroxychloroquine + azithromycin (adjusted HR, 1.35 [95% CI, 0.76-2.40]), hydroxychloroquine alone (adjusted HR, 1.08 [95% CI, 0.63-1.85]), or azithromycin alone (adjusted HR, 0.56 [95% CI, 0.26-1.21]), compared with neither drug

First I have to note that the Lancet point estimate is within the 95% interval estimated in the JAMA paper. The difference in results is striking, but not statistically significant at conventional levels. The difference between significantly greater than 1 and not significantly greater than 1 is not, itself, necessarily significant.

But I also note the coincidence that in the JAMA study the raw death rate was markedly and statistically significantly higher for patients treated with HCQ than for patients who weren’t.

“In unadjusted analyses, significant differences in in-hospital death were observed across the … hydroxychloroquine alone (n = 54, 19.9% [95% CI, 15.2%-24.7%]), … and neither-drug (n = 28, 12.7% [95% CI, 8.3%-17.1%]) groups ”

The combination of a significantly greater raw death rate and a near zero estimated effect on the risk of death from the model is due to the fact that patients treated with HCQ were sicker than patients not treated with HCQ. It isn’t surprising that an untested medicine was more likely to be used in more alarming cases. This makes the specification choices made in multiple regression to handle confounding variables critical. In particular, the choice, in both studies, to reduce continuous variables such as oxygen saturation to indicator variables for ranges must matter.

I was struck that, in the Lancet study, blood oxygen saturation was used in the regression as an indicator of saturation less than 94%. The modified variable clearly does not contain all the available information about oxygen saturation. Data on the mental status, respiratory rate, and systolic blood pressure (and other variables which were not described in the article) were summarized with a single index which was replaced with an indicator variable which took two possible values.

I think that Doctors and economists take statistics seriously in different ways. The data collecton ranges from impresseive (JAMA) to amazing (Lancet) with great care in sample selection. However, the specification is not well motivated and robustness to different specifications is not considered at all in the Lancet article (unless I missed it). Since there is a dramatic shift from the raw estimates to the estimates when confounding variables are considered, it is clearly necessary to be careful about how confounding variables were handled.