A Bayesian reanalysis of the effects of hydroxychloroquine and azithromycin on viral carriage in patients with COVID-19

Gautret and colleagues reported the results of a non-randomised case series which examined the effects of hydroxychloroquine and azithromycin on viral load in the upper respiratory tract of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) patients. The authors reported that hydroxychloroquine (HCQ) had significant virus reducing effects, and that dual treatment of both HCQ and azithromycin further enhanced virus reduction. In light of criticisms regarding how patients were excluded from analyses, we reanalysed the original data to interrogate the main claims of the paper. We applied Bayesian statistics to assess the robustness of the original paper's claims by testing four variants of the data: 1) The original data; 2) Data including patients who deteriorated; 3) Data including patients who deteriorated with exclusion of untested patients in the comparison group; 4) Data that includes patients who deteriorated with the assumption that untested patients were negative. To ask if HCQ monotherapy was effective, we performed an A/B test for a model which assumes a positive effect, compared to a model of no effect. We found that the statistical evidence was highly sensitive to these data variants. Statistical evidence for the positive effect model ranged from strong for the original data (BF+0 ~11), to moderate when including patients who deteriorated (BF+0 ~4.35), to anecdotal when excluding untested patients (BF+0 ~2), and to anecdotal negative evidence if untested patients were assumed positive (BF+0 ~0.6). The fact that the patient inclusions and exclusions are not well justified nor adequately reported raises substantial uncertainty about the interpretation of the evidence obtained from the original paper.