Statistical evidence from case series data in support of early outpatient COVID-19 treatment protocols

Abstract: When confronted with a public health emergency, significant innovative treatment protocols can sometimes be discovered by medical doctors at the front lines based on repurposed medications. We propose a statistical framework for analyzing the case series of patients treated with such new protocols, that enables a comparison with our prior knowledge of expected outcomes, in the absence of treatment. The goal of the proposed methodology is not to provide a precise measurement of treatment efficacy, but to establish the existence of treatment efficacy, in order to facilitate the binary decision of whether the treatment protocol should be adopted on an emergency basis. The methodology consists of a frequentist component that compares a treatment group against the probability of an adverse outcome in the absence of treatment, and calculates an efficacy threshold that has to be exceeded by this probability, in order to control the corresponding p-value and reject the null hypothesis. The efficacy threshold is further adjusted with a Bayesian technique, in order to also control the false positive rate. A random selection bias threshold is then calculated from the efficacy threshold to control for random selection bias. Exceeding the efficacy threshold establishes the existence of treatment efficacy by the preponderance of evidence, and exceeding the more demanding random selection bias threshold establishes the existence of treatment efficacy by the clear and convincing evidentiary standard. The combined techniques are applied to case series of high-risk COVID-19 outpatients that were treated using the early Zelenko protocol and the more enhanced McCullough protocol.

Video Presentation


E. Gkioulekas, P.A. McCullough, V. Zelenko: "Statistical analysis methods applied to early outpatient COVID-19 treatment case series data", COVID 2(8) (2022), 1139-1182
[pdf] || [doi]

E. Gkioulekas: "Supplementary material: Statistical analysis methods applied to early outpatient COVID-19 treatment case series data". figshare. Online resource. (2022),
[pdf] || [doi -- figshare]

M. Rendell: "Commentary on 'Statistical Analysis Methods Applied to Early Outpatient COVID-19 Treatment Case Series Data' by Gkioulekas, Mccullough and Zelenko: A Return Back to the Future" Journal of Healthcare Communications 7 (10) (2022), 130-135
[pdf] || [doi]

Public Outreach

I was invited to give a media interview about this work by Teryn Gregson's podcast:

Podcast: Statistics of early COVID treatments explained by Zelenko & McCullough's Mathematician | Ep. 49, Faithful Freedom podcast with Teryn Gregson, 01/04/2023

Our publication was mentioned in two substack articles by my co-author, Dr. Peter McCullough:

P.A. McCullough, "Great Texas COVID-19 Tragedy", Courageous Discourse, substack, Mar 25, 2023

P.A. McCullough, "'A Plague Upon Our House' By Special White House Advisor Dr. Scott Atlas", Courageous Discourse, substack, May 20, 2023

Disclaimer: This presentation does not necessarily represent the opinions or policies of the University of Texas -- Rio Grande Valley, but it is protected under Academic Freedom in Research and the 1st Amendmend of the United States Constitution.