loading page

Statistical analysis methods applied to early outpatient COVID-19 treatment case series data
  • Eleftherios Gkioulekas,
  • Peter A McCullough,
  • Vladimir Zelenko
Eleftherios Gkioulekas
Professor, School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX, United States
Author Profile
Peter A McCullough
Chief Medical Advisor, Truth for Health Foundation, Tucson AZ, United States
Vladimir Zelenko
Affiliate Physician, Columbia University Irving Medical Center, New York City, NY, United States


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.
18 Aug 2022Published in COVID volume 2 issue 8 on pages 1139-1182. 10.3390/covid2080084