Frequentist and Bayesian analysis methods for case series data and application to early outpatient COVID-19 treatment case series
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 very simple hybrid 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 unknown probability of an adverse outcome in the absence of treatment, and calculates a lower bound for this unknown probability, that has to be exceeded, in order to control the corresponding p-value, and reject the null hypothesis. We explain the relationship of this method with the exact Fisher test and the binomial proportion confidence interval problem. The resulting lower bound (hereafter, efficacy threshold) is further adjusted with a Bayesian technique, in order to also control the false positive rate. 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. The resulting efficacy thresholds are then compared against our prior knowledge of mortality and hospitalization rates of high-risk COVID-19 patients, as reported in the research literature.
Eleftherios Gkioulekas, Peter A McCullough, Vladimir Zelenko. Frequentist and Bayesian analysis methods for case series data and application to early outpatient COVID-19 treatment case series. Authorea. March 16, 2022.
Reviews in Cardiovascular Medicine