Statistical Analysis Methods Applied to Early Outpatient COVID-19 Treatment Case Series Data
Eleftherios Gkioulekas, Peter A Mccullough, Vladimir Zelenko
COVID, doi:10.3390/covid2080084
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.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations The following abbreviations are used in this manuscript:
Appendix A. Exact Fisher Test in the Limit of an Infinite Control Group Let N be the total number of patients in the treatment group, let a be the number of patients with an adverse outcome (hospitalization or death) in the treatment group, let M be the total number of patients in the control group, and let b be the number of patients in the control group with an adverse outcome. In this appendix we will show that in the limit of an infinite control group (M, b) with x = b/M, the p-value p(N, a, M, b) obtained from the two-tail exact Fisher test converges to p(N, a, x). In the exact Fisher test, we assume that N, M, and a + b, are fixed numbers, and under the null hypothesis, we also assume that the distribution of the total a + b patients with an adverse outcome between the treatment group and control group is random, with equal probability for every possible combination. It follows that under the null hypothesis, the probability of seeing a particular event (N, a, M, b) is given by pr The corresponding p-value is the probability of observing the event (N, a, M, b) or any other less probable event, and it is given by We note that the summation variable n is restricted by both the total size N of the treatment group and the total number a + b of the patients with an adverse outcome, so the permissible range for all possible events is..
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