Page 9 - Book of Abstracts 2021

Interactive web tools Theory of probability for life https://ideaapps.cerge-ei.cz/anti_covid/en/  x Theory of probability for life What is it about: Imagine that you belong to a group of people with a certain infection risk level. For example, if you are a worried pensioner who rarely leaves home, your infection risk level is minimal, say 1%. Now imagine 10,000 people belonging to this same group of people. How many of them will get correct test results from a rapid test? How many of them will falsely test positive and be needlessly alarmed? And how many of them will become carefree super-spreaders thanks to a false negative result? Select the infection probability and the error rate of the test used and let the statics give you the answers. ! How many people are truly infected in the group studied: When the infection probability is 20%: 2000 people are infected out of 10000. How should I interpret the test results and what does it mean: (with the chosen infection probability and test quality) Did I test positive? Then the probability that I'm actually infected is 69.2% (1800 infected out of 2600). Did I test negative? That does not necessarily mean that I'm healthy. The probability that I'm infected is not zero, but 2.7% (200 infected out of 7400) Prior probability of being infected (p) Moderate: 20% ! 20% 100% 1 1121 41 61 81 100 ! Test sensitivity (sp) 0% 90% 0 1020 40 60 80 100 ! Test specificity (sn) 0% 90% 0 1020 40 60 80 100 GUIDE CONTENT: Pavel Kocourek PROGRAMMING: Taras Hrendash, Jiří Münich PRODUCTION: Blanka Javorová, Markéta Malá BACK TO CONTENTS 7 Probability Theory for Life THE CASE OF A HUSBAND SHARING A HOUSEHOLD WITH HIS WIFE WHO IS PROBABLY INFECTED IDEA JUNE 2020 Imagine that the husband tests negative. However, before getting tested, his probability of being infected is high, say p = 80%. Let us consider 10,000 similar households. In 10,000p = 8,000 of these households the husband is infected, and in the remaining 10,000(1 – p) = 2,000 of the households the husband is healthy. Out of the healthy husbands 2,000 · sn = 1,800 test negative, but also 8,000(1 – sp) = 8,000 · 0.1 = 800 of the infected husbands test negative. It follows that in spite of testing negative, the probability that the husband is infected is p’ = 80 · 100% = 1800 + 800 30.8%. That is quite high and so he should stay in quarantine. ILLUSTRATIVE APPLICATION OUTPUT FOR THIS EXAMPLE ? 7,200 infected 200 healthy 800 infected 1,800 healthy CONTENT Pavel Kocourek PROGRAMMING Taras Hrendash, Jiří Münich PRODUCTION 7,480 test positive 2,600 test negative The calculation we have used rely on so called Bayes theorem.4 The calculation itself is not complicated, but for your convenience explore how to correctly interpret test results based on a variety of circumstances. If you understand that well, nobody should be afraid to sell a rapid test to you specifically. the online calculator does it for you. The application allows you to 10,000 tested COVID-19 TEST ERROR TEST ERROR Blanka Javorová, Markéta Malá