The three-sigma rule to define antibody positivity: is it a beauty or a beast?


Many epidemiological studies aim to estimate the proportion of individuals currently or previously infected by a given microorganism. Given that an infection inevitably leads to an immune response, this estimation exercise often requires identifying individuals who reach a minimal level of microbe-specific antibodies in their serum. This threshold invariantly is defined by the three-sigma rule: mean plus three times the standard deviation from the hypothetical antibody-negative population. Notwithstanding not being linked to a specific parametric distribution, it has the most intuitive interpretation in the context of a normal distribution. I will then discuss the problems of estimation bias and apparent control of specificity arising from applying this rule to nonnormal distributions for the seronegative population. I will use public data on antibody testing against the SARS-CoV2 to illustrate these problems. We should finally ask ourselves whether the three-sigma rule is a beautiful statistical concept or, instead, a little beast hidden in antibody data analysis.

14 Ottobre 2022

Nuno Sepúlveda
Faculty of Mathematics & Information Science, Warsaw University of Technology, Poland CEAUL
Centro de Estatística e Aplicações da Universidade de Lisboa, Portugal


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