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