22.11.2021 - CHICAS, Lancaster University, United Kingdom

The sigma rules: are they beauties or beasts in serology data analysis?

Nuno Sepúlveda

Serological data analysis has often the objective of estimating the seroprevalence, i.e., the proportion of antibody-positive (i.e., seropositive) individuals in the population. To this end, one simplifies the analysis of quantitative antibody data by classifying individuals as seropositive if their antibody levels exceed a certain threshold. Otherwise, the individuals are deemed antibody-negative (or seronegative). The threshold for antibody positivity is routinely determined by the beautiful sigma rules based on extreme quantiles of the normal distribution. In particular, the most popular rule defines this threshold as the mean plus three standard deviations from the estimated antibody distribution of the seronegative population. In this talk, I will discuss two statistical problems - estimation bias and apparent control of specificity - arising from these rules with antibody data on SARS-CoV2 antigens. Are these sigma rules beautiful statistical constructs or rather little beasts hidden in their statistical simplicity?