A generally interesting question in metabolomics relates to circumstances in which the concentration of a particular metabolite is higher in those who do not have a disease compared to those who are more likely to. The question then arises as to what level of that metabolite has a particular statistical probability of being associated with avoiding the disease. A similar question relates to predicting the statistical longevity of individuals given the existing, typically S-shaped, survival distributions. The most appropriate method for predicting the tails of these distributions is an important part of Extreme Value Theory and is known as the Generalised Pareto distribution (GPD). The GPD has two free parameters once a 'threshold' has been set. We here apply it to a published study of the relationship between the concentration of ergothioneine in plasma and the likelihood of developing pre-eclampsia (PE). We first rehearse that the statistical distributions of ergothioneine concentrations in the women with pre-eclampsia and those without pre-eclampsia are indeed different. From the empirical dataset of individuals who experienced pre-eclampsia (whether early- or late-onset) we note that the 90th percentile falls at ∼ 380 ng.mL-1. This was also the value found to give the lowest value of the mean excess in a GPD analysis. We can then use the GPD to fit the high ergothioneine observations in PE cases. Using this approach, we found that the probability of observing ergothioneine concentrations above 650 ng.mL-1 in PE cases is lower than one in 1,000. This compares very favourably with the normal incidence of PE, that is 2-7%.
Roberts et al. (2026) studied this question.