and calculated the ERS in the validation data based on those weights to avoid issues of over-fitting. We realize that the multiple regression model that includes both Es and Ec with adjustment for base covariates and phenotype-specific micronutrients may have some redundant variables in terms of statistical significance, and a further variable selection step may lead to a smaller model and a more concise measure of ERS. We wanted to retain all the identified pollutants in both versions of ERS and thus refrained from applying this additional model selection step in constructing the weights from the multivariate model.
