To estimate the weights and evaluate the performance of ERS, we randomly split the full data (all cycles combined) by a 3∶1 ratio: the larger part (n = 11586) used for estimation/training and the smaller part (n = 3847) for validation/testing. We considered two types of weights. ERS1 used regression coefficients from single-pollutant models for each pollutant in the Es and Ec sets as weights, while ERS2 used regression coefficients from a multi-pollutant model that included all members of Es and Ec simultaneously. The weights of ERS1 and ERS2 were both adjusted for base covariates and phenotype-specific micronutrients. ERS1 and ERS2 differ in terms of the weights corresponding to each pollutant, in particular, the weights in ERS2 are taking into account correlation among the pollutants in the entire Es and Ec sets. We estimated the weights using the training data 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
