Because not all environmental pollutants were measured in the entire population, we imputed unmeasured or missing pollutant data to maximize the power. We used a single imputation because our main goal was to introduce the approach of ERS, but multiple imputations after taking the uncertainty in imputed values into account would be a more appropriate approach. Imputation may be necessary for meta-analyses of multiple ERS studies in the future because it is unlikely that every cohort has a uniform set of pollutants measured. Careful data harmonization and imputation may increase the power of the analysis if correlated exposures and covariates are observed in one cohort that are predictive of exposures in another cohort where those exposures are missing. However, the imputation issue will merit a complete paper in its own right, as imputation with high dimensional data is still very much an evolving topic in statistical research [77]. In summary, the present study suggests ERS is a promising tool for integrating disease risks from multi-pollutant mixture exposures. The ERS is a simplest form of data reduction, characterizing the summary exposure
