Weighted quantile sum (WQS) mixed-effects model.

Human-relevant environmental exposures typically have complex correlation patterns and may result in a mixture effect. That is, individual exposures may be below an effect level, however, the joint action (e.g., additive toxicity) of the components may produce significant effects. Weighted Quantile Sum (WQS) Regression has been used to estimate mixture effects using an empirically weighted index associated with an outcome of interest. The current WQS regression methodology assumes independence across subjects and does not permit multiple intra-subject outcome measures, which is a research gap. We extend WQS regression to the case when the data include multiple outcome variables or repeated measures with intra-subject correlation.•Data are randomly split and the weights for the weighted index are estimated with resampling in the training set.•Inference is conducted in repeated holdout validation sets to improve the stability of WQS estimates.•A mixed-effects model is used in the holdout datasets to accommodate intra-subject correlated outcome variables for statistically valid inference relating the weighted index variables to the outcome(s). The new WQS mixed-effects model was applied to a pilot study of the impact of environmental conditions on kidney function with potential sex-specific differences in long-distance runners with repeated 20 km runs.