Partial Effects in Environmental Mixtures: Evidence and Guidance on Methods and Implications

The effects of a mixture of exposures on health outcomes are of interest to public health but pose methodological hurdles. These exposures may impact the outcome in opposing ways, which we call the positive and negative partial effects of a mixture. There has been growing interest in estimating these partial effects and their ability to inform public health interventions.

Methods like quantile g-computation (QGC) and weighted quantile sums regression (WQSr) were originally developed for estimating an overall mixture effect. These approaches, however, have not been comprehensively evaluated in their ability to estimate partial effects. We study the bias-variance tradeoffs of these approaches in estimating partial effects.

We compare QGC with sample-splitting (QGCSS) and WQSr with sample-splitting (WQSSS) and new methods including a) QGC a priori (QGCAP) and WQS a priori (WQSAP), which use prior knowledge to determine the positive and negative exposures prior to partial effects estimation; b) model-averaging (QGC-MA); and c) elastic net to determine the split (QGC-Enet). We also considered WQSr with no sample-splitting (WQSNS), repeated holdout sets (RH-WQS), and two-index model with penalized weights (WQS2i). We compared performance under a) exposure correlations, b) varying sample sizes, c) spread in the negative effect across exposures, and d) imbalance in the partial effects.

Our simulation results showed that the estimation of negative and positive partial effects grows in root mean squared error and average bias as correlation among exposures increases, sample sizes shrink, the negative effect is spread over more exposures, or the imbalance between the negative and positive effects increases. Our results are demonstrated in two examples of mixtures in relation to oxidative stress biomarkers and telomere length.

Outside of having a priori knowledge, no method is optimally reliable for estimating partial effects across common exposure scenarios. We provide guidance for practitioners of when partial effects might be most accurately estimated under particular settings. https://doi.org/10.1289/EHP14942.