Comparison of environmental mixture methods for estimating the joint effects of environmental mixtures

Quantifying the health effects of environmental mixtures remains a methodological challenge, and while many mixture methods have emerged, few have been systematically compared. We evaluated five widely used approaches-weighted quantile sum regression (WQS), two-indices WQS (2iWQS), quantile g-computation (qgcomp), Bayesian kernel machine regression (BKMR), and Bayesian weighted sums (BWS)-through simulations varying sample size, number of exposures, exposure-response functions, exposure correlations, and noise levels. We further applied these methods examine associations between prenatal indoor air pollution and childhood externalizing behaviors in the Drakenstein Child Health Study (DCHS). Simulation results showed that WQS and BWS achieved high power under directional homogeneity, with BWS generally exhibiting lower bias and more reliable coverage than WQS. BKMR controlled type I error but lost power as exposure correlation weakened or mixture dimensionality increased. Linear qgcomp performed well under moderate to strong correlation but showed reduced power in heterogeneous-effect settings. In nonlinear-effect scenarios, BKMR and nonlinear qgcomp displayed substantial bias and poor coverage, whereas simpler linear models often provided more stable inference. 2iWQS matched WQS under low correlation but deteriorated as correlation increased. In the DCHS application, WQS, BWS, and qgcomp identified significant positive joint effects of prenatal indoor air pollution on externalizing behaviors, whereas BKMR and 2iWQS did not, consistent with simulation patterns. These findings highlight tradeoffs among flexibility, power, and estimation accuracy, with no single method performing best across scenarios. We recommend a structured analytic strategy that begins with univariate analyses and integrates both directionally constrained and flexible models to yield robust and comprehensive inference.