A Permutation Test-Based Approach to Strengthening Inference on the Effects of Environmental Mixtures: Comparison between Single-Index Analytic Methods

BACKGROUND: Optimization of mixture analyses is critical to assess potential impacts of human exposures to multiple pollutants. Single-index regression methods quantify total mixture association and chemical component contributions. Single-index methods include several variants of quantile g-computation (QGC) and weighted quantile sum regression (WQSr), though each has limitations. OBJECTIVES: We developed a novel permutation test for WQSr and compared its performance to extant versions of WQSr and QGC in simulation studies and an analysis of prenatal phthalates and childhood cognition. METHODS: WQSr uses ensemble nonlinear optimization to identify weights for mixture exposures in an index associated with the outcome in a prespecified direction, with ensembles based on bootstrap resampling (WQSBS) or random subsetting of exposures (WQSRS). Statistical significance can be assessed without splitting the data (Nosplit), by splitting the data into training and test sets (Split), by repeatedly holding out test sets (RH), or by using a novel permutation test (PT) to obtain a more accurate [Formula: see text]-value. QGC instead provides a sum mixture coefficient and component coefficients with no constraints on direction. In simulations, we compared false positive rates (FPR) and power to detect true associations and accuracy in estimating mixture weights. We also estimated associations between prenatal phthalate mixtures and childhood IQ in the Conditions Affecting Neurocognitive Development and Learning in Early Childhood cohort using each method. RESULTS: FPR was well controlled at [Formula: see text] in all but the Nosplit WQSr variants. Among these methods, the WQSBS and WQSRS PT variants had the highest power (89%–98%), with lower power for QGC (85%–93%) and RH (60%–97%) or Split WQSr variants (40%–78%). WQSr methods estimated mixture weights 2–4 times more accurately than the QGC method. Coefficients for mixture associations with full scale IQ varied 3- to 4-fold across analytic methods. DISCUSSION: WQSr paired with our novel permutation test best balanced power and false positive rate when assessing a mixture effect. As new methods develop, each should be examined for performance and applicability. https://doi.org/10.1289/EHP10570