A permutation-based approach to inference for weighted sum regression with correlated chemical mixtures

Evaluating Chemical Mixtures in Epidemiological Studies to Inform Regulatory Decisions

BACKGROUND

Epidemiological studies are increasingly going beyond the evaluation of health effects of individual chemicals to consider chemical mixtures. To our knowledge, the advantages and disadvantages of addressing chemical mixtures for informing regulatory decisions-as opposed to obtaining a more comprehensive understanding of etiology-has not been carefully considered.

OBJECTIVES

We offer a framework for the study of chemical mixtures in epidemiological research intended to inform regulatory decisions. We identify a) the different ways mixtures originate (product source, pollution source, shared mode of action, or shared effect on health outcome), b) the use of indicator chemicals to address mixtures, and c) the requirements for epidemiological studies to be informative for regulatory purposes.

DISCUSSION

The principal advantage of considering mixtures is to obtain a more complete understanding of the role of the chemical environment as a determinant of health. Incorporating other exposures may improve the assessment of the net effect of the chemicals of interest. However, the increased complexity and potential loss of generalizability may limit the value of studies of mixtures, especially for mixtures based on mode of action or shared health outcomes. Our recommended strategy is to successively assess the marginal contribution of individual chemicals, joint effects with other specific chemicals, and hypothesis-driven evaluation of mixtures rather than applying hypothesis-free data exploration methods. Although more ambitious statistical approaches to mixtures may, in time, be helpful for guiding regulation, the authors believe conventional methods for assessing individual and combined effects of chemicals remain preferable. https://doi.org/10.1289/EHP11899.

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 p -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 ≤ 7 % 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.