A Quantile-Based g-Computation Approach to Addressing the Effects of Exposure Mixtures

Abstract

Background: Exposure mixtures frequently occur in data across many domains, particularly in the fields of environmental and nutritional epidemiology. Various strategies have arisen to answer questions about exposure mixtures, including methods such as weighted quantile sum (WQS) regression that estimate a joint effect of the mixture components.

Objectives: We demonstrate a new approach to estimating the joint effects of a mixture: quantile g-computation. This approach combines the inferential simplicity of WQS regression with the flexibility of g-computation, a method of causal effect estimation. We use simulations to examine whether quantile g-computation and WQS regression can accurately and precisely estimate the effects of mixtures in a variety of common scenarios.

Methods: We examine the bias, confidence interval (CI) coverage, and bias-variance tradeoff of quantile g-computation and WQS regression and how these quantities are impacted by the presence of noncausal exposures, exposure correlation, unmeasured confounding, and nonlinearity of exposure effects.

Results: Quantile g-computation, unlike WQS regression, allows inference on mixture effects that is unbiased with appropriate CI coverage at sample sizes typically encountered in epidemiologic studies and when the assumptions of WQS regression are not met. Further, WQS regression can magnify bias from unmeasured confounding that might occur if important components of the mixture are omitted from the analysis.

Discussion: Unlike inferential approaches that examine the effects of individual exposures while holding other exposures constant, methods like quantile g-computation that can estimate the effect of a mixture are essential for understanding the effects of potential public health actions that act on exposure sources. Our approach may serve to help bridge gaps between epidemiologic analysis and interventions such as regulations on industrial emissions or mining processes, dietary changes, or consumer behavioral changes that act on multiple exposures simultaneously. https://doi.org/10.1289/EHP5838.

Figure 1.

Scenario 5: Impact of copollutant confounding on the bias of the overall exposure effect estimate ($n=500$; $d=9$) for quantile g-computation (q-gcomp) and weighted quantile sum (WQS) regression at varying exposure correlations (${\mathrm{\rho }}_{X_1,X_2}$ of 0.0, 0.4, and 0.75) and varying total effect sizes ($\mathrm{\psi }={\mathrm{\beta }}_1+{\mathrm{\beta }}_2\in 0.2,0.15,0.05$). Boxes represent the median (center line) and interquartile range (outer lines of box) and outliers [points outside of the $1.5\times \text{interquartile}\text{range}\left(\text{IQR}\right)$ length whiskers] across 1,000 simulations. Corresponding figures for $d=4$ and 14 and $n=100$ ($d=4,9,\text{and}14$) are provided in Figures S3–S7.

Figure 2.

Scenario 5: Impact of copollutant confounding on the confidence interval width of individual exposure estimates ($\mathrm{\beta }$) and the overall exposure effect estimate ($\mathrm{\psi }$) for quantile g-computation (q-gcomp) under exposure correlations (${\mathrm{\rho }}_{{\mathit{X}}_1,{\mathit{X}}_2}$) from 0.0 to 0.9 ($n=500$, $d=9$, and $\mathrm{\psi }={\mathrm{\beta }}_1=0.25$).

Figure 3.

Scenario 6: Impact of unmeasured confounding on the bias of the overall exposure effect estimate (mean across 1,000 simulations; $n=500$, 2,000, or 5,000) for quantile g-computation (q-gcomp) and weighted quantile sum (WQS) regression with confounder correlation (${\mathrm{\rho }}_{X,C}$) of 0.75, ${\mathrm{\beta }}_C=0.5$, and varying the total number of noise exposures ($d\in 4,7,9,14,22,29,35$). Note that all lines for quantile g-computation are overlapping and indicate unmeasured confounding bias is similar across sample sizes and number of exposures.