Performance of variable and function selection methods for estimating the nonlinear health effects of correlated chemical mixtures: A simulation study

Abstract

Statistical methods for identifying harmful chemicals in a correlated mixture often assume linearity in exposure‐response relationships. Nonmonotonic relationships are increasingly recognized (eg, for endocrine‐disrupting chemicals); however, the impact of nonmonotonicity on exposure selection has not been evaluated. In a simulation study, we assessed the performance of Bayesian kernel machine regression (BKMR), Bayesian additive regression trees (BART), Bayesian structured additive regression with spike‐slab priors (BSTARSS), generalized additive models with double penalty (GAMDP) and thin plate shrinkage smoothers (GAMTS), multivariate adaptive regression splines (MARS), and lasso penalized regression. We simulated realistic exposure data based on pregnancy exposure to 17 phthalates and phenols in the US National Health and Nutrition Examination Survey using a multivariate copula. We simulated data sets of size N = 250 and compared methods across 32 scenarios, varying by model size and sparsity, signal‐to‐noise ratio, correlation structure, and exposure‐response relationship shapes. We compared methods in terms of their sensitivity, specificity, and estimation accuracy. In most scenarios, BKMR, BSTARSS, GAMDP, and GAMTS achieved moderate to high sensitivity (0.52‐0.98) and specificity (0.21‐0.99). BART and MARS achieved high specificity (≥0.90), but low sensitivity in low signal‐to‐noise ratio scenarios (0.20‐0.51). Lasso was highly sensitive (0.71‐0.99), except for quadratic relationships (≤0.27). Penalized regression methods that assume linearity, such as lasso, may not be suitable for studies of environmental chemicals hypothesized to have nonmonotonic relationships with outcomes. Instead, BKMR, BSTARSS, GAMDP, and GAMTS are attractive methods for flexibly estimating the shapes of exposure‐response relationships and selecting among correlated exposures.

Variable selection for discrete survival model with frailty in presence of left truncation and right censoring: Studying association of environmental toxicants on time‐to‐pregnancy

“…In this article, we have focused on the frequentist approaches for variable selection, which among other desirable properties are easier to compute. Alternatively, computationally intensive Bayesian non-parametric methods such as Bayesian kernel machine regression with variable selection have been shown to perform better than L1-penalized methods, 38,39 especially in the context of chemical mixtures with continuous outcomes. However, they need to be investigated more thoroughly in the context of survival outcomes subject to left truncation and right censoring.…”

Comparative efficacy of three Bayesian variable selection methods in the context of weight loss in obese women

“…Among these Bayesian methods, those employing spike-and-slab priors ( 10 ) or shrinkage priors ( 11 ) stand out for features selection. These methods are now widely studied and employed within the environmental epidemiological literature ( 9 , 12 ), but only a few studies have evaluated the differences and similarities of those approaches in a more general setting.…”

“…In addition, multiple co-occurring predictors can have nonlinear and nonadditive relationships with the health outcome, and most statistical methods fail to properly model those relationships. Penalised regression methods are used in this context, such as the least Absolute Shrinkage and Selection Operator (LASSO) (3) and its numerous variants (4-7), along with Bayesian variable selection methods, which have recently been developed to handle jointly multiple correlated predictors and both nonlinear and nonadditive relationships, allowing for the inclusion of prior information (8,9). Among these Bayesian methods, those employing spike-and-slab priors (10) or shrinkage priors (11) stand out for features selection.…”

Comparative Efficacy of Three Bayesian Variable Selection Methods in the Context of Weight Loss in Obese Women

“…In addition, multiple co-occurring predictors can have nonlinear and nonadditive relationships with the health outcome, and most statistical methods fail to properly model those relationships. Penalised regression methods are used in this context, such as the least Absolute Shrinkage and Selection Operator (LASSO) [3] and its numerous variants [4][5][6][7], along with Bayesian variable selection methods, which have recently been developed to handle jointly multiple correlated predictors and both nonlinear and nonadditive relationships, allowing for the inclusion of prior information [8,9].…”

“…Among these Bayesian methods, those employing spike-and-slab priors [10] or shrinkage priors [11] stand out for features selection. These methods are now widely studied and employed within the environmental epidemiological literature [9,12], but only a few studies have evaluated the differences and similarities of those approaches in a more general setting.…”