Performance of variable selection methods for estimating the non-linear health effects of correlated chemical mixtures

Abstract

OPS 05: Statistical methods to analyze mixtures, Room 114, Floor 1, August 27, 2019, 1:30 PM - 3:00 PM Background/Aim: Statistical methods for identifying harmful chemicals in a correlated mixture often assume linearity in exposure–response relationships. Non-monotonic relationships are biologically plausible (e.g., endocrine-disrupting chemicals); however, the impact of non-monotonicity on the performance of variable selection methods has not been evaluated. In a simulation study, we assessed the performance of three methods for the identification of important mixture components when exposure-response relationships are expected to be non-linear, including Bayesian kernel machine regression (BKMR), Bayesian additive regression trees (BART), and Bayesian structured additive regression with spike–slab priors (BSTARSS). We compared these methods to lasso penalised regression assuming linearity. Methods: We used data on exposure to phthalates and phenols in pregnant women from the U.S. National Health and Nutrition Examination Survey to simulate realistic exposure data using a multivariate copula, which allowed us to vary the correlation structure while preserving the observed marginal distributions. We simulated datasets of size N=250 and compared methods across 32 scenarios, varying by model size and sparsity, signal-to-noise ratio, exposure correlation structure, and shape of exposure–response relationships (including linear, S-shaped, and both symmetric and asymmetric inverse-U-shaped relationships). We compared the performance of methods in terms of their sensitivity, specificity, and estimation accuracy. Results: BKMR and BSTARSS achieved moderate to high specificity and sensitivity in most scenarios. BART achieved high specificity (>0.96), but low to moderate sensitivity (0.12–0.66). Lasso was highly sensitive (0.75–0.99), except when exposure–response relationships were symmetric inverse-U-shaped (<0.2). Performance was affected by changes in the signal-to-noise ratio but not substantially by the correlation structure. Conclusions: Penalised regression methods assuming linearity, such as lasso, may not be suitable in studies of environmental chemicals hypothesised to have non-monotonic relationships with outcomes. Instead, BKMR and BSTARSS may be used to flexibly estimate the shapes of exposure–response relationships and to select among correlated exposures in small sample size studies.