Calibrate posterior inclusion probability thresholds for BKMR significance decisions

Determine an evidence-based posterior inclusion probability (PIP) cutoff for Bayesian Kernel Machine Regression (BKMR) variable selection—covering both component-wise and hierarchical group selection—that yields reliably calibrated significance decisions, including control of Type I error at a prespecified level, across typical exposure-mixture scenarios and under plausible prior specifications in environmental epidemiology applications.

Background

Bayesian Kernel Machine Regression (BKMR) models the exposure–response function using a Gaussian Process and performs variable selection by assigning spike-and-slab priors to kernel parameters, producing posterior inclusion probabilities (PIPs) for individual exposures or pre-specified exposure groups. Researchers often use PIPs as a basis for significance decisions (e.g., declaring an exposure or group associated if its PIP exceeds a chosen cutoff).

The paper’s simulations show that PIP behavior can be sensitive to prior settings and that default hierarchical selection can lead to elevated PIPs even under the null. While using a higher cutoff (e.g., 0.95) controlled Type I error in the authors’ simulations, this choice was arbitrary and may not generalize. Hence, establishing principled, empirically validated PIP thresholds is important to ensure valid inference with BKMR in mixture analyses.