Adaptive Thresholding in Bayesian Kernel Machine Regression: Improving Sensitivity and Reliability

Music City Center 

Bayesian Kernel Machine Regression (BKMR) models complex nonlinear relationships. Conventional fixed posterior inclusion probability (PIP) thresholds (e.g., 0.5) are often used for variable selection, which can result in inconsistent test size control, influenced by the coefficient of variation (CV) and sample size. This study proposes a dynamic PIP threshold that adjusts for CV and sample size to enhance sensitivity and reliability. A logistic regression model predicted the 95th percentile of PIP (PIP(q95)) using a four-parameter Richard Curve, incorporating log-transformed CV and sample size. Simulations across 41 CV values and 6 sample sizes compared fixed and dynamic thresholds. Validation used NHANES (2011–2014) data on urinary metals and cognitive scores. The dynamic threshold maintained nominal test sizes (~5%) across all scenarios, outperforming fixed thresholds. Applied to NHANES data, cadmium was most influential, while cobalt was preserved due to the dynamic threshold. Nonlinear relationships and cumulative risk analyses confirmed significant cognitive decline at higher exposure quantiles. The dynamic threshold enhances BKMR's reliability and precision.

Bayesian Kernel Machine Regression (BKMR)

Posterior Inclusion Probability (PIP)

Environmental Health Data

Adaptive Thresholding

Mixture Selection 

Section on Bayesian Statistical Science