Methods/Statistics
Performance of Bayesian Kernel Machine Regression (BKMR): A Simulation Study Stacey Alexeeff* Stacey Alexeeff Juanran Feng Jennifer F Bobb
Background: Bayesian Kernel Machine Regression (BKMR) is a widely used statistical methodology that flexibly models complex exposure mixtures. This study expands on the simulation study in the original BKMR paper by varying the signal-to-noise ratio, evaluating larger sample sizes, and running more simulations per scenario to evaluate performance.
Methods: We conducted a simulation study to assess the performance of BKMR with 1,000 simulations per scenario. We evaluated four signal-to-noise ratios (high, moderate, low, and null) under two sample sizes (n=100 and n=400) with a mixture exposure response function that included two main effects and an interaction. We summarized the distributions of the posterior inclusion probabilities (PIPs) using boxplots and by comparing the rank ordering. We computed the bias, model standard error, empirical standard error, and coverage of the Bayesian 95% credible intervals.
Results: We found that the PIPs of truly associated exposures can vary widely, and their magnitudes depend on the signal-to-noise ratio and the sample size (Figure). For high signal-to-noise and higher sample size of n=400, truly associated exposures generally had higher PIPs than null exposures, with higher PIP rank ordering in 92% of simulations. For low signal-to-noise and lower sample size of n=100, truly associated exposures often did not have higher PIPs than null exposures, with higher PIP rank ordering in only 27% of simulations. Across scenarios, bias was low (-0.3 to 0.4), and the model standard error reflected the empirical standard error, leading to good coverage of the Bayesian 95% credible intervals (89% to 99%).
Conclusion: BKMR had low bias and credible intervals had good coverage. However, PIPs showed high variability, where null exposures may have higher PIPs than truly associated exposures, particularly in low signal-to-noise scenarios. BKMR is a reliable method, but caution is needed when interpreting PIPs.
