Bayesian Kernel Machine Regression (BKMR) has emerged as a powerful tool to detect negative health effects from exposure to complex multi-pollutant mixtures. However, its performance is degraded when data deviate from normality. In this comprehensive simulation analysis, we show that BKMR's power and test size vary under different distributions and covariance matrix structures. Our results demonstrate specifically that BKMR's robustness is influenced by the response's coefficient of variation (CV), resulting in reduced accuracy to detect true effects when data are skewed. Test sizes become uncontrolled (> 0.05) as CV values increase, leading to inflated false detection rates. However, we find that BKMR effectively utilizes off-diagonal covariance information corresponding to predictor interdependencies, increasing statistical power and accuracy. To achieve reliable and accurate results, we advocate for scrutiny of data skewness and covariance before applying BKMR, particularly when used to predict cognitive decline from blood/urine heavy metal concentrations in environmental health contexts.

翻译：贝叶斯核机器回归（BKMR）已成为检测复杂多污染物混合暴露对健康负面效应的有力工具。然而，当数据偏离正态分布时，其性能会下降。在这项综合模拟分析中，我们表明BKMR的检验功效和检验尺度在不同分布及协方差矩阵结构下存在差异。我们的结果具体表明，BKMR的稳健性受响应变量变异系数（CV）的影响，导致数据偏斜时检测真实效应的准确性降低。随着CV值增大，检验尺度会失控（> 0.05），从而导致错误检测率膨胀。然而，我们发现BKMR能有效利用与预测变量相互依赖性对应的非对角线协方差信息，从而提高统计功效和准确性。为获得可靠且准确的结果，我们建议在应用BKMR前仔细检查数据偏度和协方差结构，特别是在环境健康领域用于根据血液/尿液重金属浓度预测认知衰退的场合。