The estimation of the effect of environmental exposures and overall mixtures on a survival time outcome is common in environmental epidemiological studies. While advanced statistical methods are increasingly being used for mixture analyses, their applicability and performance for survival outcomes has yet to be explored. We identified readily available methods for analyzing an environmental mixture's effect on a survival outcome and assessed their performance via simulations replicating various real-life scenarios. Using prespecified criteria, we selected Bayesian Additive Regression Trees (BART), Cox Elastic Net, Cox Proportional Hazards (PH) with and without penalized splines, Gaussian Process Regression (GPR) and Multivariate Adaptive Regression Splines (MARS) to compare the bias and efficiency produced when estimating individual exposure, overall mixture, and interaction effects on a survival outcome. We illustrate the selected methods in a real-world data application. We estimated the effects of arsenic, cadmium, molybdenum, selenium, tungsten, and zinc on incidence of cardiovascular disease in American Indians using data from the Strong Heart Study (SHS). In the simulation study, there was a consistent bias-variance trade off. The more flexible models (BART, GPR and MARS) were found to be most advantageous in the presence of nonproportional hazards, where the Cox models often did not capture the true effects due to their higher bias and lower variance. In the SHS, estimates of the effect of selenium and the overall mixture indicated negative effects, but the magnitudes of the estimated effects varied across methods. In practice, we recommend evaluating if findings are consistent across methods.

翻译：在环境流行病学研究中，评估环境暴露及整体混合物对生存时间结局的影响十分常见。尽管高级统计方法正越来越多地应用于混合物分析，但其在生存结局中的适用性和性能尚未得到充分探索。我们筛选了当前可直接用于分析环境混合物对生存结局影响的方法，并通过模拟再现多种真实场景对其性能进行评估。依据预设标准，我们选取了贝叶斯加性回归树（BART）、Cox弹性网络、含/不含惩罚样条的Cox比例风险（PH）模型、高斯过程回归（GPR）及多元自适应回归样条（MARS），比较这些方法在估算个体暴露、整体混合物及交互作用对生存结局影响时产生的偏倚与效率差异。通过真实数据应用展示所选方法的实践效果：利用强心研究（SHS）数据，我们估算了砷、镉、钼、硒、钨和锌对美国印第安人心血管疾病发病率的影响。模拟研究表明，偏倚与方差之间存在一致性权衡。在非比例风险条件下，灵活模型（BART、GPR和MARS）优势显著——此时Cox模型因高偏倚和低方差而难以捕捉真实效应。在SHS中，硒及整体混合物的效应估计均显示负向影响，但各方法得出的效应量存在差异。实际应用中，建议评估不同方法结果的一致性。