  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.
