Ensemble survival tree models to reveal pairwise interactions of variables with time-to-events outcomes in low-dimensional setting

Unraveling interactions among variables such as genetic, clinical, demographic and environmental factors is essential to understand the development of common and complex diseases. To increase the power to detect such variables interactions associated with clinical time-to-events outcomes, we borrowed established concepts from random survival forest (RSF) models. We introduce a novel RSF-based pairwise interaction estimator and derive a randomization method with bootstrap confidence intervals for inferring interaction significance. Using various linear and nonlinear time-to-events survival models in simulation studies, we first show the efficiency of our approach: true pairwise interaction-effects between variables are uncovered, while they may not be accompanied with their corresponding main-effects, and may not be detected by standard semi-parametric regression modeling and test statistics used in survival analysis. Moreover, using a RSF-based cross-validation scheme for generating prediction estimators, we show that informative predictors may be inferred. We applied our approach to an HIV cohort study recording key host gene polymorphisms and their association with HIV change of tropism or AIDS progression. Altogether, this shows how linear or nonlinear pairwise statistical interactions of variables may be efficiently detected with a predictive value in observational studies with time-to-event outcomes.