Ensemble methods for survival function estimation with time-varying covariates
This work addresses a practical limitation in survival analysis for researchers and practitioners by extending existing forest methods to handle time-varying covariates, though it is incremental as it builds on established techniques.
The authors tackled the problem of estimating survival functions with time-varying covariates by generalizing conditional inference and relative risk forests to handle such data, and proposed a general framework for this estimation. Their results showed that the proposed forests substantially improved over the Kaplan-Meier estimate, with one of them being the best method under proportional hazard settings, while an adapted transformation forest performed best under non-proportional hazard settings.
Survival data with time-varying covariates are common in practice. If relevant, they can improve on the estimation of survival function. However, the traditional survival forests - conditional inference forest, relative risk forest and random survival forest - have accommodated only time-invariant covariates. We generalize the conditional inference and relative risk forests to allow time-varying covariates. We also propose a general framework for estimation of a survival function in the presence of time-varying covariates. We compare their performance with that of the Cox model and transformation forest, adapted here to accommodate time-varying covariates, through a comprehensive simulation study in which the Kaplan-Meier estimate serves as a benchmark, and performance is compared using the integrated L2 difference between the true and estimated survival functions. In general, the performance of the two proposed forests substantially improves over the Kaplan-Meier estimate. Taking into account all other factors, under the proportional hazard (PH) setting, the best method is always one of the two proposed forests, while under the non-PH setting, it is the adapted transformation forest. K-fold cross-validation is used as an effective tool to choose between the methods in practice.