Ensemble methods for survival function estimation with time-varying covariates

Abstract

Survival data with time-varying covariates are common in practice. If relevant, they can improve on the estimation of a 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 $L_{2}$ 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 setting, the best method is always one of the two proposed forests, while under the non-proportional hazard setting, it is the adapted transformation forest. $K$ -fold cross-validation is used as an effective tool to choose between the methods in practice.

Keywords

Survival forests time-varying covariates survival curve estimate dynamic estimation left-truncated right-censored survival data

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