Abstract
Estimation and prediction of heterogeneous restricted mean survival time (hRMST) is of great clinical importance, which can provide an easily interpretable and clinically meaningful summary of the survival function in the presence of censoring and individual covariates. The existing methods for the modeling of hRMST rely on proportional hazards or other parametric assumptions on the survival distribution. In this paper, we propose a random forest based estimation of hRMST for right-censored survival data with covariates and prove a central limit theorem for the resulting estimator. In addition, we present a computationally efficient construction for the confidence interval of hRMST. Our simulations show that the resulting confidence intervals have the correct coverage probability of the hRMST, and the random forest based estimate of hRMST has smaller prediction errors than the parametric models when the models are mis-specified. We apply the method to the ovarian cancer data set from The Cancer Genome Atlas (TCGA) project to predict hRMST and show an improved prediction performance over the existing methods. A software implementation, srf using R and C++, is available at https://github.com/lmy1019/SRF.
Highlights
In epidemiological and biomedical studies, time to an event or survival time T is often the primary outcome of interest
Instead of focusing on predicting the survival function or the survival probability as the algorithms implemented by Ishwaran et al (2008) and Steingrimsson et al (2019), we develop in this paper a random forest framework to model the heterogeneous restricted mean survival time (hRMST) directly given the baseline covariates in the presence of possibly covariate-dependent censoring
We show that the resulting survival random forest estimates of hRMST has the asymptotic normality property that can be used to obtain the point-wise confidence interval with theoretical guarantees
Summary
In epidemiological and biomedical studies, time to an event or survival time T is often the primary outcome of interest. Important quantities related to survival time include hazard rate (HR), tyear survival probability, and the mean survival time. HR is one of the most commonly used quantity due to its strong connection to the proportional hazards regression model or Cox model. The t-year survival probability is the probability of survival time greater than a pre-specified time t. It is not suitable for summarizing the global profile of T over the duration of a study (Tian et al, 2014). Mean survival time is an alternative quantity since it takes the whole distribution of T into account.
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