Interval censored recursive forests

Abstract

We propose interval censored recursive forests (ICRF), an iterative tree ensemble method for interval censored survival data. This nonparametric regression estimator addresses the splitting bias problem of existing tree-based methods and iteratively updates survival estimates in a self-consistent manner. Consistent splitting rules are developed for interval censored data, convergence is monitored using out-of-bag samples, and kernel-smoothing is applied. The ICRF is uniformly consistent and displays high prediction accuracy in both simulations and applications to avalanche and national mortality data. An R package icrf is available on CRAN and Supplementary Materials for this article are available online.

Keywords: interval censored data; kernel-smoothing; quasi-honesty; random forest; self-consistency; survival analysis.

Figure 1:

Prediction errors of methods under different simulation settings (the ICRF’s are built in a quasi-honest manner); Fu, Fu and Simonoff [2017]; Yao, Yao et al. [2019]; (*), smoothed versions; The boxes on the left column are for case-I censoring (M = 1) and those on the right column are for case-II censoring (M = 3); For each setting, the horizontal line indicates the minimum of mean error levels of the methods.

Figure 2:

Mean and 1st and 3rd quartile ϵ^INT of splitting rules and prediction rules under Case-I censoring.

Figure 3:

Prediction errors under different sample sizes for Scenario 1 and K = 1.

Figure 4:

Estimated mean truncated log survival time in the avalanche data. The size of dots at the bottom of each box represents the number of sample data points.