Survival Analysis Algorithms based on Decision Trees with Weighted Log-rank Criteria

Abstract

Survival Analysis is an important tool to predict time-to-event in many applications, including but not limitedto medicine, insurance, manufacturing and others. The state-of-the-art statistical approach is based on Coxproportional hazards. Though, from a practical point of view, it has several important disadvantages, such asstrong assumptions on proportional over time hazard functions and linear relationship between time independentcovariates and the log hazard. Another technical issue is an inability to deal with missing data directly.To overcome these disadvantages machine learning survival models based on recursive partitioning approachhave been developed recently. In this paper, we propose a new survival decision tree model that uses weightedlog-rank split criteria. Unlike traditional log-rank criteria the weighted ones allow to give different priority toevents with different time stamps. It works with missing data directly while searching the best splitting point,its size is controlled by p-value threshold with Bonferroni adjustment and quantile based discretization is usedto decrease the number of potential candidates for splitting points. Also, we investigate how to improve theaccuracy of the model with bagging ensemble of the proposed decision tree models. We introduce an experimentalcomparison of the proposed methods against Cox proportional risk regression and existing tree-basedsurvival models and their ensembles. According to the obtained experimental results, the proposed methodsshow better performance on several benchmark public medical datasets in terms of Concordance index andIntegrated Brier Score metrics.