L₁ splitting rules in survival forests

The log-rank test is used as the split function in many commonly used survival trees and forests algorithms. However, the log-rank test may have a significant loss of power in some circumstances, especially when the hazard functions or when the survival functions cross each other in the two compared groups. We investigate the use of the integrated absolute difference between the two children nodes survival functions as the splitting rule. Simulations studies and applications to real data sets show that forests built with this rule produce very good results in general, and that they are often better compared to forests built with the log-rank splitting rule.