Time-dependent tree-structured survival analysis with unbiased variable selection through permutation tests.

Incorporating time-dependent covariates into tree-structured survival analysis (TSSA) may result in more accurate prognostic models than if only baseline values are used. Available time-dependent TSSA methods exhaustively test every binary split on every covariate; however, this approach may result in selection bias toward covariates with more observed values. We present a method that uses unbiased significance levels from newly proposed permutation tests to select the time-dependent or baseline covariate with the strongest relationship with the survival outcome. The specific splitting value is identified using only the selected covariate. Simulation results show that the proposed time-dependent TSSA method produces tree models of equal or greater accuracy as compared to baseline TSSA models, even with high censoring rates and large within-subject variability in the time-dependent covariate. To illustrate, the proposed method is applied to data from a cohort of bipolar youths to identify subgroups at risk for self-injurious behavior.