Association between split selection instability and predictive error in survival trees

Objectives: To evaluate split selection instability in six survival tree algorithms and its relationship with predictive error by means of a bootstrap study. Methods: We study the following algorithms: logrank statistic with multivariate p-value adjustment without pruning (LR), Kaplan-Meier distance of survival curves (KM), martingale residuals (MR), Poisson regression for censored data (PR), within-node impurity (WI), and exponential log-likelihood loss (XL). With the exception of LR, initial trees are pruned by using split-complexity, and final trees are selected by means of cross-validation. We employ a real dataset from a clinical study of patients with gallbladder stones. The predictive error is evaluated using the integrated Brier score for censored data. The relationship between split selection instability and predictive error, is evaluated by means of box-percentile plots, covariate and cutpoint selection entropy, and cutpoint selection coefficients of variation, respectively, in the root node. Results: We found a positive association between covariate selection instability and predictive error in the root node. LR yields the lowest predictive error, while KM and MR yield the highest predictive error. Conclusions: The predictive error of survival trees is related to split selection instability. Based on the low predictive error of LR, we recommend the use of this algorithm for the construction of survival trees. Unpruned survival trees with multivariate p-value adjustment can perform equally well compared to pruned trees. The analysis of split selection instability can be used to communicate the results of tree-based analyses to clinicians and to support the application of survival trees.