Comparing Split Criteria for Constructing Survival Trees

Abstract

Various split criteria for constructing recursively partitioned trees from censored data have been proposed. However, no uniform superior split criterion is available. Wecompared five different split criteria regarding the explained variation of outcome with application to a clinical data set from a study of extracorpore al shock wave lithotripsy (ESWL) for treatment of gallbladder stones in 408 patients. The main end point was time until detection of complete stone clearance. The covariates patient age, sex, body mass index, relative gallbladder volume reduction after fatty meal, stone density, stone diameter, and stone number were analysed. The split criteria relative risk, log-rank statistic, log-rank statistic adjusted for measurement scale, partial likelihood ratio, and constant hazard likelihood ratio were compared. Model likelihood and Magee’s R ² were used as measures of information content and explained variation, respectively. In the first step, trees were constructed and validated using separate learning and validation samples, respectively. In the second step, bootstrap confidence intervals of explained variation were estimated using an internal validation procedure. There was no substantial difference between splitting algorithms in terms of explained variation. Simulation studies of pruned trees are necessary to extend our results.