Development and Modeling of Decision Tree for Survival Data with Multiple Events Using Deviance and Cox-Snell Residuals within Node Homogeneity Technique

Abstract

It is very common in medical studies for a patient to experience more than one event rather than one of interest. This led to exposing an individual to multiple risks and medical practitioners need to account for these risks concerning some prognostic factors. There are many methods of dealing with multiple events in survival data classically, however, these methods break down when considering the top-down effect of the prognostic factors concurrently and when the risks of events are correlated (competing risks). This study aimed to develop a decision tree using a within-node homogeneity procedure in survival analysis with multiple events to classify individual risks for the competing risks. Since the CART methodology involves recursive portioning of covariates into different subgroups, this study considers the use of Deviance and Modified Cox-Snell residuals as a measure of impurity in the Classification Regression Tree (CART) during the process of partitioning. The flexibility and predictive accuracy of our learning algorithm would then be compared with other existing methods through simulation and the freely available online real-life data. The results of the simulation revealed that: using Deviance and Cox-Snell residuals as a response within the node homogeneity classification tree performs better than using other residuals irrespective of performance indices. Results from empirical studies of the two real-life data that the proposed model with Cox-Snell residual (Deviance=16.6498) performs better than both the Martingale residual (deviance=160.3592) and Deviance residual (Deviance=556.8822). Conclusively, using Cox-Snell residual (Mean Square Error (MSE)=0.01783563) as a measure of impurity in CART revealed improved performance than using any other residual methods (MSE=0.1853148, 0.8043366). This implies that the proposed methods have the capability of accounting for individual effects based on the prognostic biomarkers.