A METHOD FOR DETECTING OPTIMAL SPLITS OVER TIME IN SURVIVAL ANALYSIS USING TREE-STRUCTURED MODELS

One of the most popular uses for tree-based methods is in survival analysis for censored time data where the goal is to identify factors that are predictive of survival. Tree-based methods, due to their ability to identify subgroups in a hierarchical manner, can sometimes provide a useful alternative to Coxs proportional hazards model (1972) for the exploration of survival data. Since the data are partitioned into approximately homogeneous groups, Kaplan-Meier estimators can be used to compare prognosis between the groups presented by nodes in the tree. The demand for tree-based methods comes from clinical studies where the investigators are interested in grouping patients with differing prognoses. Tree-based methods are usually conducted at landmark time points, for example, five-year overall survival, but the effects of some covariates might be attenuated or increased at some other landmark time point. In some applications, it may be of interest to also determine the time point with respect to the outcome interest where the greatest discrimination between subgroups occurs. Consequently, by using a conventional approach, the time point at which the discrimination is the greatest might be missed.To remediate this potential problem, we propose a tree-structure method that will split based on the potential time-varying effects of the covariates. Accordingly, with our method, we find the best point of discrimination of a covariate with respect to not only a particular value of that covariate but also to the time when the endpoint of interest is observed. We analyze survival data from the National Surgical Adjuvant Breast and Bowel Project (NSABP) Protocol B-09 to demonstrate our method. Simulations are used to assess the statistical properties of this proposed methodology.We propose a new method in survival analysis, which is an area of statistics that is commonly used to assess prognoses of patients or participants in large public health studies. Our proposed method has public health significance because it could potentially facilitate a more refined assessment of the effect of biological and clinical markers on the survival times of different patient populations.