Optimal Survival Trees

Survival analysis methods are required for censored data in which the outcome of interest is generally the time until an event (onset of disease, death, etc.), but the exact time of the event is unknown (censored) for some individuals. When a lower bound for these missing values is known (for example, a patient is known to be alive until at least time t) the data is said to be right-censored. A common survival analysis technique is Cox proportional hazards regression (Cox, 1972) which models the hazard rate for an event as a linear combination of covariate effects. Although this model is widely used and easily interpreted, its parametric nature makes it unable to identify nonlinear effects or interactions between covariates (Bou-Hamad et al., 2011). Recursive partitioning techniques (also referred to as trees) are a popular alternative to parametric models. When applied to survival data, survival tree algorithms partition the covariate space into smaller and smaller regions (nodes) containing observations with homogeneous survival outcomes.