Identification of prognostic factors with multivariate survival data

Multivariate survival data arises when subjects in the same group are related to each other or when there are multiple recurrences of the disease in the same subject. A common goal of survival analysis is to relate the outcome (time to event) to a set of covariates. In this paper, we focus on prognostic classification for multivariate survival data where identifying subgroups of patients with similar prognosis is of interest. We propose a computationally feasible method to identify prognostic groups with the widely used Classification and Regression Trees (CART) algorithm. The proposed method extends CART algorithm to multivariate survival data by introducing a gamma frailty to account for dependence among correlated events. The method is applied to a catheter infection data, and the performance of the method is also investigated by several simulation studies.