Analysis of Survival Data with Multiple Events

Abstract

An important aim in biomedical studies is to study how an intermediate event and prognostic factors influence the course of disease of a patient. In most cases, the effect of the intermediate event is considered a timedependent covariate and studied using extensions of the Cox proportional hazards model. Additionally, many of these studies often involve several endpoints, making the traditional approaches much more complicated. In such cases, multi-state models provide a useful tool to describe the survival process. This article aims to illustrate how multi-state models can be used as an alternative to traditional approaches. It also aims to offer guidelines for the correct use of these approaches through the analysis of survival data of patients with breast cancer. Several analyses were performed, and methods to evaluate the effect of covariates on transition intensities and to test some usual assumptions are discussed. Tree-based survival models, like the Cox proportional hazards models, are popular methods for constructing a prediction model in the field of medical research. We also present the results obtained by applying some tree-based models to the breast cancer data while showing their interpretation and utility. An overview of available software and software developed by the authors is provided to aid researchers in choosing an appropriate software tool for their purposes.