Multivariate Survival Analysis (I): Shared Frailty Approaches to Reliability and Dependence Modeling

The latest advances in survival analysis have been centered on multivariate systems. Multivariate survival analysis has two major categories of models: one is multi-state modeling; the other is shared frailty modeling. Multi-state models, although formulated differently in both fields, have been extensively studied in reliability analysis in the context of Markov chain analysis. In contrast, shared frailty modeling seems little known in reliability analysis and computer science. In this article, we focus exclusively on shared frailty modeling. Shared frailty refers to the often-unobserved factors or risks responsible for the common risks dependence between multiple events. It is well recognized as the most effective modeling approach to address common risks dependence and, more recently, the event-related dependence. The only exclusion of dependence modeling for the frailty approach is the common events type, which is best addressed by multi-state modeling. We argue that shared frailty modeling not only is perfectly applicable for engineering reliability, but also is of significant potential in other fields of computer science, such as networking and software reliability and survivability, machine learning, and prognostics and health management (PHM).