Joint Modeling of Multivariate Survival Data With an Application to Retirement

The Cox proportional hazards model has been pervasively used in many social science areas to examine the effects of covariates on timing to an event. The standard Cox model is intended to study univariate survival data where there is a singular event of interest, which can only be experienced once. However, we may additionally wish to explore a number of other complexities that are prevalent in survival data. For example, an individual may experience events of the same type more than once or may experience multiple types of events. This study introduces innovations in recurrent (repeatable) event analysis, jointly modeling several endogenous survival processes. As an example and an application, we simultaneously model two types of recurrent events in the presence of a dependent terminal event. This model not only correctly handles different types of recurrent events but also explicitly estimates the direction and magnitude of relationships between recurrences and survival. This article concludes with an example of the model to examine how the timing of retirement is associated with the risks of multiple spells of employment and childbearing. The theoretical discussions and empirical analyses suggest that the multivariate joint models have much to offer to a wide variety of substantive research areas.