Frailty Models in the Structural Equation Modeling Framework

Frailty models extend survival analysis models to accommodate recurrent events by incorporating random effects to account for the dependence among clustered event times. Despite their relevance for behavioral and social science research, frailty models remain underutilized, in part due to limited integration with commonly used analytic frameworks. This paper presents a comprehensive treatment of frailty models and their specification and estimation in structural equation modeling (SEM) programs using multilevel and multivariate model specifications. We review discrete-time and Cox survival models and demonstrate how each is specified using SEM software. We then extend these models to include random effects and outline multiple specification strategies along with their associated data structures. Using empirical data on adolescent sleep latency, we illustrate the implementation of six alternative frailty model specifications and compare their parameter estimates. Recommendations for model specifications are discussed.