Bayesian Hierarchical Frailty Models for Heterogeneity in Risk

Abstract

The effect of an intervention or exposure on time-to-event is most commonly estimated with the Cox model, which assumes proportional hazards. When heterogeneity in risk is present, the assumption of proportionality is violated and the Cox model's population-averaged estimate of the hazard ratio can underestimate the effect for an individual. In this dissertation, we develop Bayesian hierarchical frailty models that adjust for heterogeneity in risk in a way that reflects the sources of heterogeneity. We focus on the compound Poisson distribution, as it reflects a biological risk mechanism seen in many applications where an individual's risk of an event is the result of independent, competing exposure processes and it allows that some individuals have no risk of an event. In Chapter 2, we outline a hierarchical definition of the compound Poisson distribution and demonstrate Bayesian estimation of a hierarchical compound Poisson frailty model. In Chapter 3, we extend the model proposed in Chapter 2 to allow frailty distributions to vary across latent risk classes, resulting in a compound Poisson mixture frailty distribution. Risk-related covariates are used to classify participants into latent risk groups. We conclude with a discussion of future work, including ideas for a gamma frailty model with subject-specific parameters for situations in which exposure processes are observed.