Analysis of multivariate survival data with Clayton regression models under conditional and marginal formulations

The Clayton models, also called gamma frailty models, have been widely used for multivariate survival analysis. These models typically appear in either conditional or marginal formulations where covariates are incorporated through regression models. The two formulations provide us the flexibility to delineate various types of dependence of survival times on covariates, along with the availability of directly applying the likelihood method for inferences if the baseline hazard functions are parametrically or weakly parametrically specified. There are, however, fundamental issues pertaining to these models. It is not clear how the covariate effects in the two formulations are related to each other. What is the impact if misusing the conditional formulation when the true form should be marginal, or vice versa? These problems are investigated, and the relationship of the covariate coefficients between conditional and marginal regression models is established. Furthermore, empirical studies are carried out to assess how censoring proportion may affect estimation of covariate coefficients. A real example from the Busselton Health Study is analyzed for illustration.