Estimating lifetime medical costs under a semi-parametric gamma frailty copula model

The analysis of lifetime medical costs with censored data presents several statistical challenges. The assumption of independent censoring may be valid on the time scale, but is not reasonable on the cost scale. The censoring pattern on the cost scale is thus typically induced to be dependent. Of more concern is the fact that the cost distribution is potentially nowhere identifiable in a parametric setting due to this censoring. Methods to date have avoided this problem by estimating nonparametric time-restricted costs or the joint distribution of costs and survival. To remedy this, I propose a semi-parametric gamma frailty copula model which estimates the marginal lifetime medical cost distribution. This model assumes a Clayton's copula structure using the Laplace transform of a gamma distribution. An overview of cost data and its statistical challenges are discussed in Chapter 1. The model along with a description of the inference procedure are found in Chapter 2. Local consistency and asymptotic properties of the model are developed in Chapter 3. Model checking procedures are examined in Chapter 4. In Chapter 5, I present numerical study results from simulations and two examples from randomized clinical trials. Finally, I conclude with a discussion in Chapter 6.