Copula Function For Estimating Medical Lifetime Costs

Estimation and prediction of medical costs are important tasks in medical studies. It's well known that the medical costs of the patient are always associated with their health states which are often modeled by a dynamic process in a period. In this paper, we develop a new method to estimate total treatment costs over a finite period, we use a Markov process to describe the dynamic movements of patients between health states, on restricts the dependents of future event on past event, the period a patient is on one state and still change to another is named a sojourn time, the costs is the sum of all the cost on sojourn.If one is interested in the lifetime cost, the cost should be summed up to the failure time, however the complete observation of the lifetime cost is not always feasible since some subjects may be censored before the failure time, and as usual in survival analysis, the endpoint of observation may be set before the trail. This leads the induced dependent observations of cost data, which is prevalent issue in the survival analysis and actuarial studies. In this paper, copula model is proposed to fit the terminal events and the medical costs. One attractive feature of copula model is that the margins do not dependent on the choice of the dependency structure, and consequently we can model and estimate the dependency and the margins separately.The two-stage estimation procedure is applied for the statistical inference with partial likelihood and multivariate pseudo-maximum likelihood used to obtain the margins. The asymptotic properties of the estimators have been established as well. Finally, a simulation is performed to asses the proposed model and methodologies.