Understanding Dynamic Status Change of Hospital Stay and Cost Accumulation via Combining Continuous and Finitely Jumped Processes

Abstract EN

The Coxian phase-type models and the joint models of longitudinal and event time have been extensively used in the studies of medical outcome data.

Coxian phase-type models have the finite-jump property while the joint models usually assume a continuous variation.

The gap between continuity and discreteness makes the two models rarely used together.

In this paper, a partition-based approach is proposed to jointly model the charge accumulation process and the time to discharge.

The key construction of our new approach is a set of partition cells with their boundaries determined by a family of differential equations.

Using the cells, our new approach makes it possible to incorporate finite jumps induced by a Coxian phase-type model into the charge accumulation process, therefore taking advantage of both the Coxian phase-type models and joint models.

As a benefit, a couple of measures of the “cost” of staying in each medical stage (identified with phases of a Coxian phase-type model) are derived, which cannot be approached without considering the joint models and the Coxian phase-type models together.

A two-step procedure is provided to generate consistent estimation of model parameters, which is applied to a subsample drawn from a well-known medical cost database.