# Insert "Price" to Coxian Phase-Type Models: An Application to Hospital Charge and Length of Stay Data

## TL;DR

This paper bridges RGRST and Coxian Phase-Type models to jointly analyze hospital charge and length of stay data, introducing a 'price' measure for medical stages and providing an estimation algorithm, demonstrated on real hospital data.

## Contribution

It establishes a novel connection between RGRST and CPH models, enabling combined analysis and new insights into hospital stay costs.

## Key findings

- Derived a measure of 'price' for each medical stage.
- Developed a two-stage estimation algorithm.
- Applied the method to real hospital data from NY.

## Abstract

In this paper, we discuss the connection between the RGRST models (Gardiner et al 2002, Polverejan et al 2003) and the Coxian Phase-Type (CPH) models (Marshall et al 2007, Tang 2012) through a construction that converts a special sub-class of RGRST models to CPH models. Both of the two models are widely used to characterize the distribution of hospital charge and length of stay (LOS), but the lack of connections between them makes the two models rarely used together. We claim that our construction can make up this gap and make it possible to take advantage of the two different models simultaneously. As a consequence, we derive a measure of the "price" of staying in each medical stage (identified with phases of a CPH model), which can't be approached without considering the RGRST and CPH models together.A two-stage algorithm is provided to generate consistent estimation of model parameters. Applying the algorithm to a sample drawn from the New York State's Statewide Planning and Research Cooperative System 2013 (SPARCS 2013), we estimate the prices in a four-phase CPH model and discuss the implications.