# An Alternative Formulation of Coxian Phase-type Distributions with Covariates: Application to Emergency Department Length of Stay

## TL;DR

This paper introduces a new covariate-inclusive Coxian phase-type modeling approach for emergency department length of stay, improving computational efficiency and accounting for patient heterogeneity.

## Contribution

It reformulates Coxian models to incorporate covariates, reducing computational time and enhancing modeling of patient heterogeneity in ED stay analysis.

## Key findings

- Model effectively captures patient heterogeneity.
- Reduces computational time compared to previous methods.
- Successfully applied to real hospital data.

## Abstract

In this paper we present a new methodology to model patient transitions and length of stay in the emergency department using a series of conditional Coxian phase-type distributions, with covariates. We reformulate the Coxian models (standard Coxian, Coxian with multiple absorbing states, joint Coxian, and conditional Coxian) to take into account heterogeneity in patient characteristics such as arrival mode, time of admission and age. The approach differs from previous research in that it reduces the computational time, and it allows the inclusion of patient covariate information directly into the model. The model is applied to emergency department data from University Hospital Limerick in Ireland.