Modeling the Length of Stay of Respiratory Patients in Emergency Department Using Coxian Phase-Type Distributions With Covariates

Variability and unpredictability are typical features of emergency departments (EDs) where patients randomly arrive with diverse conditions. Patient length of stay (LOS) represents the consumption level of hospital resources, and it is positively skewed and heterogeneous. Both accurate modeling of patient ED LOS and analysis of potential blocking causes are especially useful for patient scheduling and resource management. To tackle the uncertainty of ED LOS, this paper introduces two methods: statistical modeling and distribution fitting. The models are applied to 894 respiratory diseases patients data in the year 2014 from ED of a Chinese public tertiary hospital. Covariates recorded include patient region, gender, age, arrival time, arrival mode, triage category, and treatment area. A Coxian phase-type (PH) distribution model with covariates is proposed as an alternative method for modeling ED LOS. The expectation-maximization (EM) algorithm is used to implement parameter estimation. The results show that ED LOS data can be modeled well by the proposed models. Distributions of ED LOS differ significantly with respect to patients’ gender, arrival mode, and treatment area. Using the fitted Coxian PH model will assist ED managers in identifying patients who are most likely to have an extreme ED LOS and in predicting the forthcoming workload for resources.