Modeling the length-of-stay of patients with geriatric diseases or alcohol use disorder using phase-type distributions with covariates

The hospital length-of-stay (LOS), as an important measure of the effectiveness of healthcare, represents the level of medical requirement and is highly related to the treatment costs. As the human life expectancy has being increased rapidly in the past few decades, there is a pressing need to improve health systems for geriatric patients. Similarly, the alcohol use disorder (AUD), as a chronic relapsing brain disease related to severe problem drinking, has caused negative impacts to society and put patients’ health and safety at risk. In both cases, more efficient hospital management is in demand due to increasing requirements for long-term hospital treatment and the continuously rising medical cost. In order to improve the healthcare efficiency, an accurate modeling of the LOS data and the further analysis of potential influencing factors are necessary. In this paper, we utilize the Coxian Phase-Type (PH) distribution and apply Maximum Likelihood Estimation (MLE) to fit the patient flow information of both geriatric patients and AUD patients collected in a hospital. The influences of the covariates of age, gender, admission type, admit source, and financial class on LOS are assessed and compared through Expectation-Maximization (EM) algorithms. The results show that the LOS data of both types of patients can be modeled well, and the differences with respect to covariates can be accurately identified by the proposed methods. Using the fitted Coxian PH distribution and the estimated coefficients of covariates will provide a guide for better decision-making in healthcare service and resource allocation.