The Distribution Study Of Inpatients’ Length Of Stay Based On Hospital Data

Hospital inpatient beds are important medical resources, and hospital length of stay (LOS) is a valid proxy to estimate the consumption of hospital resources. However, the average LOS does not reflect the nature of the underlying distribution. Decisions based on the average LOS could result in heavy loss if the underlying distribution is asymmetric. Understanding the distribution of LOS is extremely necessary to hospital bed management and medical insurance actuarial method.This paper focuses on the estimation of hospital LOS distribution by using data collected from Hefei Medical Insurance Management Center. Firstly, this paper analyses the hospital LOS. Then, we fit the data through the Gamma, lognormal. Weibull and phase-type (PH) distributions. The Gamma, lognormal and Weibull distributions are fitted through the MATLAB software. And the phase-type distribution is fitted via the expectation maximization (EM) algorithm through the Visual Studio 2010 software. Then the proper distributions and parameters are chosen based on the goodness of fit tests. The result shows that Coxian distribution is better than other distributions and the phase is determined by specific data, which means that larger phase is not always perfect. In the end, we propose a survival tree based on patients’age, gender and the hospital rank information via the Coxian distribution. The survival tree divides patients into groups, which is helpful to clinical process. Moreover, this paper provides an empirical evidence for traditional operational research models and verifies common service time distributions about queueing models, expecting to offer help for the future model research. Finally, the shortcomings and prospect of the study are discussed.