Modeling hospital length of stay by Coxian phase-type regression with heterogeneity

Hospital length of stay (LOS) is an important measure of healthcare utilization and is generally positively skewed and heterogeneous. We fit a Coxian phase-type distribution to LOS and identify the hidden states of the underlying latent homogeneous Markov model. We demonstrate that selecting an appropriate number of phases and a regression model for hazard rates can account for some heterogeneity in LOS. Reversible jump MCMC method enables us to dynamically uncover the hidden stochastic Markov structure. A classification method is used to assign patients to different LOS groups. The methodology is illustrated with application to hospital admissions for acute myocardial infarction in the 2003 Nationwide Inpatient Sample from the Healthcare Utilization Project.