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. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) method enables us to dynamically uncover the hidden stochastic Markov structure. A classification method is used to assign patients to different latent LOS groups according to their mean LOS in hospitals.Increasing availability of patient LOS and cost data permits joint analysis accounting for their possible correlations. A bivariate Coxian phase-type/log-normal (CPH-LN) model is proposed to assess the impacts of covariates simultaneously. Under marginal specification through parametric models for LOS and cost, shared random effects are introduced in the model as regressors and the model is easily estimated using SAS Proc NLMIXED.We also propose an innovative method for the consideration of two-level correlations between LOS and cost. In our model, we are concerned with intra-hospital correlations, cross-equation correlations at both the hospital level and patient level. Full maximum likelihood (FML) is used to derive parameter estimates. A simulation study is conducted to illustrate our method.The methodologies are illustrated with application to hospital admissions for acute myocardial infarction (AMI) in the 2003 Nationwide Inpatient Sample (NIS) from the Healthcare Utilization Project (HCUP).
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