A Stochastic Process Model for the Distribution of Hospital Charges and Length of Stay
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Hospital length of stay (LOS) and total charge on discharge are two important measures of healthcare utilization and are generally positively skewed. A lognormal distribution for charge and a Phase-Type distribution for LOS are widely used assumptions in the relevant health statistics literature, but we are aware of no attempt to derive these two marginal distributions and the joint distribution of charge and LOS from some fundamental but simple assumptions. In this thesis, we propose a continuous-time stochastic process model to explain the emergence of various distributions of charge and LOS. Our model is simple because it relies only on a few basic behavioral assumptions about patient/doctor discharge decisions and its interaction with the potential charge accumulation process. From this model, an expression can be derived for the joint and marginal distributions of charge and LOS. Therefore our model could be useful to uncover the hidden connection between the underlying treatment dynamics that patients experience and the observable charge-LOS data. Our model is shown to have a close connection to the widely used Phase-Type model and could be easily extended in different directions. Possible applications of our model include evaluating the impact of policy change on charge-LOS distributions, optimizing bed use in hospital and formulating various important distributions in healthcare data, such as distributions of DRG (Diagnosis-Related Group) code and discharge destination. Our model can be fitted by real data. The availability of joint distribution of charge and LOS makes it possible to apply full maximum likelihood estimation (FML). Moreover, we show that under some restriction, the underlying stochastic process model can be completely identified from available charge and LOS data. Our methodologies are illustrated by application to samples drawn from two publicly-available healthcare databases (SPARCS 2013 and NIS 2012).