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We extend the model used in Gardiner et al. (2002) and Polverejan et al.(2003) through deriving an explicit expression for the joint probabilitydensity function of hospital charge and length of stay (LOS) under a generalclass of conditions. Using this joint density function, we can apply the fullmaximum likelihood method (FML) to estimate the effect of covariates on chargeand LOS. By FML, the endogeneity issues arisen from the dependence betweencharge and LOS can be efficiently resolved. As an illustrative example, weapply our method to real charge and LOS data sampled from New York StateStatewide Planning and Research Cooperative System 2013 (SPARCS 2013). Wecompare our fitting result with the fitting to the marginal LOS data generatedby the widely used Phase-Type model, and conclude that our method is moreefficient in fitting.

Stochastic Process and Health Data: A Full Maximum Likelihood Method to Hospital Charge and Length of Stay Data