An alternative formulation of Coxian phase‐type distributions with covariates: Application to emergency department length of stay

Abstract

In this article, we present a new methodology to model patient transitions and length of stay in the emergency department using a series of conditional Coxian phase‐type distributions, with covariates. We reformulate the Coxian models (standard Coxian, Coxian with multiple absorbing states, joint Coxian, and conditional Coxian) to take into account heterogeneity in patient characteristics such as arrival mode, time of admission, and age. The approach differs from previous research in that it reduces the computational time, and it allows the inclusion of patient covariate information directly into the model. The model is applied to emergency department data from University Hospital Limerick in Ireland, where we find broad agreement with a number of commonly used survival models (parametric Weibull and log‐normal regression models and the semiparametric Cox proportional hazards model).

Phase-type models for competing risks, with emphasis on identifiability issues

“…As noted by Rizk et al (2021), the representation for Coxian competing risks models given in the previous subsection, turns out to be very well suited for statistical inference. We consider below for simplicity the case of right-censored competing risks data without covariates, while a note on the inclusion of covariates is given in the end, following the suggestion of Rizk et al (2021).…”

“…The recent article by Rizk et al (2021) motivates an extension of the canonical model ( p, Q) of Sect. 2.3 to the case of multiple absorbing states.…”

“…≥ λ m . Rizk et al (2021) present formulas for going from the above canonical representation to the Coxian model representation for the case K = 2. Example 5 (cont.)…”

“…Coxian phase-type models have recently been successfully applied in health care studies. For example, Faddy et al (2009), McGrory et al (2009), Tang et al (2012) and Rizk et al (2021) model hospital length of stay by Coxian phase-type models.…”

“…Phase-type models with multiple absorbing states have earlier been considered by, e.g., McClean et al (2010) and Rizk et al (2021) in the modeling of patient pathways in hospitals. The former paper is concerned with the calculation of some key performance indicators like absorption probabilities and expected length of stay.…”