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).

中文翻译：

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带有协变量的Coxian相类型分布的另一种表示形式：应用于急诊科住院时间

在本文中，我们提出了一种新的方法，该方法使用一系列带有协变量的条件Coxian相类型分布来模拟急诊科的患者过渡和住院时间。我们重新制定了Coxian模型（标准Coxian，具有多个吸收状态的Coxian，联合Coxian和有条件Coxian），以考虑到患者特征的异质性，例如到达模式，入院时间和年龄。该方法与以前的研究不同之处在于，它减少了计算时间，并且允许将患者协变量信息直接包含到模型中。该模型已应用于爱尔兰利默里克大学医院的急诊科数据，