A conditional approach for modelling patient readmissions to hospital using a mixture of Coxian phase‐type distributions incorporating Bayes' theorem

Abstract

The number of elderly patients requiring hospitalisation in Europe is rising. With a greater proportion of elderly people in the population comes a greater demand for health services and, in particular, hospital care. Thus, with a growing number of elderly patients requiring hospitalisation competing with non-elderly patients for a fixed (and in some cases, decreasing) number of hospital beds, this results in much longer waiting times for patients, often with a less satisfactory hospital experience. However, if a better understanding of the recurring nature of elderly patient movements between the community and hospital can be developed, then it may be possible for alternative provisions of care in the community to be put in place and thus prevent readmission to hospital. The research in this paper aims to model the multiple patient transitions between hospital and community by utilising a mixture of conditional Coxian phase-type distributions that incorporates Bayes' theorem. For the purpose of demonstration, the results of a simulation study are presented and the model is applied to hospital readmission data from the Lombardy region of Italy. Copyright © 2016 John Wiley & Sons, Ltd.

Predicting elderly patient length of stay in hospital and community care using a series of conditional Coxian phase-type distributions, further conditioned on a survival tree

“…Once the survival tree is used to categorise elderly patients according to length of stay at the initial hospital stage, the conditional Coxian phase-type distribution is employed for each cohort separately during the subsequent stages, taking into account each individual's length of stay, at both the previous and current stages, in the determination of the transition rate parameters for the current stage. Previous research [6] has shown the conditional Coxian phase-type distribution to outperform the standard Coxian phase-type distribution when considering a number of stages within an overall aggregate system, for a population assumed to be homogeneous. This paper presents the phase-type survival tree as a front-end for this composite methodology, able to account for a heterogeneous population.…”

“…However, with the aim of this research to model the movement of elderly patients through an ordered sequence of care stages, an approach is employed which can take into account the length of stay at a previous stage in the determination of transition rates for the current stage of care. Such an approach is the conditional Coxian phase-type distribution [6] where the system of stages is considered using two stages at a time. Once the information from the first stage is used to inform the distributional form for the second stage, the process repeats, whereby the second stage is used to inform that for the third stage, and so on.…”

“…This paper introduces a methodology which can account for some of this variability by making predictions for subgroups of the population, known as cohorts, each of which may be modelled by a separate distribution. This is carried out by extending the conditional Coxian phase-type distribution [6], a method which calculates the conditional probability for length of stay at the current stage of care, based on the length of stay experienced at the previous care stage, to be further conditioned on a phase-type survival tree [7]. This latter technique may be used to partition elderly patients into cohorts based on their length of stay at the initial hospital stage, in such a way so that patients in different cohorts have a significantly different length of stay distribution.…”

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

“…In this section, we derive the mixture form of a conditional Coxian distribution (but also present a novel reformulation of the joint Coxian model as a mixture model in Appendix B). The conditional Coxian phase‐type model was used by Gordon et al 22 to model patient transitions between hospital and community. Following the pathway in Figure 3, the model is fitted over two consecutive stations at a time.…”

Queue hurdle Coxian phase-type model for two-stage process of population-based cancer screening

“…To further understand the process of hospitalization, Marshall et al incorporated the Bayesian belief networks with CPH distributions to take into account the effect of patient information on hospital length of stay (Marshall and McClean 2003). Under this context, Gordon et al further modelled multiple patient transitions between hospital and community by using the mixture of conditional CPH distributions for assessing the efficacy of providing alternative care in the community in preventing hospital readmission (Gordon et al 2016).…”