A Conditional Approach for Modelling Patient Re-admissions in Hospital using a mixture of Coxian phase-type distributions incorporating Bayes Theorem

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.

Discrete Conditional Phase-type Model Utilising a Multiclass Support Vector Machine for the Prediction of Retinopathy of Prematurity

Retinopathy of prematurity (ROP) is a rare disease in which retinal blood vessels of premature infants fail to develop normally, and is one of the major causes of childhood blindness throughout the world. The Discrete Conditional Phase-type (DC-Ph) model consists of two components, the conditional component measuring the inter-relationships between covariates and the survival component which models the survival distribution using a Coxian phase-type distribution. This paper expands the DC-Ph models by introducing a support vector machine (SVM), in the role of the conditional component. The SVM is capable of classifying multiple outcomes and is used to identify the infant's risk of developing ROP. Class imbalance makes predicting rare events difficult. A new class decomposition technique, which deals with the problem of multiclass imbalance, is introduced. Based on the SVM classification, the length of stay in the neonatal ward is modelled using a 5, 8 or 9 phase Coxian distribution.