The Conditional Phase-type distribution: Graphical Models for Continuous Non-Normal Data:The Conditional Phase-type (C-Ph) distribution:

Conditional Gaussian (CG) distributions allow the inclusion of both discrete and continuous variables in a model assuming that the continuous variable is normally distributed. However, the CG distributions have proved to be unsuitable for survival data which tends to be highly skewed. A new method of analysis is required to take into account continuous variables which are not normally distributed. The aim of this paper is to introduce the more appropriate conditional phase-type (C-Ph) distribution for representing a continuous non-normal variable while also incorporating the causal information in the form of a Bayesian network.

Discrete Conditional Phase-type model (DC_Ph) for patient waiting time with a logistic regression component to predict patient admission to hospital

Discrete Conditional Phase-type (DC-Ph) models are a family of models which represent skewed survival data conditioned on specific inter-related discrete variables. The survival data is modeled using a Coxian phase-type distribution which is associated with the inter-related variables using a range of possible data mining approaches such as Bayesian networks (BNs), the Naïve Bayes Classification method and classification regression trees. This paper utilizes the Discrete Conditional Phase-type model (DC-Ph) to explore the modeling of patient waiting times in an Accident and Emergency Department of a UK hospital. The resulting DC-Ph model takes on the form of the Coxian phase-type distribution conditioned on the outcome of a logistic regression model.

The Coxian phase-type distribution as a contribution to the multilevel model of in-hospital mortality

This paper presents multilevel models that utilize the Coxian phase-type distribution in order to be able to include a survival component in the model. The approach is demonstrated by modeling patient length of stay and in-hospital mortality in geriatric wards in Italy. The multilevel model is used to provide a means of controlling for the existence of possible intra-ward correlations, which may make patients within a hospital more alike in terms of experienced outcome than patients coming from different hospitals, everything else being equal. Within this multilevel model we introduce the use of the Coxian phase-type distribution to create a covariate that represents patient length of stay or stage (of hospital care). Results demonstrate that the use of the multilevel model for representing the in-patient mortality is successful and further enhanced by the inclusion of the Coxian phase-type distribution variable (stage covariate).

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.

The Coxian Phase-type distribution with a Hidden Node

Healthcare providers are under increased pressure to ensure that the quality
of care delivered to patients are off the highest standard. Modelling quality of
care is difficult due to the many ways of defining it. This paper introduces a potential
model which could be used to take quality of care into account when modelling
length of stay. The Coxian phase-type distribution is used to model length of stay
and quality of care incorporated into this using a Hidden Markov model. This model
is then applied to