Simulating Coxian Phase-type Distributions for Patient Survival

Coxian phase-type distributions are a special type of Markov model that can be used to represent survival times in terms of phases through which an individual may progress until they eventually leave the system completely. Previous research has considered the Coxian phase-type distribution to be ideal in representing patient survival in hospital. However, problems exist in fitting the distributions. This paper investigates the problems that arise with the fitting process by simulating various Coxian phase-type models for the representation of patient survival and examining the estimated parameter values and eigenvalues obtained. The results indicate that numerical methods previously used for fitting the model parameters do not always converge. An alternative technique is therefore considered. All methods are influenced by the choice of initial parameter values. The investigation uses a data set of 1439 elderly patients and models their survival time, the length of time they spend in a UK hospital.

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.

Investigating the efficiency of fitting Coxian phase-type distributions to health care data

Coxian phase-type distributions are becoming a popular means of representing survival times within a health care environment. They are favoured as they show a distribution as a system of phases and can allow for an easy visual representation of the rate of flow of patients through a system. Difficulties arise, however, in determining the parameter estimates of the Coxian phase-type distribution. This paper examines ways of making the fitting of the Coxian phase-type distribution less cumbersome by outlining different software packages and algorithms available to perform the fit and assessing their capabilities through a number of performance measures. The performance measures rate each of the methods and help in identifying the more efficient. Conclusions drawn from these performance measures suggest SAS to be the most robust package. It has a high rate of convergence in each of the four example model fits considered, short computational times, detailed output, convergence criteria options, along with a succinct ability to switch between different algorithms.

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.

Using Coxian Phase-Type Distributions to Identify Patient Characteristics for Duration of Stay in Hospital

Coxian phase-type distributions are a special type of Markov model that describes duration until an event occurs in terms of a process consisting of a sequence of latent phases. This paper considers the use of Coxian phase-type distributions for modelling patient duration of stay for the elderly in hospital and investigates the potential for using the resulting distribution as a classifying variable to identify common characteristics between different groups of patients according to their (anticipated) length of stay in hospital. The identification of common characteristics for patient length of stay groups would offer hospital managers and clinicians possible insights into the overall management and bed allocation of the hospital wards.

Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities

Discrete Conditional Phase-type (DC-Ph) models consist of a process component (survival distribution) preceded by a set of related conditional discrete variables. This paper introduces a DC-Ph model where the conditional component is a classification tree. The approach is utilised for modelling health service capacities by better predicting service times, as captured by Coxian Phase-type distributions, interfaced with results from a classification tree algorithm. To illustrate the approach, a case-study within the healthcare delivery domain is given, namely that of maternity services. The classification analysis is shown to give good predictors for complications during childbirth. Based on the classification tree predictions, the duration of childbirth on the labour ward is then modelled as either a two or three-phase Coxian distribution. The resulting DC-Ph model is used to calculate the number of patients and associated bed occupancies, patient turnover, and to model the consequences of changes to risk status.