Using Prior Information on Parameters to Eliminate Dependence on Initial Values in Fitting Coxian Phase Type Distributions to Length of Stay Data in Healthcare Settings

Background: Modeling length of stay (LOS) data in healthcare settings using Coxian phase type (PH) distributions is becoming increasingly popular. However, dependence on initial values is a persistent difficulty in parameter estimations. This paper explores the utility of prior information on the parameters to address this difficulty. Methods: Maximum likelihood methods were used to estimate parameters of PH distributions that best fit simulated datasets with various sample sizes arising from PH distributions of various numbers of phases and parameters, using randomly generated initial values. Estimated values for the parameters resulting from different initial values were compared to the known values to assess the extent to which estimates depend on initial values; the impacts of sample sizes, existence of prior information, as well as the number of parameters with prior information were assessed. Results: Without prior information, parameter estimates depend on initial values for all PH distributions and all sample sizes. Prior information on one or more parameters led to more concentrated estimates, with higher number of parameters with prior information or larger sample sizes leading to more concentrated estimates. For example, with a sample size of 500, the estimates for a parameter with known value of 0.706 without prior information had a wide range of 1.523; using prior information for two parameters narrowed that range down to 0.156. For 3-phase PH distributions, prior information on 3 parameters appeared to be sufficient to eliminate dependence on initial values, even for small sample sizes. For 4-phase PH distributions, prior information on 5 parameters and a moderate sample size were needed to eliminate such dependence. Conclusions: Combination of prior information on parameters and sufficient sample sizes can eliminate dependence on initial values in fitting PH distributions to LOS data

Is it beneficial to increase the provision of thrombolysis? - a discrete-event simulation model

Background: Although Thrombolysis has been licensed in the UK since 2003, it is still administered only to a small percentage of eligible patients. Aim: We consider the impact of investing the impact of thrombolysis on important acute stroke services, and the effect on quality of life. The concept is illustrated using data from the Northern Ireland Stroke Service. Design: Retrospective study. Methods: We first present results of survival analysis utilizing length of stay (LOS) for discharge destinations, based on data from the Belfast City Hospital (BCH). None of these patients actually received thrombolysis but from those who would have been eligible, we created two initial groups, the first representing a scenario where they received thrombolysis and the second comprising those who do not receive thrombolysis. On the basis of the survival analysis, we created several subgroups based on discharge destination. We then developed a discrete event simulation (DES) model, where each group is a patient pathway within the simulation. Coxian phase type distributions were used to model the group LOS. Various scenarios were explored focusing on cost-effectiveness across hospital, community and social services had thrombolysis been administered to these patients, and the possible improvement in quality of life, should the proportion of patients who are administered thrombolysis be increased. Our aim in simulating various scenarios for this historical group of patients is to assess what the cost-effectiveness of thrombolysis would have been under different scenarios; from this we can infer the likely cost-effectiveness of future policies. Results: The cost of thrombolysis is offset by reduction in hospital, community rehabilitation and institutional care costs, with a corresponding improvement in quality of life. Conclusion: Our model suggests that provision of thrombolysis would produce moderate overall improvement to the service assuming current levels of funding.peer-reviewe

A systematic review of the prediction of hospital length of stay:Towards a unified framework

Hospital length of stay of patients is a crucial factor for the effective planning and management of hospital resources. There is considerable interest in predicting the LoS of patients in order to improve patient care, control hospital costs and increase service efficiency. This paper presents an extensive review of the literature, examining the approaches employed for the prediction of LoS in terms of their merits and shortcomings. In order to address some of these problems, a unified framework is proposed to better generalise the approaches that are being used to predict length of stay. This includes the investigation of the types of routinely collected data used in the problem as well as recommendations to ensure robust and meaningful knowledge modelling. This unified common framework enables the direct comparison of results between length of stay prediction approaches and will ensure that such approaches can be used across several hospital environments. A literature search was conducted in PubMed, Google Scholar and Web of Science from 1970 until 2019 to identify LoS surveys which review the literature. 32 Surveys were identified, from these 32 surveys, 220 papers were manually identified to be relevant to LoS prediction. After removing duplicates, and exploring the reference list of studies included for review, 93 studies remained. Despite the continuing efforts to predict and reduce the LoS of patients, current research in this domain remains ad-hoc; as such, the model tuning and data preprocessing steps are too specific and result in a large proportion of the current prediction mechanisms being restricted to the hospital that they were employed in. Adopting a unified framework for the prediction of LoS could yield a more reliable estimate of the LoS as a unified framework enables the direct comparison of length of stay methods. Additional research is also required to explore novel methods such as fuzzy systems which could build upon the success of current models as well as further exploration of black-box approaches and model interpretability

Integrating visualisation into the systems modelling toolkit: Applications to clinical and health process systems

Many areas of modern society, including healthcare, can be thought of as process systems. Such systems can be understood in terms of a sequence of inputs, work activities and outputs which become difficult to understand and control as a result of complexity arising from interactions between components within these system. Such complexity can hamper the ability to make decisions relating to these process systems. Operations Research/Management Science (OR/MS) has responded to this challenge with the development of systems models, which create a representation of the system under investigation that can be used to help make decisions about the process system. OR/MS literature has developed a wide variety of techniques for systems modelling, including computational, statistical and mathematical approaches to assisting decision-making. This suite of methods can be referred to as the OR/MS toolkit for systems modelling. OR/MS practice often involves the use of visualisation to aid undertanding, interpret results from systems modelling, or otherwise assist OR/MS practitioners in working with systems. This widespread use of visualisation has occurred due to its ability to flexibly and intuitively represent large amounts of information. However, there has been little discussion within OR/MS literature on the use of visualisation as a tool for systems modelling. Likewise, there is a lack of explicit knowledge on how visualisation should be applied in an OR/MS context, and a lack of reported, general knowledge on how to integrate visualisation with conventional OR/MS tools. Given that visualisation provides an intuitive means for understanding complex information, this presents an opportunity for OR/MS experts to better model process systems and provide support for decision-makers by making use of visualisation as a tool for systems modelling. This thesis seeks to advance the use of visualisation in systems modelling by addressing these gaps. We provide a systematic review on the use of visualisation within OR/MS literature, and from this synthesise a series of general visualisation principles to guide beneficial visualisation properties, and a series of general visualisation practices which suggest means of following these principles. We then use the results of this synthesis to develop an original Visual Systems Modelling Framework which provides a method for integrating visualisation into the systems modelling toolkit. This framework draws from established OR/MS theory and practice by explicitly setting out a conceptual model describing the system, the intended purpose of modelling the system, and plans for any conventional OR/MS tools which will be used to model the system. It links these aspects of conventional OR/MS methodology to the visualisation principles identified by the systematic literature review. The thesis provides illustrative case studies of this framework in action by applying it in the development of four models for clinical or health process systems. First, we describe several novel contributions to literature on the conventional OR/MS toolkit that were made in the development of these models. These include a novel dissimilarity measure that can be used to compare and group sequences of ordinal data where sequence length can vary, and systematic validation of a method of clustering survival data using Coxian Phase-Type distributions. These contributions are then used in the case studies which follow the Visual Systems Modelling Framework. The first case study is in the context of the care of Traumatic Spinal Cord Injury (TSCI). The care of TSCI involves several healthcare processes working together in unison to treat a patient who may have many different co-existing injuries resulting from the same event which lead to the spinal cord injury. This heterogeneity among patients results in organisational uncertainty regarding the specific care pathways taken by patients, making it almost impossible to make decisions which will improve care processes for this patient group. Before improvements to this system can be made, a greater understanding of the TSCI healthcare process is required. The Visual Systems Modelling Framework is applied in this system to generate new insights and promote discussion about TSCI healthcare processes. The second case study is in the context of investigating the role of neurorehabilitative physiotherapy in the recovery of stroke survivors. There are open questions within clinical literature on stroke rehabilitation regarding what physiotherapy regimens lead to better patient outcomes. In this application, the Visual Systems Modelling Framework is used to allow clinical researchers the ability to identify patterns in and explore the relationships between physiotherapy regimens and patient health, thereby developing an understanding which can improve the care provided in stroke rehabilitation. The third case study is in the same neurorehabilitative system as the second case study. In this application, the Visual Systems Modelling Framework is used to develop a model which predicts patient outcomes based on their received physiotherapy regimen. This assists clinical researchers seeking to identify what physiotherapy regimens are likely to improve patient outcomes. The final case study is in the context of planning an major clinical trial in stroke rehabilitation which uses an adaptive trial design. Adaptive clinical trials use prespecified rules to adjust the behaviour of the trial based on data as it is accrued by the trial. These rules can be used to address ethical concerns regarding giving patients experimental treatments which appear to be ineffective, enforce balancing of important prognostic factors across treatment arms, or any number of other desired features. However, such designs can lead to complex and counter-intuitive behaviour in the trial, requiring both careful planning and understanding of these behaviours. In this application, the Visual Systems Modelling Framework is used to model this clinical trial to assist planning and communicate the behaviours arising from the adaptive trial design. Through these four case studies, this thesis provides illustrations of how the Visual Systems Modelling Framework can be used across multiple systems, each with their own requirements and modelling purpose. This thesis demonstrates how visualisation can be integrated in the OR/MS systems modelling toolkit, and contributes to OR/MS literature by providing a method for applying visualisation as a systems modelling tool

A Joint Model for Multistate Disease Processes and Random Informative Observation Times, with Applications to Electronic Medical Records Data

Multistate models are used to characterize individuals\u27 natural histories through diseases with discrete states. Observational data resources based on electronic medical records pose new opportunities for studying such diseases. However, these data consist of observations of the process at discrete sampling times, which may either be pre-scheduled and non-informative, or symptom-driven and informative about an individual\u27s underlying disease status. We have developed a novel joint observation and disease transition model for this setting. The disease process is modeled according to a latent continuous time Markov chain; and the observation process, according to a Markov-modulated Poisson process with observation rates that depend on the individual\u27s underlying disease status. The disease process is observed at informative or non-informative sampling times, with possible misclassification error. We demonstrate that the model is computationally tractable and devise an expectation-maximization algorithm for parameter estimation. Using simulated data, we show how estimates from our joint observation and disease transition model lead to less biased and more precise estimates of the disease rate parameters. We apply the model to a study of secondary breast cancer events, utilizing mammography and biopsy records from a sample of women with a history of primary breast cancer

Hybrid Stochastic Models for Remaining Lifetime Prognosis

The United States Air Force is developing its next generation aircraft and is seeking to reduce the risk of catastrophic failures, maintenance activities, and the logistics footprint while improving its sortie generation rate through a process called autonomic logistics. Vital to the successful implementation of this process is remaining lifetime prognosis of critical aircraft components. Complicating this problem is the absence of failure time information; however, sensors located on the aircraft are providing degradation measures. This research has provided a method to address at least a portion of this problem by uniting analytical lifetime distribution models with environment and/or degradation measures to obtain the remaining lifetime distribution

New Developments on the Estimability and the Estimation of Phase-Type Actuarial Models

This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes. The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In particular, this objectivity is achieved via a carefully designed distribution function sensitivity measure, under which the threshold will become an experiment-based quantity. The proposed measure which is validated to be innately sound, is then applied to assess and improve the estimability of several statistical models, the focus being placed on the PTAM. Secondly, Markov chain Monte Carlo (MCMC) algorithms are proposed for inference on the PTAM and the DMPTM. Up to now, the MCMC algorithms for continuous phase-type distributions have been applied via the Gibbs sampler which consists of two iterative steps: a data augmentation step and a posterior sampling step. However, owing to unique structures of the PTAM and the DMPTM, this Gibbs sampler turns out to be inadequate, giving rise to problems occurring in either the data augmentation step or the posterior sampling step. To circumvent these difficulties, we methodologically extend the existing Gibbs sampling methodology in terms of rejection sampling and data cloning. The proposed algorithms are then applied to calibrate the PTAM and the DMPTM based on simulated and real-life data. Experimental results show that the proposed MCMC algorithms, as a stochastic approximation technique, achieve estimation results that are comparable to those obtained by deterministic approximation techniques, which can also be seen as a contribution made to the field of approximate inference

Queues in series with blocking

This piece of work describes a hospital's Critical Care Unit and uses different mathematical techniques to model the behaviour seen there. The main factor that is included in these models is the problem of bed blocking in the Unit. Blocking is defined as patients who are well enough not to be in the Critical Care Unit, but remain there, for any number of reasons. These patients are using up an expensive and limited resource. The mathematical techniques that the models are built on are extensively reviewed and analysed. These are the Coxian Phase Type Distribution and Networks of Queues with Blocking Equations. Both techniques are described in detail and their distributions analysed under different circumstances. The final chapter shows how the two distributions can be used to model a complex situation such as the one found in the Critical Care Unit. The models are tested and compared. Finally, the models are tested under a number of 'what if scenarios to predict the effect of changing certain factors on the actual Unit