Costing mixed coxian phase-type systems in a given time interval

Previously we have introduced a modelling framework to classify individuals in Mixed Coxian Phase-type Systems. We here add costs and obtain results for moments of total costs in (0, t], for an individual, and a cohort arriving at time zero. Based on data from the Belfast City Hospital Stroke Unit we use the overall modelling framework to obtain results for total cost in a given time interval to facilitate planners who have limited time horizons for budget planning.peer-reviewe

Costing hospital resources for stroke patients using phase-type models

Optimising resources in healthcare facilities is essential for departments to cope with the growing population’s requirements. An aspect of such performance modelling involves investigating length of stay, which is a key performance indicator. Stroke disease costs the United Kingdom economy seven billion pounds a year and stroke patients are known to occupy long periods of time in acute and long term beds in hospital as well as requiring support from social services. This may be viewed as an inefficient use of resources. Thrombolysis is a therapy which uses a clot-dispersing drug which is known to decrease the institutionalisation of eligible stroke patients if administered 3 h after incident but it is costly to administer to patients. In this paper we model the cost of treating stroke patients within a healthcare facility using a mixture of Coxian phase type model with multiple absorbing states. We also discuss the potential benefits of increasing the usage of thrombolysis and if these benefits balance the expense of administering the drug.peer-reviewe

Phase-type survival trees and mixed distribution survival trees for clustering patients' hospital length of stay

Clinical investigators, health professionals and managers are often interested in developing criteria for clustering patients into clinically meaningful groups according to their expected length of stay. In this paper, we propose two novel types of survival trees; phase-type survival trees and mixed distribution survival trees, which extend previous work on exponential survival trees. The trees are used to cluster the patients with respect to length of stay where partitioning is based on covariates such as gender, age at the time of admission and primary diagnosis code. Likelihood ratio tests are used to determine optimal partitions. The approach is illustrated using nationwide data available from the English Hospital Episode Statistics (HES) database on stroke-related patients, aged 65 years and over, who were discharged from English hospitals over a 1-year period.peer-reviewe

Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit

The problem of hospital patients’ delayed discharge or ‘bed blocking’ has long been a challenge for healthcare managers and policymakers. It negatively affects the hospital performance metrics and has other severe consequences for the healthcare system, such as affecting patients’ health. In our previous work, we proposed the phase-type survival tree (PHTST)-based analysis to cluster patients into clinically meaningful patient groups and an extension of this approach to examine the relationship between the length of stay in hospitals and the destination on discharge. This paper describes how PHTST-based clustering can be used for modelling delayed discharge and its effects in a stroke care unit, especially the extra beds required, additional cost, and bed blocking. The PHTST length of stay distribution of each group of patients (each PHTST node) is modelled separately as a finite state continuous-time Markov chain using Coxian-phase-type distributions. Delayed discharge patients waiting for discharge are modelled as the Markov chain, called the ‘blocking state’ in a special state. We can use the model to recognise the association between demographic factors and discharge delays and their effects and identify groups of patients who require attention to resolve the most common delays and prevent them from happening again. The approach is illustrated using five years of retrospective data of patients admitted to the Belfast City Hospital with a stroke diagnosis

Demand-Side Management for Energy-efficient Data Center Operations with Renewable Energy and Demand Response

In recent years, we have noticed tremendous increase of energy consumption and carbon pollution in the industrial sector, and many energy-intensive industries are striving to reduce energy cost and to have a positive impact on the environment. In this context, this dissertation is motivated by opportunities to reduce energy cost from demand-side perspective. Specifically, industries have an opportunity to reduce energy consumption by improving energy-efficiency in their system operations. By improving utilization of their resources, they can reduce waste of energy, and thus, they are able to prevent paying unnecessary energy cost. In addition, because of today‘s high penetration of renewable generation (e.g. wind or solar), many industries consider renewable energy as a promising solution to reduce energy cost and carbon pollution, and they have tried to utilize renewable energy to meet their power demand by installing on-site generation facilities (e.g. PV panels on roof top) or making a contract with renewable generation farms. Moreover, it is becoming common for energy markets to allow industries to directly purchase electricity from them while providing the industries with day-ahead and real-time electricity price information. In this situation, industries have an opportunity to adjust purchase and consumption of energy in response to time-varying electricity price and intermittent renewable generation to reduce their energy procurement cost, which are called demand response. Considering these opportunities, it is anticipated that the industrial sector can save a significant amount of energy cost, however, time-varying behavior, uncertainty and stochasticity in system operations, power demand, renewable energy, and electricity price make it challenging to determine optimal operational decision. Motivated by the aforementioned opportunities as well as challenges, this dissertation focuses on developing decision-making methodologies tailored for demand-side energy system operations to improve energy-efficiency based on energy-aware system operations and reduce energy procurement cost by utilizing renewable energy and demand response in an integrated fashion to optimally reduce energy cost. For practical application, this dissertation considers real-world practices in data centers including their operations management and power procurement for the following research tasks: (i) develop a server provisioning algorithm that dynamically adapts server operations in response to heterogeneous and time-varying workloads to reduce energy consumption while providing performance guarantees based on time-stability; (ii) propose stochastic optimization models for optimal energy procurement to determine purchase and consumption of energy based on day-ahead and real-time energy market operations considering utilization of renewable energy based on demand response; (iii) suggest a decision-making model that integrate the proposed server provisioning algorithm with energy procurement to achieve energy-efficiency in data center operations to reduce both energy consumption and energy cost against variability and uncertainty. In terms of methodologies, this study uses operations research techniques including deterministic and stochastic models, such as, queueing analysis, mixed-integer program, Markov decision process, two-stage stochastic program, and probabilistic constrained program. In conclusion, this dissertation claims that renewable energy, demand response, and energy storage are worth to be considered for data center operations to reduce energy consumption and procurement cost. Although variability and uncertainty in system operations, renewable generation, and electricity price make it challenging to determine optimal operational decisions, numerical results show that the proposed optimization problems can be efficiently solved by the developed algorithm. The proposed decision-making methodologies can also be extended to other industries, and thus, this dissertation study would be a good starting point to study demand-side management in energy system operations

Modelling activities at a neurological rehabilitation unit

A queuing model is developed for the neurological rehabilitation unit at Rookwood Hospital in Cardiff. Arrivals at the queuing system are represented by patient referrals and service is represented by patient length of stay (typically five months). Since there are often delays to discharge, length of stay is partitioned into two parts: admission until date ready for discharge (modelled by Coxian phase-type distribution) and date ready for discharge until ultimate discharge (modelled by exponential distribution). The attributes of patients (such as age, gender, diagnosis etc) are taken into account since they affect these distributions. A computer program has been developed to solve this multi-server (21 bed) queuing system to produce steady-state probabilities and various performance measures. However, early on in the project it became apparent that the intensity of treatment received by patients has an effect on the time, from admission, until they are ready for discharge. That is, the service rates of the Coxian distribution are dependent on the amount of therapy received over time. This directly relates to the amount of treatment allocated in the weekly timetables. For the physiotherapy department, these take about eight hours to produce each week by hand. In order to ask the valuable what-if questions that relate to treatment intensity, it is therefore necessary to produce an automated scheduling program that replicates the manual assignment of therapy. The quality of timetables produced using this program was, in fact, considerably better than its alternative and so replaced the by-hand approach. Other benefits are more clinical time (since less employee input is required)and a convenient output of data and performance measures that are required for audit purposes. Once the model is constructed a number of relevant hypothetical scenarios are considered. Such as, what if delays to discharge are reduced by 50%? Also, through the scheduling program, the effect of changes to the composition of staff or therapy sessions can be evaluated, for example, what if the number of therapists is increased by one third? The effects of such measures are analysed by studying performance measures (such as throughput and occupancy) and the associated costs

Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields

This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners

Analyst-driven development of an open-source simulation tool to address poor uptake of O.R. in healthcare

Computer simulation studies of health and care problems have been reported extensively in the academic literature, but the one-off research projects typically undertaken have failed to create an enduring legacy of widespread use by healthcare practitioners. Simulation and other modelling tools designed and developed to be used routinely have not fared much better either. Following a review of the literature and a survey of frontline analysts in the UK NHS, we found that one reason for this is because simulation tools have, to date, not been developed with the requirements of the end-user in the heart of the development process. Starting with a thorough needs assessment of NHS based healthcare analysts, this study outlines a set of practical design principles to guide development of simulation software tool for conducting patient flow simulation studies. The overall requirement is that patient flow be modelled over a number of inter-connected points of delivery while capturing the stochastic nature of patient arrivals and hospital length of stay, as well as the dynamic delays to patient discharge and transfer of care between different points of care delivery. In ensuring a cost-free solution that is both versatile and user-friendly, and coded in an increasingly popular language among the envisaged end users, the tool was implemented is the R programming language and software environment, with the user interface implemented in the interactive R-Shiny application. The talk will provide an overview of the project lifecycle including an illustrative example of an empirical simulation study concerning the centralisation of an acute stroke pathway

Operations research models for investigation and improvement of the hyperacute stroke care system

Stroke is the third most common cause of death and the sixth major cause of disability around the world with ischemic stroke accounting for around 80% of all strokes. It has been clinically indicated in treating ischemic stroke patients that maximum benefits can be achieved with the speediest arterial recanalization by effective and fast application of existing acute therapies. These therapies comprise either (1) dissolving the blood clot using Intravenous Tissue Plasminogen Activator (IV tPA) treatment or (2) physically removing the clot from the artery using endovascular thrombectomy treatment. These treatments should be performed within the hyperacute time window of 6 hours from stroke onset. For nearly two decades until late 2014, the intravenous thrombolysis delivered to patients was the most effective treatment for stroke patients. This was administrated within a maximum of 4.5 hours from stroke onset. In early 2015, results of five clinical trials from different parts of the world demonstrated the effectiveness of the endovascular thrombectomy therapy. This was provided within 6 hours of stroke onset for the eligible stroke patients who already have received thrombolysis treatment. Research presented in this thesis is the first attempt to quantify the link between the earlier treatment and long-term benefits for the hyperacute stroke patients. Moreover, with the gradual emergence of new evidence about effectiveness of the endovascular thrombectomy treatment in the hyperacute stroke care systems, new questions were raised in the clinical literature since not all hospitals have the expertise and equipment required for delivering the endovascular thrombectomy treatment. Some of the most burning questions were formulated in an Editorial article published in the Journal of the American Medical Association (JAMA) by Warach and Johnson (2016). These questions mainly concern the issue of treatment pathway selection between two groups of hospitals with different facilities and expertise to support new investigations in the hyperacute stroke care system by comparing the long-term benefits for individual patients. This research demonstrates how Operations Research (OR) models can be used to answer these and other questions in the hyperacute stroke care system. It is specifically focused on OR models for investigation and improvement to provide better understanding of the complex decisions arising in the hyperacute stroke care system. The main aimof this thesis is to investigate the issue of design, development and validation of OR models used for investigation and improvement of the hyperacute stroke care system. Thus, this work addresses very recent and important questions in the field to support more effective and efficient provision of the services to stroke patients. Three OR models for investigation and improvement are designed and validated in this thesis: (1) ’IV tPA’ model, (2) ‘Endovascular Thrombectomy’ model, and (3) ‘Individual Patient’ model. The first two OR models are used to provide an understanding of the long-term population benefits of faster access to stroke treatment interventions. Based on the first two OR models, one minute earlier of IV tPA and endovascular thrombectomy interventions respectively on average provide 1.8 days and 3.2 extra days of healthy life for the stroke patients. The third OR model is used to provide assistance with maximizing the individual patient’s life-time benefits over two pathways of the hyperacute stroke care system. Finally, we present a novel validation framework that is used to validate all three OR models developed in this thesis. This research contributes to OR/MS literature by design, development and validation of OR models used to provide an improved understanding of the long-term population and individual patient’s benefits due to faster delivery of stroke treatment interventions in the hyperacute stroke care system. A discussion on the validation of OR models is also novel and further addresses the existing gaps in OR/MS literature