Asymptotic results on a class of adaptive multi-treatment designs

The play-the-winner (PW) rule is an important method in clinical trials where patients can be assigned to one of the two treatments. In the PW rule, the probability of the next patient to be assigned to a particular treatment only depends on the response of the current patient. In this paper, we consider a general kind of PW rule for multi-treatment adaptive designs, in which the probability that a treatment is assigned to the next patient depends upon both the response of the previous patient and an estimated parameter, e.g., the observed success rate. Using this kind of adaptive designs, more information of previous stages are used to update the model at each stage, and more patients may be assigned to better treatments. The strong consistency and the asymptotic normality are established for the allocation proportions.     

Modelling admissions booking of elective in-patients into a treatment centre

As part of the modernisation of the UK National Health Service,specialist centres called treatment centres are being introducedthat cater solely for routine elective treatment for a relativelysmall number of conditions. In principle, such centres can adoptnew methods of operation, e.g. organising booked admissionson a cyclic basis, organised to make efficient use of treatmentresources. Assuming such a mode of operation, explicit cyclicformulae are derived for the mean and variance of bed demand.These take account of systematic differences between the lengthsof stay of different patient groups and also the effects ofemergency admissions. Using these formulae, optimisation methodsare discussed that have the potential for contributing to resourceplanning and to assist the process of booking patient admissions.Such optimisation methods can be used to help reduce overallcapacity needs or, conversely, to make better use of the capacityavailable.     

Combining Data Mining and Discrete Event Simulation for a value-added view of a hospital emergency department

While simulation models have furthered understanding of the operations of emergency departments (EDs) and the dynamics of the ED within the healthcare system, they only model patient treatment implicitly, tracing the paths patients follow through the ED. By identifying the core patient treatments provided by the ED and incorporating them into a Discrete Event Simulation model, this paper provides insight into the complex relationship between patient urgency, treatment and disposal, and the occurrence of queues for treatment. The essential characteristics of the presented model are used to indicate a generally applicable methodology for identifying bottlenecks in the interface between an ED and a hospital ward.     

The costs and benefits of bowel cancer service developments using discrete event simulation

Colorectal cancer includes cancerous growths in the colon, rectum and appendix and affects around 30?000 people in England each year. Maximizing health benefits for patients with colorectal cancer requires consideration of costs and outcomes across the whole service. In an era of scarce healthcare resources, there is a need to consider not only whether technologies and services may be considered clinically effective, but also whether they are cost-effective, that is, whether they represent value for money for the health service. Through the development of a whole disease model, it is possible to evaluate the cost-effectiveness of a range of options for service development consistently within a common framework. Discrete event simulation has been used to model the complete colorectal cancer patient pathway from patient presentation through to referral and diagnosis, treatment, follow-up, potential recurrence, treatment of metastases and end-of-life care. This simulation model has been used to examine the potential cost-effectiveness of different options for change across the entire colorectal cancer pathway. This paper provides an empirical demonstration of the potential application of modelling entire disease areas to inform clinical policy and resource allocation decision-making.     

Register-based description of treatment processes in hospital care

This paper outlines the possibilities of establishing an information system based on the coherent processes a patient passes when getting in touch with hospital care. The information system represents an attempt to improve the basis for comparisons between hospital departments, for medical audits, for prognoses and for economic appraisals in health care. Current information systems on hospital care — in Denmark — only contain information on certain events, and these events cannot be seen consecutively.The work is based on register data from the county of Copenhagen for the year 1983.The work has shown that it is possible, with relatively few resources, to link elements in the treatment process to coherent processes for a single patient or to groups of patients. Furthermore the work has shown that even a simple registration of outpatient work constitutes a substantial improvement in hospital statistics.The paper was presented as a short paper at the 11th conference of EURO Working Group: OR Applied to Health Services, which took place in Enschede, The Netherlands 29th July – 2nd August 1985. The paper is based on a report [1] made up jointly by representatives from the County of Copenhagen and the Danish Hospital Institute.     

Literature review on multi-appointment scheduling problems in hospitals

This paper presents a review of the literature on multi-appointment scheduling problems in hospitals. In these problems, patients need to sequentially visit multiple resource types in a hospital setting so they can receive treatment or be diagnosed. Therefore, each patient is assigned a specific path over a subset of the considered resources and each step needs to be scheduled. The main aim of these problems is to let each patient visit the resources in his or her subset within the allotted time to receive timely care. This is important because a delayed diagnosis or treatment may result in adverse health effects. Additionally, with multi-appointment scheduling, hospitals have the opportunity to augment patient satisfaction, allowing the patient to visit the hospital less frequently. To structure the growing body of literature in this field and aid researchers in the field, a classification scheme is proposed and used to classify the scientific work on multi-appointment scheduling in hospitals published before the end of 2017. The results show that multi-appointment scheduling problems are becoming increasingly popular. In fact, multi-appointment scheduling problems in hospitals are currently gaining progressively more momentum in the academic literature.     

Modelling activities at a neurological rehabilitation unit

A queuing model of a specialist neurological rehabilitation unit is studied. The application is to the Neurological Rehabilitation Centre at Rookwood Hospital (Cardiff, UK), the national rehabilitation unit for Wales. Due to high demand this 21-bed inpatient facility is nearly always at maximum occupancy, and with a significant bed-cost per day this makes it a prime candidate for mathematical modelling. Central to this study is the concept that treatment intensity has an effect on patient length of stay. The model is constructed in four stages. First, appropriate patient groups are determined based on a number of patient-related attributes. Second, a purpose-built scheduling program is used to deduce typical levels of treatment to patients of each group. These are then used to estimate the mean length of stay for each patient group. Finally, the queuing model is constructed. This consists of a number of disconnected homogeneous server queuing systems; one for each patient group. A Coxian phase-type distribution is fitted to the length of time from admission until discharge readiness and an exponential distribution models the remainder of time until discharge. Some hypothetical scenarios suggested by senior management are then considered and compared on the grounds of a number of performance measures and cost implications.     

A Simulation Model for Planning Services for Renal Patients in Europe

A discrete-event simulation model is being developed to provide information for national and regional health planners about the effect of different treatment policies and practices on the increasing numbers of patients with irreversible kidney failure. The simulation program, written in Pascal using Pascal-SIM, describes the activities of individual patients whose progress through treatment depends on their characteristics and treatment history, as well as on treatments availability. Programming techniques have been developed to cope with the multiple scheduling of patient entities and the resultant queue-management problems. In order to provide simulation runs on request, for any population group, appropriate data is selected from the European Dialysis and Transplant Association Registry data base for use in the simulation program. Results are shown on a computer screen while the simulation is running, and are saved for further analysis to provide feedback to the requesting organization.     

Optimization models for radiotherapy patient scheduling

The efficient radiotherapy patient scheduling, within oncology departments, plays a crucial role in order to ensure the delivery of the right treatment at the right time. In this context, generating a high quality solution is a challenging task, since different goals (i.e., all the activities are scheduled as soon as possible, the patient waiting time is minimized, the device utilization is maximized) could be achieved and a large set of constraints (i.e., every device can be used by only one patient at time, the treatments have to be performed in an exact time order) should be taken into account. We propose novel optimization models dealing with the efficient outpatient scheduling within a radiotherapy department defined in such a way to represent different real-life situations. The effectiveness of the proposed models is evaluated on randomly generated problems and on a real case situation. The results are very encouraging since the developed optimization models allow to overcome the performance of human experts (i.e., the number of patients that begin the radiotherapy treatment is maximized).      

Simulation based analysis of patient arrival to health care systems and evaluation of an operations improvement scheme

Various demands of different patients over both medical resource and time domains in health care systems raise requests of strategies for balanced system capacity from an operations perspective. In this paper, a quantitative modeling technique with both patient arrival and associated treatment process integrated are used to characterize health care system performance and evaluate system efficiency. The patient arrival process is described as a dynamic random Poisson process and patient treatments are characterized as consumption processes of various health care resources over time with a view of the “product line” used. The waiting time of patients and usage of health care resources are proposed as system performance measures based on their means, variances, and confidence intervals. A simulation considering patients with several various diseases is given to find a mechanism of conflicting factors in decisions of balanced system capacity, and an operation scheme of “evenly balanced load for bottlenecks” is obtained based on analysis of simulation outputs. Simul8 provides the software environment for the simulation.     

A multi-phase DES modelling framework for patient-centred care

We provide a framework for simulating the entire patient journey across different phases (such as diagnosis, treatment, rehabilitation and long-term care) and different sectors (such as GP, hospital, social and community services), with the aim of providing better understanding of such processes and facilitating evaluation of alternative clinical and care strategies. A phase-type modelling approach is used to promote better modelling and management of the specific elements of a patient pathway, using performance measures such as clinical outcomes, patient quality of life, and cost. The approach is illustrated using stroke disease. Approximately 5% of the United Kingdom National Health Service budget is spent treating stroke disease each year. There is an urgent need to assess whether existing services are cost-effective or new interventions could increase efficiency. This assessment can be made using models across primary and secondary care; in particular we evaluate the cost-effectiveness of thrombolysis (clot busting therapy), using discrete event simulation. Using our model, patient quality of life and the costs of thrombolysis are compared under different regimes. In addition, our simulation framework is used to illustrate the impact of internal discharge queues, which can develop while patients are awaiting placement. Probabilistic Sensitivity Analysis of the value parameters is also carried out.     

Asymptotic Solutions of the Field-Noyes Model for the Belousov Reaction—I. Homogeneous Oscillations

Multiple-time-scale techniques are used to solve the non-linear autonomous system used by Field and Noyes to model the chemical oscillations of the Belousov reaction. An asymptotic representation, valid for a wide range of parameters, is found for a spatially homogeneous limit-cycle solution. For certain values of the parameters, two limit-cycle solutions are shown (asymptotically) to exist. For parameter values for which the limit cycle appears to be unique, it is shown to be linearly stable. The asymptotic solution is shown to correspond excellently to the numerical solution calculated by Field and Noyes for one set of parameters.     

Quality control of wastewater treatment: A new approach

This paper presents a new approach to quality control of wastewater treatment. The first part formulates basic principles of statistical process control (SPC) and Taguchi Method. Then it is shown that the classical SPC technique used in industry, cannot be to applied to wastewater treatment plants without adaptation and that the Taguchi Method is inapplicable in this case. This is followed by an example from literature, which demonstrates the problems of applying the SPC method to wastewater treatment. The third part of the paper presents a case study where the performance of a greywater treatment plant is examined. The performance is analyzed by means of cross-correlation between input and output parameters. A new approach to SPC of wastewater treatment, either “Dynamic SPC” or “linear regression SPC”, is presented, and a permeability coefficient is developed (the ratio of the output and input energies). Both are proposed as monitoring tools for wastewater treatment systems.     

On the Moments and the Distribution of the Cost of a Semi Markov Model for Healthcare Systems

In this paper we extend our previous semi-Markov reward model which attached costs to duration in states, by including costs of making a transition from one state to another. Theoretical results concerning the moments and consequently the distribution of interval costs for every member and of the total cost per unit period at any time and also through time intervals are obtained and provided in analytic form for the semi Markov reward model with discounting. The results are applied to an open healthcare system. In the healthcare domain such transition costs allow us to evaluate the overall costs of therapy or clinical intervention where an operation or other treatment may be an option. This model can be used for strategic approaches to planning and evaluating long-term patient care. The results demonstrate the potential of the model to demonstrate differential costs of different therapeutic strategies and explore optimal solutions.     

Bayesian estimation of generalized gamma shared frailty model

Multivariate survival analysis comprises of event times that are generally grouped together in clusters. Observations in each of these clusters relate to data belonging to the same individual or individuals with a common factor. Frailty models can be used when there is unaccounted association between survival times of a cluster. The frailty variable describes the heterogeneity in the data caused by unknown covariates or randomness in the data. In this article, we use the generalized gamma distribution to describe the frailty variable and discuss the Bayesian method of estimation for the parameters of the model. The baseline hazard function is assumed to follow the two parameter Weibull distribution. Data is simulated from the given model and the Metropolis–Hastings MCMC algorithm is used to obtain parameter estimates. It is shown that increasing the size of the dataset improves estimates. It is also shown that high heterogeneity within clusters does not affect the estimates of treatment effects significantly. The model is also applied to a real life dataset.     

A Posteriori Error Estimators and Adaptivity for Finite Element Approximation of the Non-Homogeneous Dirichlet Problem

Techniques are developed for a posteriori error analysis of the non-homogeneous Dirichlet problem for the Laplacian giving computable error bounds for the error measured in the energy norm. The techniques are based on the equilibrated residual method that has proved to be reliable and accurate for the treatment of problems with homogeneous Dirichlet data. It is shown how the equilibrated residual method must be modified to include the practically important case of non-homogeneous Dirichlet data. Explicit and implicit a posteriori error estimators are derived and shown to be efficient and reliable. Numerical examples are provided illustrating the theory.     

A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization

Intensity Modulated Radiotherapy Treatment (IMRT) is a technique used in the treatment of cancer, where the radiation beams are modulated by a multileaf collimator allowing the irradiation of the patient using non-uniform radiation fields from selected angles. Beam angle optimization consists in trying to find the best set of angles that should be used in IMRT planning. The choice of this set of angles is patient and pathology dependent and, in clinical practice, most of the times it is made using a trial and error procedure or simply using equidistantly distributed angles. In this paper we propose a genetic algorithm that aims at calculating good sets of angles in an automated way, given a predetermined number of angles. We consider the discretization of all possible angles in the interval [0 \(^{\circ }\) , 360 \(^{\circ }\) ], and each individual is represented by a chromosome with 360 binary genes. As the calculation of a given individual’s fitness is very expensive in terms of computational time, the genetic algorithm uses a neural network as a surrogate model to calculate the fitness of most of the individuals in the population. To explicitly consider the estimation error that can result from the use of this surrogate model, the fitness of each individual is represented by an interval of values and not by a single crisp value. The genetic algorithm is capable of finding improved solutions, when compared to the usual equidistant solution applied in clinical practice. The genetic algorithm will be described and computational results will be shown.     

Heuristics for integrated optimization of catheter positioning and dwell time distribution in prostate HDR brachytherapy

High dose-rate (HDR) brachytherapy is one kind of radiotherapy used to treat different forms of cancer, such as prostate cancer. When this treatment is used for prostate cancer, a radioactive source is moved through catheters implanted into the prostate. For each patient, a treatment plan is constructed. This plan determines for example catheter positions and dwell time distribution, that is, where to the radioactive source should stop and for how long.     

Sampling issues for optimization in radiotherapy

A wide variety of optimization problems and techniques are used in radiation treatment planning. The problems typically involve large amounts of data, derived from simulations of patient anatomy and the properties of the delivery device. We investigate a three phase approach for their solution based on sampling of the underlying data that determines optimal beam angles, wedge orientations and delivery intensities in patient examples. Phase I uses multiple coarse samplings of the data and linear programming to adapt the sampling and determine a collection of promising angles to use. Phase II solves the adapted sample problems as mixed integer programs using only the promising angles. Phase III refines the sampling further, and fixes most of the discrete decision variables to reduce computation times. Particular emphasis will be given to general principles that are applicable to large classes of treatment planning problems. Specific examples show enormous increase in speed of planning, without detriment to the solution quality. This material is based on research supported by the National Science Foundation Grant ACI-0113051 and the Air Force Office of Scientific Research Grant FA9550-04-1-0192.