Analysing Patient Flow in Australian Hospitals Using Dynamic Modelling and Simulation Techniques

Transcription

1 Flinders University School of Computer Science, Engineering and Mathematics Analysing Patient Flow in Australian Hospitals Using Dynamic Modelling and Simulation Techniques by Thomas McLoughlin Supervised by Dr Shaowen Qin Submitted to the School of Computer Science, Engineering, and Mathematics in the Faculty of Science and Engineering in partial fulfilment of the requirements for the degree of Master of Information Technology at Flinders University - Adelaide Australia November 2013 Page 1 of 33

2 DECLARATION I certify that this work does not incorporate without acknowledgment any material previously submitted for a degree or diploma in any university; and that to the best of my knowledge and belief it does not contain any material previously published or written by another person except where due reference is made in the text. Signature: Date: Thomas McLoughlin Page 2 of 33

3 CONTENTS DECLARATION... 2 ACKNOWLEDGEMENTS... 4 ABSTRACT... 5 INTRODUCTION... 6 LITERATURE REVIEW... 7 OVERVIEW OF SIMULATION METHODS... 7 SIMULATION VERSUS OTHER APPROACHES... 7 APPLICATIONS OF SIMULATION IN HEALTHCARE... 8 OVERVIEW OF THE SIMULATION PROCESS... 9 CONCEPTUAL MODELLING REVIEW OF SIMULATION TECHNIQUES Discrete Event Simulation System dynamics Agent-based Simulation PROBLEM DESCRIPTION METHOD CONCEPTUAL MODEL Modelling objectives Model inputs and outputs Model contents Assumptions and simplifications IMPLEMENTATION RESULTS FURTHER WORK REFERENCES Page 3 of 33

4 ACKNOWLEDGEMENTS I would like to thank a number of people for their help and support throughout year. First and foremost, I would like to thank my supervisor, Dr Shaowen Qin. Not only has Shaowen been of great assistance to me throughout the project, but has somehow (against all odds) managed to remain patient with me despite the various mishaps that have occurred throughout the year. I would also like to thank all my friends at university, in particular Alex, Saad, Yasir and Cyrus, who have helped make this year much easier for me. Finally, I would like to thank both my family and all the staff at Flinders University. Page 4 of 33

5 ABSTRACT Computer simulation been used successfully in a wide variety of industries, providing a low-cost, risk-free space for experimentation. Despite its wide success, however, their use within hospital management remains far less widespread than in many other industries. This project aims to demonstrate how computer simulations can be used to analyse and improve the overall performance of hospital operations. The work presented here can be divided into two parts. For the first part, a review of the available literature into simulation modelling is performed. For the second part, the insights gained from the literature review are then used to design and implement a computer simulation model to help with a real-world issue faced by the Flinders Medical Centre. The literature review first provides a brief overview of the applications of simulation modelling within health care. After this, the simulation modelling process is explored in more detail. Firstly, an overview of the activities and phases involved in simulation modelling are discussed. Secondly, the development of conceptual models for computer simulations is discussed. Finally, an overview of three different simulation techniques, namely discrete event simulation modelling, system dynamics modelling, and agent-based simulation modelling are discussed. Using the insights gained from this review, a simulation model is constructed for modelling the transfer of patients between the Flinders Medical Centre and the Repatriation General Hospital. The Flinders Medical Centre and the Repatriation General Hospital currently have an arrangement that allows patients to be transferred from the Flinders Medical Centre to the Repatriation General Hospital. Patients may be transferred to help alleviate access block and emergency department overcrowding. The intention of the model is to evaluate the effectiveness of this policy. The model has been implemented using the proprietary software package AnyLogic [11], and uses discrete event modelling to capture the problem domain as a process-centric system. Page 5 of 33

6 INTRODUCTION Throughout the developed world, the cost of healthcare services has been increasing steadily increasing over the last century. In Australia, overall expenditure on healthcare has risen from around 6% of GDP in the late 1960s to around 9.5% in 2012 [1]. Furthermore, most OECD countries spend in excess of 10% of their GDP, with the USA spending in excess of 16% [2]. The rising costs are commonly attributed to a number of different causes. One such cause is the increase in costs is the availability of new medical treatments - the administering such treatments increases the complexity of health services to be delivered, ultimately increase the cost pressure on healthcare. Changing demographics, such as the increasing average age within OECD countries, are also commonly cited as a cause of rising healthcare costs. Spending on hospitals represents a large proportion of overall healthcare spending, accounting for roughly 39.8% of all healthcare expenditure in Australia in 2012 [3]. As a result, finding new ways to improve the efficiency of hospitals, enabling them to deliver better services to patients at a lower cost, is increasingly important and will continue to be so in the future. Simulation methods are likely to be an invaluable tool in the future to help hospitals identify improvements. This project aims to demonstrate how simulation methods can be used to improve hospital operations and management. The work presented here can be divided largely into two parts. For the first part, an overview of simulation modelling is presented based on a survey of current literature. For the second part, a simulation model is developed of a real world scenario will be produced, guided by the literature surveyed in the first part. The chosen problem is to develop a model that captures the current practice of transferring patients between the Flinders Medical Center and the Repatriation General Hospital. The intention of the model is to help evaluate the effectiveness of this policy for alleviating access block and emergency department overcrowding. At a more fundamental level, the model is also intended to demonstrate how dynamic modelling and simulation can be applied to hospital operations management. Page 6 of 33

7 LITERATURE REVIEW OVERVIEW OF SIMULATION METHODS Simulation methods involve the construction of a model of the system being studied on a computer. Once constructed, the model provides a virtual space where experiments can be performed to assess the effect changes will have on the system being modelled. Within hospital operations, a model of a hospital (or some part of a hospital) could be produced and used to perform experiments to help improve the overall performance of the hospital. Possible experiments could be analysing the effect of purchasing additional medical imaging equipment, hiring additional doctors and nurses, or changing the layout of the hospital. Experimenting on a virtual model has many inherent advantages over performing real world experiments: 1. Experimentation is risk-free and does not require real world operations to be disrupted. 2. The cost of performing experiments significantly reduced. 3. The results of experiments can be obtained almost instantly. 4. Many different experiments can be performed over a small time period. 5. Experiments that cannot feasibly be performed in the real world are often possible in a virtual environment. In addition for providing a space for experimentation, simulation models can produce graphical output can often be used as a powerful communication aid. For example, if changes in the layout of a hospital are proposed, a graphical output showing the effect of the changes on the operation of the hospital can be produced. This graphical output can be used to help communicate both the proposed changes and the benefits afforded by them. Consequently, simulation models can be used as tool to help propel change within an enterprise. SIMULATION VERSUS OTHER APPROACHES As was discussed in the last section, simulation modelling offers a number of advantages over performing real world experimentation. Simulation, of course, is not the only technique that can be used to analyse a health care systems. Other modelling techniques can be used, which range from simple spreadsheets to the formation of analytical models using sophisticated mathematical techniques. Simulation methods have a number of advantages over other approaches [4]: Page 7 of 33

8 1. Simulation methods are able to model variability: Simulation methods are well suited to modelling variability and its effects. Using analytical methods, modelling variability often presents significant challenges. Furthermore, many systems cannot be modelled analytically at all. 2. Simulation methods are less restrictive than other methods: Due to the complexity of many real world problems, analytical methods often require restrictive assumptions to be made in order to make the problem more tractable to a solution. Simulation methods, on the other hand, are often much more flexible and enable and can be used to model problems in a greater level of detail. 3. Simulation methods are often more transparent and more easily understood: Analytical methods are difficult to understand for anyone unfamiliar with the particular methods used. Consequently, it is often difficult for the models to instill any confidence from others in nonexperts. Simulation models, in contrast, often appear much more transparent. Graphical output and animations produced can help improve understanding and confidence. Furthermore, the fact that simulations can often model the problem situation in a more direct manner (as discussed in points 1 and 2) also helps improve confidence. APPLICATIONS OF SIMULATION IN HEALTHCARE The use of simulation modelling is not as widespread within health care than many other areas. Despite this, the literature surveyed that there are many examples of simulation modelling being used successfully within healthcare. Mielczarek and Uzialko-Mydlikowska[5] conducted a survey of simulation modelling in the healthcare sector that reviewed 168 papers published between 1999 and As part of the survey, the authors categorised the aims of the papers by purpose, revealing a diverse array of applications for simulation methods. The paper identified four broad application areas that were encountered: Epidemiology, health promotion, and disease prevention; health care systems operation; health and care systems design and medical decision-making. The category Epidemiology, health promotion, and disease prevention was divided into three subcategories: Health policy evaluation and planning, Evaluation of intervention and treatment programs, Spread of infectious diseases. The category Health care systems operation were divided into the following categories: Estimating and evaluating the potential effect of the organizational changes, Diagnosis of the system, Staff scheduling, Determining the optimal capacity of the hospital resources, resource allocation, appointment systems. Page 8 of 33

9 Barijis [6] divides healthcare simulations into four broad categories: 1. Clinical simulation: simulations used to study, analyse, and replicate the behaviour of biological process within the human body. 2. Operational simulation: simulations used for capturing, analysing and studying health care operations, service delivery scheduling, healthcare business processes and patient flow. 3. Managerial simulation: simulation is mainly used as a tool for managerial purposes, decision making policy implementation and strategic planning. 4. Educational simulation: simulation used mainly for educational and training purposes. OVERVIEW OF THE SIMULATION PROCESS This section provides a simplified overview of the overall development process. The process presented here was discussed in the paper Verification and Validation of Simulation Models by Sargent [7]. Figure 1 shows the main tasks performed during the development, as well as the main entities (systems and artefacts) involved in those tasks. Figure 1: An overview of the simulation modelling process (taken from Sargent[7]) Page 9 of 33

10 Every simulation begins with a problem entity. The problem entity is the system (real or proposed), idea, situation, policy, or phenomena to be modelled [7]. Once a problem entity is known and agreed upon, work can begin on developing the simulation model. Rather that implementing an executable model immediately, however, it is common practice to develop a first develop a conceptual model of the problem. A conceptual model is a simplified representation of the problem entity in a format that is independent on the final programming language or software package that the computerized model will eventually be created. It is often stated that conceptual model is also independent of the actual modelling techniques (e.g. discrete event simulation, agent-based simulation) that will be used to implement the model. However, some authors (for example, see Gunal [8]) argue that, in practice, the planned modelling techniques do inevitably influences the development of the conceptual model. The process of developing the conceptual model is referred to as analysis and modelling. Analysis and modelling is depicted in figure 1 as a link between the problem entity and conceptual model to indicate that the both these entities are involved in the conceptual modelling process. Once a conceptual model has been produced, work can begin on developing the computerized model. The computerized model is the model that can actually be executed on the computer, allowing virtual experimentation to be performed. This phase of the models development is usually referred to as the models implementation. A variety of different tools could be used to implement the model. For example, for some models, it is possible that a simple spreadsheet would suffice. In other instances, a general purpose programming language such as C++ or Java could be used to implement the model. Many specialist simulation software packages are also available. The majority of these specialist packages could be described as visual interactive modelling systems (VIMS) [4, 9]. VIMS packages provide an interactive GUI that allow models to be implemented in a visual and interactive manner. These modelling tools often require some knowledge of programming to be used effectively. However, the level of programming required is usually considerably less than would be the case when the model is implemented using a programming language alone. A variety of simulation methods can be used to implement a simulation model. The best technique to use is highly dependent on the specific problem entity and model requirements. The three main modelling techniques applicable to hospitals simulations include Discrete Event Simulation, System Page 10 of 33

11 Dynamics and Agent-Based Simulation. Of these, discrete event simulation is the most widely used within health care[. Simulation methods will be discussed in more detail in this section. The final stage shown in the figure is experimentation. During this stage, experimentation is performed on the computer model to gain some further understanding of the problem entity being studied. For some simulation projects, such as scientific studies, a further understanding of the problem entity may be the entire goal of the simulation project, meaning that the goals of the simulation have been reached. For other projects, however, it is required that the findings of the model developed be enacted in some way. For example, suppose a simulation model is developed to determine the optimal staffing requirements for a hospital. If experiments with the computerized model identify changes that should be made, these changes will need to be put into effect at the actual hospital. To ensure the accuracy of a developed model, validation and verification of the model must be performed throughout the model development lifecycle. Various types of validation and verification that are performed are shown on the figure. Specifically, these are: 1. Conceptual model validation, 2. Computerized model verification, 3. Operational validation, and 4. Data validity checking. Conceptual model validation, computerised model verification and operational validation are each performed at the end of the analysis and modelling, implementation and experimentation phases, respectively. Data validity checking, in contrast, is relevant to each stage of development. Conceptual model validation involves devising and performing tests to ensure that the conceptual model provides a suitable and accurate representation for the purpose of the simulation being developed. Computerized model verification involves checking that the computerized model forms and accurate and complete representation of the conceptual model being produced. Computerized model verification does not, however, involve testing that the overall suitability of the model. Testing the computerised model is fit for purpose is the goal of operational validation. Sargent [4] defines operational validity as determining that the model s output behaviour has sufficient accuracy for the model s intended purpose over the domain of the model s intended applicability. Data Page 11 of 33

12 validity is defined as ensuring that the data necessary for model building, model evaluation and testing, and conducting the model experiments to solve the problem are adequate and correct [4]. As mentioned earlier, data validity is relevant to each development phase. There is not necessarily an ideal time to perform data validity checks during a particular phase, but it should probably be performed both at the start of each phase when the relevant data is collected, and at the end to ensure the correct data is still being used and all relevant data has been incorporated. The discussion here presented the simulation development process as if it were a sequence of steps, each completed sequential in-order. In particular, the sequence of steps was as follows: 1. Analysis and modelling of the problem entity is performed to produce a conceptual model 2. The conceptual model is then taken as a blueprint used to implement a computerized model 3. The computerized model is used to perform virtual experiments on the system being studied. Changes can be made based on the results of these experiments (if necessary). While this may be viewed a good first approximation for the model development process, it should noted that, in practice, model development should be performed iteratively, with the above steps performed many times over a number of cycles. For large simulation projects this is particularly important, as it is unlikely that all the details and requirements for the model can be fully grasped with a single attempt. Instead, such a model should be produced incrementally, with additional details and feature added each model increment. CONCEPTUAL MODELLING A mentioned in the previous section, a conceptual model is a model produced of the problem entity (the real system being studied) that is independent of the final modelling software or programming language used to implement the model. A conceptual model is an abstraction of the simulation model that is derived from the relevant parts of the real system. The conceptual model therefore acts as a bridge between the real system and the final computer model. Robinson CM [10] defines a conceptual model formally as... a non-software specific description of the computer simulation model (that will be, is or has been developed), describing the objectives, inputs, outputs, content, assumptions and simplifications of the model. Page 12 of 33

13 Figure 2 illustrates the relationship between the conceptual model and other systems and artefacts. The diagram is similar figure 1 in the previous section, but shows the relationship being described here slightly more clearly. Figure 2: The relationship between the conceptual model and other modelling systems and artefacts (taken from [10]). The definition of a conceptual model given above is deserving of some further elaboration. The definition identifies key elements that the conceptual features that the model should contain; specifically, these are the objectives, inputs, outputs, content, assumptions and simplifications. The model objective is simply a statement of the models purpose. The objective defines both the goal of the model and, equally importantly, the overall scope of the model. A conceptual model without a well defined goal or scope can easily become very complex, resulting in a model that is often of poor quality, difficult to grasp, and extremely difficult (or even impossible) to convert into a computerised model. For this reason, defining a clear objective is probably the most important aspect to get right within the conceptual model. The inputs and outputs are the key factors that will be of interest when performing any virtual experiments with final simulation model. Inputs are generally parameters that will need to be adjusted and altered before running any virtual experiments. Output includes any information that will need to be tracked or recorded when the virtual experiments are performed. Typically, the experimenter will be interested in either the exploring the relationship between the input and outputs, or determining the specific input that produces some form of optimal output. For example, Page 13 of 33

14 suppose a model is constructed to determine the number beds that are required for a proposed hospital. The number of beds available will should most likely be specified as a model input, as this will enable the number of beds to be varied allowing experiments to be performed. The patient arrival rate should probably also be specified as an input because the experimenter will want to test the limits of the hospitals capacity. Outputs will include factors such as the total number of beds occupied, or total beds available. Attempting to get a clear idea of the inputs and outputs is a useful starting point when constructing any conceptual model. Focusing on devising inputs and outputs will help elicit a clear and well-defined objective for the model, as well as the models overall contents. In addition to the inputs and outputs, the model may contain other contents. Often, this includes other parameters that are not specifically inputs or outputs to the model, but need to be included nonetheless for the model to function correctly. For example, when modelling patient flow within a hospital, the average treatment time of particular treatments or operations may need to be modelled. Rather than modelling this as an input or output of the model, these may be modelled based on statistics collected from the hospital. The final elements of the conceptual model that need to be discussed are the simplifications and assumptions. Because conceptual modelling involves forming an abstraction of a real world system, making simplifications and assumptions is unavoidable. Robinson [10] makes a clear distinction between simplifications and assumptions. The definitions he provides for both are as follows: Assumptions are made either when there are uncertainties or beliefs about the real world being modelled. Simplifications are incorporated in the model to enable more rapid model development and use, and to improve transparency. Assumptions and simplifications are therefore distinct concepts. Assumptions are made as a consequence of a lack of data or knowledge about the real system being modelled. In contrast, simplifications do not arise from lack of knowledge, but a rather deliberately made for the purposes of making producing simpler models, or to simplify the modelling process itself. Page 14 of 33

15 Robinson [10] also provides brief description of a general framework for the development of a conceptual model. The framework defines five activities undertaken in order to produce the conceptual model: 1. Understanding the problem situation 2. Determining the modelling and general project objectives 3. Identifying the model outputs (responses) 4. Identifying the model inputs (experimental factors) 5. Determining the model content (scope and level of detail), identifying any assumptions and simplifications While these activities can be followed in order, the ordering does not need to be strictly adhered to. Furthermore, it is expected that the model be constructed iteratively, so each step will be performed more than once over one or more cycles. The following diagram depicts the discussed framework. Figure 3 depicts the modelling framework diagrammatically. Figure 3: A framework for developing a conceptual model (Taken from [10]) Page 15 of 33

16 Robinson [10] discusses a number of characteristics of good conceptual models. Good conceptual models are: 1. Valid - the model is sufficiently accurate for its purpose 2. Credible - the model can be believed by all stakeholders of the model (which may include stakeholders with a non-technical background) 3. Feasible - it must be plausible that a simulation model can be produced from the conceptual model within any relevant constraints, such as time, money and resources. 4. Useful - the model must be presented in a format that it is useful for the implementers of the simulation model. 5. Simple - The model should be simple. This has overarching benefits in that it makes the model more easier to understand, easier to implement, and easier to modify and maintain. REVIEW OF SIMULATION TECHNIQUES There are three main methods used that are applicable to healthcare simulations, namely Discrete Event Simulations (DES), System Dynamics (SD), and Agent-Based modelling (ABM). In addition to these three methods, modern software simulations packages, such as AnyLogic[11], often make combining aspects of each of these three methods possible. Simulations that combine more than one of these three methods are sometimes referred to as multi-method simulations. Each method has its own strengths and weakness making some methods more applicable to some certain situations than others. In this section we discuss the characteristics of each method, including the methods advantages and disadvantages. DISCRETE EVENT SIMULATION DES is one of the oldest simulation methods and is the most widely used methods for hospital simulations. DES simulation techniques are used to model process-centric systems. Using a DES technique, systems are modelled as a sequence of operations that are performed on entities such as patients, blood samples, or documents. A DES simulation model consists of five core elements, which are defined in table 1. Page 16 of 33

17 Component Entities Processes Network Sources Sinks Resources Explanation Items that operations or processes are being performed on as part of the system being simulated. Possible entities include patients, blood tests and documents. Activities or actions that are performed on entities. Examples may include performing an operation on a patient, analysing a blood sample, or reviewing a document The network defines the order that entities undergo processes. This may be thought of as a flowchart of the process. Introduces entities to the network Removes entities from the network Resources may be required for a process to occur and are temporarily acquired by that process. Examples of resources could include doctors, medical equipment, or receptionists Table 1: Elements of discrete event simulation models An understanding of each of these elements is most easily understood with an example. Suppose a model is proposed for simulating the waiting times for patients visiting a doctor at a health care clinic. The overall process of the model can be represented the flowchart shown in figure 4. The flowchart shows the overall journey taken by patients who visit the clinic. Figure 4: A simplified model for patients visiting a health care clinic Page 17 of 33

18 As can be seen in the flowchart, patients first arrive at the clinic and queue to see a receptionist. After seeing the receptionist, the patients then queue and wait to see a doctor. After seeing the doctor, the patients queue to see the receptionist again before finally leaving the clinic. For simplicity, it is assumed that no patients arriving at the clinic have prior appointments, and that services are provided on a first-come first-serve basis. To model this system using DES methods, processes could be defined for queuing to first see a receptionist, seeing the receptionist upon arrival, queuing to see a doctor, seeing the doctor, queuing to see a receptionist before leaving, and finally seeing the a receptionist before. An entity could be defined to represent patients, and two resources could be defined to represent receptionists and doctors respectively. The network can be thought of as the connections depicted in the above flowchart - the network defines the order in which patients undertake the defined processes. Finally, sources and sinks are defined to introduce patients to the network representing patients arriving and leaving the clinic respectively. Table 2 summarises the components described here. Component Entities Resources Processes Sources Sink Network Uses within the model Patients Doctors, receptionists Queue for receptionist, see receptionist, queue for doctor, see doctor Patient enters clinic Patient leaves clinic Connections between processes, sources and sinks (the flowcharts topology). Table 2: Mapping between simulation components and their uses within the described model DES models have been by far the most widely used simulation methodologies for hospital simulations in the past. This is perhaps not surprising as DES has a number of characteristics that make this methodology particularly attractive for such models. DES models can be developed and defined on the level of an individual patient. Furthermore, individual patients can be tracked as the model is running, and it is easy to determine exactly how much time each patient spends in a particular queue or process. In many respects, this makes the developments of such models easier Page 18 of 33

19 and the results of the simulation can be more easily understood. Importantly, the ability to track individual patients is very useful for implementing visual representations of the model, as the movements of individual patients can be displayed instead of relying of graphs showing aggregate data that is less easily understood. DES models also enable stochastic factors common to hospital systems to be easily implemented. Examples of such factors may include patient arrivals, appointments and the length of stay of patients. There are some disadvantages to the DES technique that may make it less suitable for many applications. In particular, the fact that DES simulations focus on the level of individual patients may make DES models too detailed and difficult to apply for modelling. This is particularly true at when modelling very broad systems; for example, producing a realistic overall model of the healthcare system in Australia would be difficult using just DES techniques. Furthermore, DES models tend to assume that an overall ordered process is being followed, which can sometimes make DES models too inflexible to sufficiently capture some applications. SYSTEM DYNAMICS System dynamics simulations, like DES simulations, have been around for along time. SD dates back the late 1950s when the first SD languages, SIMPLE (Simulation of Industrial Management Problems with Lots of Equations) and later DYNAMO (DYNamic MOdelling) were developed [12]. However, far fewer SD models have been produced for healthcare applications, particularly for hospital simulations. Furthermore, SD is often less well understood within the operations research community; so the SD and DES modelling communities have historically been largely segregated[13]. In recent years this trend has been changing, and there is now a much greater awareness of SD modelling than there has been in the past. SD simulations model systems as a set of dynamic variables. A set of variables is defined that captures the entire state of the system being modelled, and rules and relationship between these state variables are defined that will determine the evolution of the systems state over time. From a computational perspective, SD simulations model the system as a set of differential equations that track instantaneous changes in a dynamic system [8]. Unlike DES simulations, all SD simulations are deterministic, and cannot model stochastic factors directly (although, the overall aggregate effect of stochastic factors can still often be captured within an SD model). SD models are also continuous, Page 19 of 33

20 meaning that all state variables take on a continuous range of values and very continuously over time. When developing SD models, typically two models are developed: 1. A qualitative model: represented by a causal loop diagram (CLD) 2. A quantitative model: represented by a stock-flow diagram (SFD) and accompanying relationship between variables needed to define the exact model behaviour in enough detail to be executable. The qualitative model is first developed to gain a better overall understanding of the model. After the qualitative model has been developed and a CLD finalised, the CLD is converted into an SFD, adding any details and making refinements were necessary. A CLD depicts the main variables in the model, and the general (qualitative) relationships between those variables. The CLD will also allow any feedback loops in the model to be easily identified. To illustrate the use of CLDs, we will illustrate this with an example found in Brailsford [13]. Suppose a model is to be developed for factors affecting the patient waiting lists for all public hospitals. A preliminary CLD for such a system is shown in figure 5 below. Figure 5: A preliminary closed loop diagram (from Brailsford [13]) This CLD shows a relationship between the referral rate, bed occupancy and waiting lists. The diagram communicates that referral rates tend to increase bed occupancy, and that bed occupancy tends to increase waiting lists; however, the model also suggests that waiting list also decrease the referral rate - as a result, the model contains a stabilising feedback loop that should ultimately limit any growth in waiting times to a finite level. Page 20 of 33

21 Suppose that the model is then modified to show to include political pressure to reduce waiting times. The model could then be modified as shown below, Figure 6: Modified closed loop diagram (from Brailsford [13]) The model shows that political pressure generates addition money to be spent on additional beds to reduce waiting times. However, the money for extra beds also has the unintended effect of again increasing the willingness for doctors to refer more patients. Consequently, the effect of the additional spending on beds may ultimately not result in the expected reduction in waiting times. SD models are a useful first step on the way to developing an executable SD model of a system. However, sometimes the construction of a CLD can, by itself, be a useful exercise even if a quantitative model is never produced. As can be seen by the above example, even simple qualitative models can offer useful insights that can aid understanding and help improve the decision making process. Once the CLD is completed, work on a SFD can begin. An SFD is very similar to a CLD diagram, except it contains some additional details necessary for producing an executable model. SFDs have four key elements: Page 21 of 33

22 Sources / sinks Flows Stocks Auxiliary variables The concepts of and SFDs are based on an analogy of water flowing through pipes and accumulating in stocks. Using the water analogy, a stock represents a tank of water whose level can vary over time; in a hospital simulation, a stock may represent the number of patients occupying beds, or the number of nurses currently working at the hospital. Flows are variables that cause the levels of stocks to change over time. A flow could represent that a water flow rate into a stock; but could also represent the patient admission rate to the hospital. Sources and sinks represent infinite reservoirs that can introduce or remove flows from the system. Auxiliary are variables that are neither stocks nor flows but are still shown on the SFD. Figure 7 shows a SFD based on the simple system from which the first CLD above was developed. Figure 7: A stock flow diagram for the described model (from Brailsford [13]) The clouds represent sources and sinks, introducing and absorbing flows of patients. The rectangle surrounding the occupied beds variable indicates that this variable is a stock. The referral rate and discharge rates are the models flows. The waiting list is an auxiliary variable that is a function of the occupied beds, and influences the referral rate. SD models can be a powerful tool level for analysing and modelling aspects of the healthcare sector at a high level (i.e. strategic level). SD and can capture complicated factors (such as political Page 22 of 33

23 pressure in the earlier model) that would be very difficult to model with other techniques. SD models are relatively simple, meaning that they can be developed quickly and are more easily understood. However, SD is less appropriate for modelling systems at low level. Once obvious weakness in healthcare is that it is difficult to create useful SD models that are capable of tracking individual patients. Rather, SD models will tend to lump patients together as aggregated data. SD models are also deterministic, so SD models may not be able to accurately handle many stochastic factors that often need to be modelled. AGENT-BASED SIMULATION Agent-based modelling and simulation techniques are much newer than both SD and DES techniques and did not achieve widespread use until the early 1990s. Even today, agent-based modelling is techniques are still relatively unknown outside academia. The key idea behind ABS is that, rather than modelling the behaviour of an entire system, the system is decomposed and modelled as a number interacting autonomous agents. Each agent exhibits its own state and behaviour, and may interact with its and environment as well as other agents. The overall behaviour of each agent is ultimately self-determined, however, that behaviour may be influenced by its interactions with its environment and other agents. Under an ABS, the overall behaviour of the system emerges as a consequence of these interactions. Agents can be used to model people, vehicles or animals; but they can also be used to model more complex systems such as entire countries. The only requirements are that the state and behaviour of the system can be defined, and there is some mechanism for the agent to interact with other agents in the system being modelled. Figure 8: Agent-based simulations decompose the problem entity into individually autonomous but interacting subsystems called agents Page 23 of 33

24 Agent-based techniques are very powerful and can potentially be used to build very sophisticated models of healthcare systems. These methods potentially allow the construction of detailed models at a level of detail similar to DES models, without the requirement of defining a rigid process of elements to follow. However, the additional power and flexibility offered by agent-based techniques means the process of modelling systems with this technique can be much more difficult. Furthermore, there is far less information available in the literature regarding how ABS can be applied to healthcare systems. One of the most common uses for agent-based simulation within healthcare is in the area of epidemiology, where ABS techniques are used to simulate the spread of infectious diseases. In such a model, individual people could be modelled as agents with their own behaviour, and conditions could be defined where an infection can be transmitted from one agent to another. Some authors have argued that agent-based techniques have the greatly improve hospital simulation modelling. For example, in the paper Agent-based modelling and simulation for hospital management [14], it is argued that traditional simulation models have largely neglected the impact of individual human decision making, and instead individuals have been modelled as passive work pieces or resources. The paper argues that this has adversely affected the accuracy of these models. Furthermore, it is suggested that integrating agent-based simulation techniques with traditional methods will enable the construction of models that can sufficiently capture and simulate the effects of individual decision-making. Page 24 of 33

25 PROBLEM DESCRIPTION Two current issues faced by the Flinders Medical Centre (as well as many Australian hospitals) are access block and emergency department overcrowding. Access block is the term that describes the delay emergency department patients who need hospital admission experience in the when their inpatient bed is unavailable [15]. Access block leaves patients stranded in the emergency department, which may lead to the related problem of emergency department overcrowding. Access block and emergency department overcrowding have a number of adverse effects [15]: 1. Increase adverse incidents such as medical errors and missed diagnostic tests 2. Increased length of patient stay 3. Increases in staff stress levels 4. Decrease in patient privacy Access block occurs largely when beds are unavailable because the hospital has no capacity to admit any more inpatients. However, the fact that not all hospitals operate at the same capacity means that a policy of transferring patients between hospitals can help alleviate the issue. As a result, the Flinders Medical Centre have made an arrangement with the Repatriation General Hospital allowing them to transfer patients to help free up hospital beds to help reduce overcrowding and access block. The Flinders Medical Centre may transfer up to a certain number of patients per day the Repatriation General Hospital. The patients to be transferred are taken from the emergency department rather the hospital itself. Each patient transferred must have been assessed to ensure that it is appropriate for him or her to be transferred. For example, the patient must be healthy enough to be transferred without posing a risk to their health. Sufficient resources must also be available at the Repatriation General Hospital to provide an appropriate level of care for the patient. For this project, a model is produced to investigate the effects of the policy of transferring patients between the Flinders Medical Centre and the Repatriation General Hospital. The developed model is intended to help predict the overall effectiveness of the policy, and to identify any problems or unintended consequences of such a policy. Page 25 of 33

26 METHOD In this section, the processes used and decisions made while developing the simulation model is discussed. The section will first discuss the conceptual model, and will then continue to discuss the computerised model derived from the conceptual model. CONCEPTUAL MODEL To assist with the development of the conceptual model, the conceptual modelling framework by Robinson [10] outlined previously in this report has been used. Following this framework, the conceptual model consists of the following elements: objectives, inputs, outputs, content, assumptions and simplifications. MODELLING OBJECTIVES The purpose of the simulation is to determine to assess the effectiveness of transferring patients between hospitals as a means of reducing access block and emergency department overcrowding (congestion). The key measures of access block and congestion considered are: 1. Bed waiting times - the amount of time spent by patients queuing in the emergency for a hospital bed 2. Emergency department queue sizes - the total number of patients waiting in the emergency department for a hospital bed. MODEL INPUTS AND OUTPUTS The key inputs of the simulation are: 1. The number of patient arrivals to Flinders Medical Centre s Emergency department per day. 2. The number of patient arrivals to Repatriation General Hospital Emergency per day. 3. The maximum number of patients that can be transferred per day. The key simulation outputs are: 1. The mean bed waiting times at the Flinders Medical Centre. 2. The mean queue size at the Flinders Medical Centre. Page 26 of 33

27 In addition to these inputs, other inputs allowing adjustment adjustments to be made to hospital parameters have also been included. This is done partly because obtaining reliable hospital data is difficult, but it also helps to increase the flexibility of the model, allowing a greater variety of changes or scenarios to by simulated. The additional hospital parameters included are: 1. The mean treatment time (in days) for patients staying at the Flinders Medical Centre. 2. The standard deviation in treatment times at Flinders Medical Centre. 3. The mean treatment time (in days) for patients staying at the Repatriation General Hospital. 4. The standard deviation in treatment times at Repatriation General Hospital. 5. The number of beds available at the Flinders Medical Centre. 6. The number of beds available at the General Repatriation Hospital. MODEL CONTENTS The overall patient flow through of patients through Flinders Medical Centre (FMC) is depicted in the diagram below: Figure 9: A diagram depicting the overall patient flow Each patient first arrives at the emergency department. Patients will then receive any emergency treatments required, before entering a queue to be admitted to the hospital. At this point, patients may be transferred to the Repatriation General Hospital (RGH); otherwise, patients will simply wait until a bed becomes available. Once a bed becomes available and a patient is admitted to hospital, the patient will then acquire the bed and commence treatment. Once the hospital treatment is Page 27 of 33

28 complete, the patient releases the bed, freeing the bed for other patients to use. The patient will then leave the hospital. To model patient transfers, it is assumed that all patient transfers occur at 10:00 each day, and that up to a set number of patients can be transferred each day. The decision regarding whether or not to transfer patients is decided based on difference between the queue sizes of the two hospitals. Transferring a patient from the FMC to the RGH will take on average one hour, but may vary between half and hour and three hours. The hospital operating hours was also included in the model. The hospital wards are assumed to be open to newly arriving patients between 8am and 8pm. Patients are able to to acquire beds at any time during the day. Treatments, however, can only commence during the hospitals opening hours. ASSUMPTIONS AND SIMPLIFICATIONS A number of assumptions and simplifications were made in order to develop the simulation: 1. To incorporate the RGH into the model, it is assumed that the patient flow pattern for patients at the RGH is identical to the pattern followed by the FMC patients in the section above. Furthermore, patients can be transferred from between either hospital (that is, patients can be transferred from the RGH to the FMC or from the FMC to the RGH). 2. The ED treatment time was not modelled. The treatment time was not included because it has no significant effect on the output of the simulation (that is, it does not affect ER queue length and patient waiting times). 3. Only inpatient flows arriving from emergency were modelled. Other inpatient or outpatients flows were not included. 4. All patients will be admitted to hospital (that is, no patient will discharged immediately after receiving ED treatment) 5. No patients will leave the ED or hospital early without receiving treatment. 6. Resources other than beds (e.g., available nurses, doctors, medical equipment) were not included. 7. All patients receive treatment 8. Other process times are assumed to be normally distributed. Page 28 of 33

29 IMPLEMENTATION The simulation model was developed using the software package AnyLogic [11]. AnyLogic is a proprietary simulation development tool based on the Eclipse Framework. AnyLogic supports the use of DES modelling, system dynamics and agent-based modelling, as well as multi-method simulation (that is, it allows a combination of the three techniques to be used within a single model). Model development using AnyLogic typically requires a combination of visual modelling and programming in the Java language. The developed simulation can largely be described as a discrete event simulation. Most parts of the model could sufficiently be represented by AnyLogic s Enterprise Library, which is a library for building process-centric discrete event simulations [16]. Patients are introduced to the network with source elements and removed with sink elements. Hospital treatments and transport delays were modelled using service elements. The resource pool element was used to model hospital beds, and seize and release elements were linked to acquire and free beds respectively. Some aspects of the model, however, were not modelled with Enterprise Library components. For example, to model the operating hours of the hospital wards, a statechart with two states (an open state and a closed state) was used. Conditions were entered so that the current state will automatically switch between open and closed based on the time of the day. Entry conditions were entered into each state to take action to open or close the wards. A trigger condition was also created check if for patients to transfer periodically at 10am each day. If there are patients to transfer, patients are taken from one queue and moved to transfer point at the other hospital. Page 29 of 33