Reducing waiting time in a radiotherapy department using simulation and process mining

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Reducing waiting time in a radiotherapy department

using simulation and process mining

Laurence van Brenk

October 2020

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Reducing waiting time in a radiotherapy department

using simulation and process mining

Student

Laurence van Brenk

Student number: 10244042 Mentor Nori Mangnus Software Consultant ChipSoft, I&S Orlyplein 10, Amsterdam Tutor Danielle Sent Assistant Professor

Amsterdam UMC, University of Amsterdam, Medical Informatics Meibergdreef 9, Amsterdam SRP duration April 2019 - October 2020 SRP location ChipSoft Orlyplein 10, Amsterdam

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Abstract

Introduction: The demand for radiotherapy is increasing, which could lead to a longer waiting time. Waiting time is defined as the time from referral to first treatment. It is important that the waiting time is as short as possible, as research shows that longer waiting times have a negative effect on patient outcome. The goal of this study was to decrease the waiting time for the delivery of radiother-apy. Operations research (OR) techniques, such as simulation, can be used to address this problem.

Methods: A literature study and simulation study were performed. The litera-ture study extended an existing review and explored current achievements with OR in improving the efficiency at radiotherapy departments. In the simulation study, multiple simulation experiments explored ways to reduce waiting times at a radiotherapy clinic. To support the simulation methodology, process mining was utilized to create a process model and identify delays in the process.

Results: Searching the literature, thirteen articles were found. Ten articles ad-dressed a scheduling problem, of which six focused on the scheduling of treat-ments. The three remaining articles were on the subject of throughput optimiza-tion or capacity analysis. All thirteen articles reported a potential improvement in performance. For the simulation study, the process mining efforts indicated the longest delay at the clinic was between registration and first appointment. In a simulation experiment, discarding designated blocks in the schedules of the radiation oncologists for planning first appointments resulted in a reduction of 29 hours in median waiting time.

Discussion: Most of the literature focused on using OR to address scheduling problems. Improvements in waiting times were achieved, but there were no re-ports on real world implementations of the proposed solutions. In the simulation experiments, discarding designated blocks in the schedule of the radiation oncol-ogists for planning first appointments reduced waiting times. The feasibility of discarding these blocks is in the real world is unclear, as scheduling outside these blocks currently only occurs in deliberation with the radiation oncologist. Future research should explore how improvements found with OR translate into the real world.

Keywords: Waiting times; Radiotherapy; Operations research; Computer simu-lation; Process mining.

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Samenvatting

Introductie: De vraag naar radiotherapie neemt toe, wat kan leiden tot een lan-gere wachttijd. Wachttijd wordt gedefinieerd als de tijd van verwijzing tot de eerste behandeling. Het is belangrijk dat de wachttijd zo kort mogelijk is, om-dat uit onderzoek blijkt om-dat langere wachttijden een negatief effect hebben op de uitkomst van de behandeling. Het doel van dit onderzoek was om de wachttijd voor het krijgen van radiotherapie te verkorten. Operations research (OR) tech-nieken, zoals simulatie, kunnen worden gebruikt om dit probleem aan te pakken. Methode:Zowel een literatuurstudie als een simulatiestudie zijn uitgevoerd. De literatuurstudie bouwde voort op een bestaand literatuuronderzoek en onder-zocht de huidige prestaties die behaald zijn met OR in het verbeteren van de ef-ficiëntie op radiotherapieafdelingen. In het simulatieonderzoek is met meerdere simulatie-experimenten onderzocht hoe de wachttijden in een radiotherapiekli-niek kunnen worden verkort. Ter ondersteuning van de simulatiemethodologie werd process mining gebruikt om een procesmodel te maken en oponthoud in het proces te ontdekken.

Resultaten: Dertien artikelen werden gevonden in de literatuur. Tien studies pakten planningsproblemen aan, waarvan zes gericht waren op de planning van behandelingen. De drie overige studies gingen over doorvoeroptimalisatie of ca-paciteitsanalyse. Alle dertien artikelen noemden mogelijke verbeteringen in de prestaties van het proces. In de simulatiestudie gaf onderzoek met process min-ing aan dat het langste oponthoud in de kliniek plaatsvond tussen de registratie en de eerste afspraak. In een simulatie-experiment waarin de blokken in het rooster van de radiotherapeuten voor het inplannen van de eerste afspraak wer-den genegeerd werd een verkorting van 29 uur in de mediane wachttijd behaald. Discussie:De literatuur richtte zich vooral op het gebruik van OR om problemen in de planning aan te pakken. Studies bereikten verbeteringen in de wachttijden, maar implementaties van de voorgestelde verbeteringen werden niet genoemd. In de simulatie-experimenten slaagde het negeren van roosteringsblokken voor de eerste afspraak met de radiotherapeut ervoor dat de wachttijd verminderde. De haalbaarheid van het negeren van deze blokken in de praktijk is nog niet duidelijk. Op dit moment wordt namelijk alleen buiten deze blokken gepland in overleg met de radiotherapeut. Vervolgonderzoek moet uitwijzen hoe verbe-teringen die behaald zijn met OR zich vertalen naar de realiteit.

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General introduction

Radiotherapy, the treatment of cancer with ionizing radiation, has a major role in cancer treatment, alongside surgery and chemotherapy. As the demand for oncologic care increases, the demand for radiotherapy will increase [1]. It is im-portant that patients receive their treatment in time, and continue to do so when demand increases. In the Netherlands, there are target standards for the waiting time of radiotherapy, set by the Dutch Society for Radiotherapy and Oncology (NVRO) [2]. These target standards dictate the maximum number of days be-tween patient admission and the start of treatment. Radiotherapy centers should give their best effort to stay within these target standards. This can be a chal-lenge, as the process of delivering radiotherapy consists of multiple preparation steps, such as imaging and treatment planning. These steps depend on each other, each needing limited resources, such as expensive equipment and special-ized staff. To keep waiting times below the target standards, and maximize the patient capacity of a center, this process should be optimized to be as efficient as possible. Operations research (OR) offers mathematical optimization techniques that can be applied to improve efficiency. In this study, the goal is to minimize waiting times for the delivery of radiotherapy.

1.1 Waiting times and capacity in radiotherapy

In patients receiving radiotherapy, ionizing radiation is used to destroy targeted tumor cells. Generally, the radiation is delivered externally using a linear acceler-ator (linac). The treatment may be combined with surgery or chemotherapy. Both

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curative and palliative treatments are given. Palliative patients have an urgency level of acute or subacute. For example, an acute patient might have a tumor pressing on the spinal cord, leading to pain and imminent paralyses. Curative patients have a regular urgency level.

Radiotherapy is part of the treatment for about 50% of all new cancer patients [3]. The demand for oncological care, and therefore radiotherapy, is increasing in the Netherlands [1]. Data from The Netherlands Cancer Registry lists 71,000 new cancer patients in 2000, which has increased to about 111,000 in 2016 [4]. The costs of oncological care now take up a larger part of the healthcare budget than before, 3.71% in 2003 and 5.95% in 2015 [5]. As the demand for radiotherapy increases, waiting time targets could be harder to maintain with current patient capacity. Patient capacity is the maximum number of patients that can be treated given the current resources. Efficiency improvements can be implemented to de-crease waiting times and inde-crease patient capacity, sometimes without expanding resources.

Limits on waiting time are essential, as literature reviews by Chen et al. [6] and Huang et al. [7] show that longer waiting times for radiotherapy have a negative effect on the probability of controlling the volume of the tumor at the primary location (local control). Chen et al. describe that in some cases, this may lead to decreased survival. While most of the published research found in these reviews focusses on breast cancer and head and neck cancers, Chen et al. remarks that there is no evidence to suspect delay is safe in any context, and a principle of keeping waiting times as short as reasonably achievable should be applied. Longer waiting times may not only lead to a lower probability of local control and survival, but may have other effects on the well-being of the patient, such as decreased quality of life in the form of worsening of symptoms or psychological distress [8]. Furthermore, as the volume of the tumor will continue to increase between imaging and the first radiation treatment, minimizing this delay will benefit the treatment precision [9]. Other research shows that patients’ level of concern is higher during the waiting period before treatment [10]. Finally, re-search of patients’ attitudes towards waiting times shows that in a trade-off be-tween waiting times and receiving treatment further from home, patients accept some waiting time, but are not willing to do so if it meant the effectiveness of their treatment would be reduced [11].

The NVRO has set target standards for radiotherapy in the Netherlands that dic-tate the maximum length of the period between the referral to the radiation

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on-cologist and the start of treatment. Currently, the target standard for regular patients require that institutions treat 80% of patients within 21 days, and 100% within 28 days. Similarly, they should treat 80% of subacute patients within 7 days and 100% within 10 days. All acute patients should be treated within the same day [2].

As shown in Figure 1.1, the process of delivering radiotherapy consists of two stages: the pretreatment stage and treatment stage. In the pretreatment stage, imaging techniques, such as computer tomography (CT) or magnetic resonance imaging (MRI), are used to determine the exact location of the tumor. The tu-mor and its healthy surrounding organs will then be contoured on the images for the development of a treatment plan. The treatment plan maximizes the radia-tion dosage to the tumor, while minimizing the level of radiaradia-tion to the healthy surrounding organs to avoid adverse effects.

Consultation Imaging Contouring

Referral Treatment planning Radiation treatment Waiting time Pretreatment phase Treatment phase

Figure 1.1– Basic overview of the radiotherapy delivery process

In the treatment stage, the radiation is delivered in short daily treatment ses-sions, known as fractions. Depending on the type of care required, a patient may receive many fractions during their treatment, while others may receive only a single fraction. Some research focusses on delivering fewer fractions while achieving the same results [12]. This can increase patient capacity, while also decreasing the number of required visits by patients.

1.2 Approach of this study

The goal of this study is to evaluate and improve the efficiency of the delivery of radiotherapy by means of non-medical decision making, such as resource plan-ning. More specifically, we aim to reduce waiting times. Waiting time in this con-text is defined as the time from referral to the first treatment session for patients. To accomplish this goal, this study has to identify inefficiencies, or bottlenecks,

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and develop and evaluate possible interventions that optimize the efficiency of the process.

To increase the efficiency of the delivery of radiotherapy, we firstly focus on what approaches to this problem have been explored in the literature. Secondly, we aim to identify the process itself and the delays that are present within the pro-cess. Thirdly, we focus on discovering what factors influence these delays. This study will focus on the use of OR techniques to approach the problem. The mathematical optimization techniques offered by OR are used to optimize opera-tional and logistical problems. In healthcare, it can be used to optimize efficiency and reduce costs. For example, OR can be used for allocating beds, planning op-erating rooms, and scheduling staff. Furthermore, techniques found in OR can be applied to other types of problems, such as the optimization of the beam angle and dosage plan of radiotherapy patients.

Chapter 2 presents the workflow of the healthcare delivery process at a radio-therapy department. The literature study in Chapter 3 presents an overview of current literature on OR in radiotherapy. Chapter 4 presents a case study of a radiotherapy clinic in the Netherlands. Finally, the results are discussed in Chapter 5.

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Chapter 2

Radiotherapy workflow

Before we can optimize the process of delivering radiotherapy, it is essential to understand the workflow at a radiotherapy department. In this chapter, an overview of the workflow at a radiotherapy department is given. Literature pro-vided essential information on the general workflow. More in depth information was provided in interviews that were part of our case study. These interviews took place at the Erasmus MC in Rotterdam and the Maastro Clinic in Maastricht. Participants included a radiation therapist team leader, a radiation therapist, a consultant business management, a radiation oncologist, and a team leader of administration.

A general overview of the workflow for a patient’s treatment, based on interviews and literature [13–21], is presented in Figure 2.1. However, exceptions and de-viations exist to the workflow as displayed in the figure. Sometimes they are a result of department policy. Consequently, there can be some minor differences between institutions. For example, the various checks in the process may dif-fer slightly between institutions. A department might not plan a peer review of the treatment plan after it is finished, because the optimal treatment would have already been discussed in a regularly scheduled session. These regularly sched-uled consults between radiation oncologists are not displayed in Figure 2.1, as a patient can be discussed at any point in the pretreatment phase.

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2.1 Regular patient flow

Before a patient visits the radiotherapy department, they have to be diagnosed and referred to a radiation oncologist. When a patient is diagnosed, a treatment plan is made and one or more treatment options are chosen. About 50% of new patients receive radiotherapy at some point during their treatment [3]. Gener-ally, patients that may be eligible for radiotherapy are discussed between the referring specialists and the radiation oncologist in a multidisciplinary consult. These consults are scheduled on fixed times and dates.

Once a decision is made to include radiotherapy in the treatment for the patient, they are referred to a radiation oncologist. Referrals are scheduled by triage in a care pathway for a certain tumor group, and assigned a radiation oncologist by determining their current workload. Referrals for radiotherapy may come from all kinds of specialists. The type of care required is communicated in the referral. For example, patients can be referred for their primary curative treatment or for acute palliative therapy, which require different actions to be taken.

First consultation Imaging Referral Radiation treatment Follow-up Treatment checkup

Mold/Mask Contouring_organs

Contouring target volume Treatment planning Treatment plan check radiation therapist Treatment plan check radiation oncologist Finalize

treatment plan Physics check

Radiation oncologists peer review Contouring

check

Figure 2.1 – An overview of the radiotherapy delivery process. Dashed outlines indicate steps that do not always have to be executed. Deviations to the process as displayed here do occur.

The first appointment of the patient is a consult with the radiation oncologist. In some institutions however, a physician assistant will initially see the patient. They will retrieve routinely collected information from the patient, and the visit

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with the radiation oncologist will follow afterwards. The radiation oncologist will make their final judgement on the next steps to be taken. Sometimes the decision may be not to choose for radiotherapy after all. In some cases the patient will receive surgery in combination with radiotherapy. In those cases there will be a consult before and after the surgery.

The next step is imaging, where a scan of the target area is made. If the patient requires a mold during treatment, to secure the target area in place during treat-ment, an appointment for the mold room precedes imaging. Thereafter, the mold is used during imaging, as the patient is positioned identically during imaging and treatment. Generally, images are made with a CT scan located at the radio-therapy department. Some patients require additional imaging, in that case a positron emission tomography-CT (PET-CT) scan or MRI scan is made. As most radiotherapy departments do not have the equipment for these scans, an appoint-ment with the radiology departappoint-ment of the institution is scheduled. If only a CT scan is required, it may be possible to combine the appointment of the first con-sult with the scan. However, the potential of combining these appointments is dependent on the planning procedures of the department, and therefore varies between institutions.

After imaging, the target volume and vital organs are contoured on the images. Typically, the radiation therapist will contour the vital organs, and the radiation oncologist will contour the target volume. Images from certain tumor locations are more complex to contour than others, therefore the duration of contouring can vary significantly. Recently, automatic contouring is becoming more preva-lent [22]. However, the results of automatic contouring are currently still manu-ally edited afterwards.

With the tumor and its surroundings contoured, the development of the treat-ment plan can start. Similarly to contouring, recent developtreat-ments allow the use of automated treatment planning systems [23]. If an institution has such a sys-tem available, treatment planning usually starts there. The initial treatment plan created by that system will then be further developed manually by the radiation therapist. Once the treatment plan is complete, it needs to be verified, firstly by another radiation therapist and thereafter by a radiation oncologist. The radia-tion therapist will then finalize the treatment plan. Finally, a clinical physicist verifies the plan.

During treatment preparation, the radiation oncologist may discuss a patient in a consultation with their peers. Regular patients are usually discussed in fixed

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meetings, which take place a couple of times a week to every day, depending on the policy of the tumor group and the department. Typically, the radiation on-cologist discusses their decisions on a patient shortly after the first consultation. Furthermore, complex patients and treatment plans may be discussed in these meetings, for example, when a radiation therapist has questions that arise while making the treatment plan.

After all preparations are complete, the treatment sessions can begin. The exact number of fractions that a patient receives varies. This is mostly dependent on the tumor group, as there are guidelines for each group. These guidelines are not the same around the world, and may change at any point when research pro-vides new insights. During the duration of treatment, a couple of short checkup appointments are scheduled with the radiation oncologist. After treatment is finished, follow-up appointments are scheduled as well.

2.2 Deviations

For acute patients the process is slightly different. In most cases, these patients require palliative treatment to stop a tumor from pressing on the spine, causing pain and imminent paralysis. Departments are able to treat these patients on the same day as the first consultation. These patients only require a CT, without any additional imaging. Moreover, they require a less complex treatment plan, which allows for fewer checks from co-workers and takes less time to develop. Similarly, the contouring is quicker, as there is less concern about the vital organs in the patients that receive palliative treatment. Only a single fraction is given, and these patients are only present for a single day.

Sub-acute patients receive palliative treatment for complaints they might have, such as pain, a bleeding tumor, or difficulty swallowing. These patients receive their first radiation treatment about a week after their first consultation. The pro-cess is similar to that of acute patients, in that there is no additional imaging, and the treatment plan is simpler. However, in these cases, there is more flexibility in the treatment technique. Sometimes the vital organs are still taken into account for these patients, but in a way that is manageable in a week of preparation time. Some patients might be considered for proton therapy. Compared to the com-monly applied radiotherapy using photons, the radiation dosage is delivered to a narrower range of depth, allowing for greater control over the level of radiation

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exposure to the healthy surrounding organs. For patients where proton therapy is a consideration, a comparison between treatment plans for proton and pho-ton therapy is made. In this comparison, a benefit of propho-ton therapy has to be proven for the healthcare insurance company. This means two treatment plans are made. In case the patient will receive proton therapy, the treatment plan for photon therapy is kept as a backup. This way, in case there are any holdups during proton therapy, the patient can still receive photon therapy.

There are other exceptions to the regular workflow, where adjustments are made during the pretreatment phase of specific cases. For example, at any point during the workflow, it could be decided that adjustments need to be made at a previous step. This means that at all points in the workflow, as displayed in Figure 2.1, a step back can be taken, or a step can be repeated.

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Chapter 3

Radiotherapy in operations

research: a scoping review

3.1 Introduction

The discipline of OR uses mathematics and computer science to assist in deci-sion making. Commonly, OR attempts to solve optimization problems, where the goal is to optimize a specific value, such as the minimization of costs, or the maximization of profits. In OR, mathematical techniques are used to find the op-timal, or near opop-timal, solutions to these optimization problems. There are nu-merous problems that can be addressed with OR, some outside the scope of this review. For example, in radiotherapy treatment planning, a given dosage should be delivered to the tumor while minimizing the radiation dosage to healthy ar-eas, a medical problem where OR can be applied. However, in this study, the focus will be on the usage of OR for logistical problems. These are optimization problems for the management of resources and workflow.

In healthcare, OR has been used for various optimization purposes, such as plan-ning operating rooms and scheduling staff [24]. By using OR for these purposes, efficiency improvements and costs reductions can be realized. For radiotherapy, OR can be applied to minimize waiting times, and maximize the utilization of resources.

By reviewing the literature, OR techniques and proposed workflow interventions of previous research can be identified and evaluated. This will provide insight in

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the methods by which efficiency can be improved at radiotherapy departments. In our case study in the next chapter, waiting time reduction at a radiotherapy clinic is studied. As optimizations to the efficiency of the process can be very specific to a particular institution, this literature study will provide insight in achieved solutions for a variety of cases. This way, a more general overview on how to reduce waiting times can be presented.

Based upon an existing review on the subject of OR applied to logistical problems in radiotherapy by Vieira et al. [21], which reviewed articles between 2000 and 2015, we will focus on extending that review with recent research. Vieira et al. observed an increasing number of articles on the subject over time. Therefore, we believe an update of their review will provide a significant amount of additional articles.

3.2 Preliminaries: operations research techniques

Perspectives of what is and is not an OR technique may differ among researchers, as there is no consensus on a definition of OR [25]. For the purposes of this review, we will adhere to the identification and classification used by Vieira et al. [21]. They classified six different groups of techniques: constructive heuristics, metaheuristics, mathematical programming, queueing theory, Markov decision processes, and computer simulation.

Constructive heuristics attempt to find a solution by building on a candidate so-lution step by step, using a rule of thumb to improve with each step [26, 27]. Metaheuristics are heuristic approaches that are less problem specific. Com-pared to other heuristic approaches, they try to avoid local optima, where an optimal is found among similar possible solutions, but not among all possible solutions [27, 28]. All heuristic approaches are approximate methods. The ad-vantage of this is that computation time is relatively low, therefore solutions are found more quickly than with exact approaches. However, a disadvantage is that the solutions found are likely not the optimal solutions, and the relative quality compared to this optimal solution is often unknown [27].

Mathematical programming is a method to optimally allocate scarce resources using mathematics. An objective value is optimized by systematically choosing input values within set constraints and calculating the objective function.

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Math-ematical programming finds optimal solutions at the cost of lengthy computa-tional time [29].

Queueing theory is the mathematical representation of queues. It can be used to balance the costs that come with allocating resources to offering a service and the waiting times for that service. It uses performance measurements such as average queue length and average waiting time in the queue [27].

Markov decision processes are used to model sequential decision making under uncertainty. For each decision, both the outcome of that decision and future decision making opportunities are taken into account. They can be applied to find optimal decision making policies for decision making problems [30]. Computer simulation is a method that imitates a real world system on a com-puter. This digital representation of the real world system can be adjusted rela-tively easy, making simulation an ideal technique for experimenting with “what-if” scenarios [31].

3.3 Methods

This review focused on the application of OR for logistical optimization for ra-diotherapy, as opposed to medical optimization problems such as the beam angle and dose optimization. As we extend the literature review of Vieira et al. [21], this review follows their methods closely. Although search and selection methods were very similar, a few changes to their methods were made.

Six databases were searched for literature: Scopus, PubMed (MEDLINE), Ovid Embase, Web of Science, EBSCO Business Source Premier (BSP), and ORchestra. These were the same databases previously searched by Vieira et al. [21]. The databases were selected on based on their coverage of academic disciplines. As the subject of OR in radiotherapy may appear in both medical and business re-search, the collection of databases had to cover multiple academic disciplines. Scopus and Web of Science both have a very broad coverage of academic dis-ciplines, and contain records of many different areas of research. PubMed and Ovid Embase are both databases containing medical research, while EBSCO BSP is a database aimed at business research. ORchestra is a database maintained by the Center for Healthcare Operations Improvement and Research within the

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Uni-versity of Twente. It is specifically focused on research applying OR techniques in healthcare.

The search query consisted of three parts, combining the field of radiotherapy, logistical problems, and OR techniques. Each part contained terms related to these subjects. These parts were then connected by the AND operator. Although the search query was based on the one used by Vieira et al. [21], some additions were made. The full search query, including the differences to Vieira et al., is presented in Appendix A.

As some changes to the query were made, the search query was not limited to records after the time period investigated by Vieira et al. [21], 2000 to 2015. In-stead, we limited the results to records of 2000 and later, allowing for the discov-ery of new articles in the period of time searched previously by Vieira et al. We followed the decision of Vieira et al. to exclude articles before 2000, as these are likely not relevant for the purposes of this review, due to the fast developments made in information technology. To extend the reach of the search query, the re-sults were not limited to journal papers, conference papers, and book chapters, as they were in Vieira et al. Furthermore, the results were limited to the English language. The search query was finalized and records were collected on June 25, 2019.

Records were included and excluded in agreement with the criteria declared by Vieira et al. [21]. All included records had to use an OR technique and address a logistical problem in radiotherapy. Therefore, records addressing medical op-timization challenges were excluded. Records addressing macro planning were excluded as well, as the decision was made to focus on the decision making pro-cess of any single institution. Additionally, records had to contain enough infor-mation for data extraction. A master’s student Medical Informatics screened all articles for relevance using Covidence. First, the titles and abstracts of all records were screened, and subsequently the full-text of selected articles.

In the course of screening titles and abstracts, a list was received of articles screened by Vieira et al. [21]. This opened the option of omitting those articles from the screening process. However, it was decided to continue screening all articles from the period between 2000 and 2015. As these articles were screened again, the decision to include or exclude them was made independently from the previous decisions by Vieira et al.

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We extracted the following data from each record included: The subject of the research, the OR method(s) used, the extent of implementation, the (potential) impact on performance, and the conclusions of the case study. This followed the data extraction of Vieira et al. [21], except the hierarchical level was not ex-tracted, as it did not contribute to our goals. The subject of the research consists of the problem that the researchers attempt to resolve and the intervention that they want to implement as a solution. The OR method was classified by using the previously mentioned six groups. The extent of implementation was assessed by using the same six point scale as used by Vieira et al., described in Table 3.1. To record the impact on performance of the proposed intervention, we recorded the outcome measures used, and the results of the intervention. In cases where multiple methods or interventions were used, we recorded the most impactful results that were achieved. If the potential impact was not clearly stated, the conclusion of the authors on their OR technique and intervention was recorded.

Phase Description

I Computational experiments with fictitious data II Computational experiments with real data III Computational experiments show benefits to client IV Results of computational experiments validated by client V Intervention implemented in practice

VI Performance evaluation after intervention

Table 3.1– Extent of implementation scale as defined in Vieira et al. [21]

3.4 Results

A total of 651 records were found in the six databases searched. After removing duplicates, 416 titles and abstracts were screened. The full-text was screened of 28 articles, of which 13 were finally included. An overview of the number of records included, excluded, and the reasons for exclusion can be found in the PRISMA diagram in Figure 3.1. As conference abstracts did not contain enough information to extract data from, these were excluded. A description of all in-cluded articles can be found in Table 3.2.

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Records identiﬁed through database searching (n = 651) Scopus (n = 253) PubMed (n = 101) Embase (n = 150) Web of Science (n = 88) EBSCO BSP (n = 10) ORchestra (n = 49)

Records after duplicates removed (n = 416)

Records screened (n = 416)

Records excluded (n = 388)

Included in Vieira et al. (n = 27)

Full-text articles assessed for eligibility

(n = 28)

Full-text articles excluded, with reasons

(n = 15)

Conference abstract (n = 7) Inaccessible (n = 4) Not addressing a logistics problem

in radiotherapy (n = 2) Not using OR technique (n = 2) Additional records identiﬁed through

other sources (n = 0)

Studies included (n = 13)

Figure 3.1– PRISMA diagram

3.4.1 Scheduling

Ten of the included articles addressed some form of scheduling. Six articles addressed patient treatment scheduling, one of which did so in combination with dosimetry scheduling. One other article addresses the scheduling of physi-cians in the pretreatment phase. Further scheduling articles addressed admission scheduling, radiation therapist scheduling, and scheduling of on-call physicists. To address the scheduling problems, the authors mostly used metaheuristics or mathematical programming approaches. Legrain et al. [36] used both methods in their approach. Two articles used different methods: Gocgun [35] used a Markov

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Reference Subject OR method Extent of im-plementation

Potential impact on performance

Babashov et al. [14]

Capacity analysis of

radiotherapy planning process

CS IV Mean reduction in waiting time of 6.5%

Bauza and Chow [32]

Scheduling of on-call physicists

CS III Mean number of shifts reduced from

16.48 to 11.84 for physicists with 10 or more shifts

Bolsi et al. [33] Throughput optimization in proton therapy

CS IIIa Increase in patient throughput by

approximately 30% Fava et al. [34] Throughput optimization in

proton therapy

CS III Up to 45.4% increased patient

throughput

Gocgun [35] Treatment scheduling MDP + MP I Outperformed current policy in low

capacity situations Legrain et al. [36] Treatment and dosimetry

scheduling

MH + MP III Decrease in number of patients

breaching target standards from 19 to 1 Lv et al. [37] Inpatient admission

scheduling

MP III Increased admission rate from 45.52%

to 73.89% Maschler and

Raidl [38]

Treatment scheduling MH I Outperformed reference method on all

benchmarks based on objective value Niroumandrad and

Lahrichi [18]

Psysician pre-treatment scheduling

MH III Decrease of median pre-treatment

phase by 1 day

Riff et al. [39] Treatment scheduling MH III Decrease in average number of waiting

days from 49.21 and 55.93 to 28.41 Vieira et al. [20] Radiation therapist scheduling MP IV Increase in fulfillment of primary (90.0%

to 99.1%) and secondary (82.4% to 98.9%) target standards

Vogl et al. [40, 41] Treatment scheduling MH I Combined approach of methods delivers

better results in large problem instances CS: Computer Simulation; MDP: Markov Decision Proces; MH: Metaheuristics; MP: Mathematical Programming.

a_{Proposed solution was already in use at the time of research.}

Table 3.2– Results

decision process in combination with mathematical programming, and Bauza and Chow [32] used Monte Carlo simulations to schedule on-call physicists. Articles on treatment scheduling often make reference to existing work, while improving upon their approach. The model of Gocgun [35] was the same as Sauré et al. [42], which was included in the review of Vieira et al. [21]. However, they improved on the scheduling model by also considering cancelation of treat-ments. Maschler and Raidl [38] extended their previous work on the scheduling of particle therapy patients by now considering that the therapy sessions should be scheduled at roughly the same time each day. Similarly, Legrain et al. [36] improves their existing model, included in the Vieira et al. review, by now taking the dosimetry scheduling into account. Vogl et al. [41] builds upon their own research on a genetic algorithm for scheduling particle therapy patients [40]. A

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new approach to the treatment scheduling problem that takes current waiting times into account is proposed by Riff et al. [39]. They compare their local search algorithm directly to methods previously proposed in a study by Petrovic et al. [43], included in the Vieira et al. review.

In contrast, articles on other subjects stated that it was necessary to discover new solutions. Lv et al. [37] investigated admission scheduling in an inpatient radiotherapy department. They stated that this was a unique challenge, as most patients receiving radiotherapy in the United States are outpatients, while most are inpatients in China, and therefore they would not be able to copy existing solutions. Vieira et al. [20] used a mixed linear integer programming model to schedule radiation therapists, as the problem of planning radiation therapists was not addressed so far in existing research.

3.4.2 Throughput and capacity

Three articles were found on the subject of throughput optimization or capacity analysis. All three used simulation methods for their approach. Babashov et al. [14] simulated the entire planning process of a radiotherapy department. Their sensitivity and scenario analysis on the department they studied did not find any major possible improvements. The best improvement they found resulted in a 6.5% mean reduction in waiting time. They concluded that the resource levels were in balance with each other and the system was running close to its maximum capacity.

Bolsi et al. [33] and Fava et al. [34] both used Monte Carlo simulations to deter-mine if remote patient positioning was a way to improve patient throughput for proton therapy. Bolsi et al. researched the medical feasibility of the technique foremost, and the patient throughput as a secondary objective. Fava et al. further expanded the research on patient throughput by testing with more parameters. They showed that the benefit of remote patient positioning on the throughput varies, depending on the number of treatment rooms, the transporter speed, and time used for imaging and setup correction. In a best case scenario, 45.4% in-creased throughput could be achieved.

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3.5 Discussion

3.5.1 Main findings

We found a total of 13 articles, of which 11 were published after 2015. When added to the 33 articles found by Vieira et al. [21], this would result in a total of 46 articles on the subject of OR in radiotherapy. Scheduling problems were the most studied in the articles found, with 10 out of 13 articles addressing some form of scheduling. Treatment scheduling was the subject of 6 of those articles and was also the most prominent type of scheduling in the review of Vieira et al. Therefore it is not surprising that the articles we found on this subject used existing work to compare to and improve upon. Metaheuristics was the most prominent technique for scheduling.

Although some additions were made to the search query compared to Vieira et al. [21], no additional relevant articles from the 2000-2015 period were included as a result of this. However, two articles were included from that period that they excluded in their screening: Bolsi et al. [33] and Fava et al. [34]. Additionally, one relevant record was found that they did not find in their search, but the full-text was inaccessible. Legrain et al. [36] is dated from 2015, but likely after Vieira et al. finalized their search, and therefore not included in their review.

Both Babashov et al. [14] and Vieira et al. [20] indicated that the results were val-idated by the institution of their case study, and therefore scored highest on the implementation scale. In this study a larger proportion of studies using fictitious data was found compared the literature found by Vieira et al. [21]. The remote patient positioning and imaging procedure tested by Bolsi et al. [33] was already in use at the Paul Scherrer Institute at the moment of their research. This was the only case where a proposed intervention was reported as implemented. How-ever, in this case the implementation existed before they modeled the potential impact on patient throughput. As the implementation was not a consequence of the experiments, it was not rated as an implementation of the proposed interven-tion.

In 3 cases fictitious data was used, and were therefore rated the lowest on the im-plementation scale. Research using real data provides stronger evidence of the potential impact of the proposed intervention. However, real data can be applied in different ways. For example: Niroumandrad and Lahrichi [18] experimented with pseudo real instances, and then tested their metaheuristic on the real case

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of The Center Intégré de Cancérologie de Laval. Others mostly reported on their generated experiments based on real data. Arguably, this method provides re-sults that are not as specific to one particular center. However, as Niroumandrad and Lahrichi shows, a study could use the real data as well as generated data, to provide results as close to the real world as possible.

All studies reported a potential beneficial impact on performance. However, performance of a proposed intervention was often dependent on the parameters used for the model. This suggests that the feasibility of implementation is depen-dent on the specifics of a particular case. Fava et al. [34] showed, for example, that the benefits of a remote patient positioning procedure is very dependent on the speed of the positioning and imaging itself, the transport speed to the treat-ment room, and the number of treattreat-ment rooms.

Some articles use an objective value as outcome measure to indicate performance, others use a more straightforward outcome measure, such as the average number of waiting days per patient. Objective values are a great method to determine if a scheduling method is evidently better, considering all possible drawbacks and benefits together. However, when the exact impact on the waiting times or other similar values are not directly reported, it makes the results harder to compare and not effective to report without an explanation of the formulation of the objective value. Articles using more directly interpretable outcome measures often used waiting days per patient or the number of times that the waiting time of a patient violated the target standard or deadline.

3.5.2 Strengths and limitations

Most of the strengths and limitations of this study are very similar to those of Vieira et al. [21], as we followed their methods closely. Our extended search strat-egy did not result in more relevant articles from the time period they searched. This shows the strength and exhaustiveness of the search strategy that formed the basis for the search strategy we used. The search for articles on the subject of OR in radiotherapy is challenging. Articles can be published in various types of journals, because of the multidisciplinary nature of the research. The inclusion of all types of records in our search strategy did not result in any useful new discoveries. Any conference abstracts we found did not contain enough informa-tion to be included, and we could not locate any follow-up full text articles of the

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same authors, except for Babashov et al. [14], where the published article was already in our results.

In our screening strategy we did not use a second researcher to verify the screen-ing process. However, a large number of articles were screened by Vieira et al. [21] before, and the selection of relevant articles in that screening was largely identical to ours, as only two extra articles were included from the time period they investigated. Therefore, we are confident our selection procedure is valid. A limitation of our search strategy is the absence of snowballing, which did re-sult in additional articles for citeauthorvieira2016. However, we did not find any indication that relevant articles were missing.

Vieira et al. [21] already identified two areas where bias might be present. Firstly, the implementation stages could be subject to publication bias, as articles can be published before an implementation procedure is started. However, we do not have any indication that implementation has progressed further than reported. Secondly, as there are no strict boundaries of what is considered an OR technique, researcher bias might be introduced.

3.5.3 Comparison to other studies

Aside from Vieira et al. [21], no other reviews were found that cover the use of OR for logistical problems in radiotherapy. Some of the included articles do pro-vide a short overview of OR in healthcare or radiotherapy. For example, Gocgun [35] summarized literature on advanced scheduling methods, OR in radiother-apy, and the method they planned to use. These overviews are not as compre-hensive as Vieira et al. While Niroumandrad and Lahrichi [18] provide their own overview of related literature, they introduce it with a reference to the literature review by Vieira et al.

Other published reviews exist of OR in healthcare [44], simulation in healthcare [45], OR in intensive care unit management [46], and simulation used to investi-gate overcrowding in emergency departments [47]. In healthcare research, there are reviews of the effects of radiotherapy waiting times on local control and sur-vival [6, 7]. Furthermore, González Ferreira et al. [48] reviewed the effects of radiotherapy treatment delay as a result of interrupted treatment schedules on outcome.

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3.5.4 Interpretation, implications and impact

Some studies refer to previous studies as using the same method, but not quite having the same level of detail. For example, Gocgun [35] mentioned that Sauré et al. [42] used the same method, but did not take cancelation into account. Legrain et al. [36] expanded their own previous research with the scheduling of dosimetry as an addition to their treatment scheduling algorithm. This suggests that continued progress is being made in the comprehensiveness and usefulness of the models. These references were most prominent in articles on treatment scheduling, which is also the most commonly studied subject in our results. This shows that this has become a developed area of research.

Some of the studies develop models necessary for advanced forms of therapy. The remote patient positioning procedure of Bolsi et al. [33] and Fava et al. [34] is specific to proton therapy centers. Furthermore, Maschler and Raidl [38] and Vogl et al. [40, 41] developed particle therapy treatment scheduling models. This form of therapy differs in the number of fractions and the duration of those frac-tions from photon therapy, therefore requiring different schedules. Vieira et al. [21] recommended future research on the capacity allocation of new imaging and treatment devices.

3.5.5 Future work

As Vieira et al. [21] stated, macro planning is an important area of research that was not included in the study. In Chapter 1 we mentioned the increasing demand for oncological care in the Netherlands. Furthermore, an increase in new cancer patients in Europe of about 16% is projected from 2012 to 2025 [1]. Macro plan-ning methods could be very useful in anticipation of this increase. Vieira et al. mentioned they could only find one study on the subject in a separate search. An overview of macro planning research could be a subject of future research. The most prominent subject of OR in radiotherapy is scheduling, of which many articles focus on treatment scheduling. Future research on this subject could experiment more with integrated scheduling approaches, combining pretreat-ment and treatpretreat-ment scheduling. Increased usage of real world data could further strengthen evidence of the benefits of these scheduling approaches. Further re-porting on the implementation of these scheduling algorithms or other interven-tions would strengthen the evidence even further.

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The maturity model used to evaluate the extent of implementation could be more detailed, as Vieira et al. [21] already mentioned. A challenge that comes with us-ing the model is that it is hard to objectively determine if a proposed intervention actually shows a benefit large enough to start an implementation process. More-over, not showing any impactful improvements does not exclude the study from being validated. For Babashov et al. [14] this was the case, as their simulation model was validated, but experiments could not find significant improvements for the efficiency of the system. Future research could reevaluate this maturity model, defining clearer boundaries to each step and abolishing the linearity of the model.

3.6 Conclusion

In this updated review, we found 13 new articles on the subject of OR in radio-therapy. Similarly to the original review, most of the articles studied some kind of scheduling. The research on scheduling is mature, with studies improving on existing work. Other areas are not as frequently researched. Some articles show very promising potential improvements. Moreover, many use real data in experi-ments, although there is still room for improvement. Implementation efforts that resulted from the proposed interventions are still absent.

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Chapter 4

Process mining and simulation of

a radiotherapy department

4.1 Introduction

Waiting times for radiotherapy should be kept as short as reasonably possible, as longer waiting times have negative effects on patients [6–8]. The demand for radiotherapy is also increasing [1]. Literature using OR techniques shows that potential efficiency improvements can be made at radiotherapy departments. In this chapter we will use simulation to explore potential ways to decrease waiting times and test patient capacity at the Maastro Clinic, a radiotherapy clinic in Maastricht.

The Maastro Clinic publishes their waiting time statistics on their website, us-ing the same categories as the NVRO uses for their target standards [49]. Most patients already receive their treatment within the target standards, although each month a small portion receives their treatment after the maximum waiting period.

Computer simulation is a technique used to experiment with “what-if” scenarios in a process. As the digitally imitated process of a simulation can be adjusted much easier than the process in the real world, simulation allows for the rela-tively easy evaluation of various changes in the process [31]. In this research, potential efficiency improvements to the process of delivering radiotherapy will

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be experimented with using discrete-event simulation, a simulation approach suitable for studying queueing systems [25].

Before a process can be simulated, the process has to be represented in a model. The development of this process model is seen as the most challenging and crit-ical part of a simulation study [31]. When the model itself is flawed, the results of the simulation are as well. Possible errors include making the model oversim-plified by modelling the desired behavior instead of the real world behavior of the process, or making the model too complex by including excessive detail [50]. Making a good process model is often described as being an art as much as it is a science [31, 50].

Process mining is a collection of techniques where data is related to a process model. By using process mining, it is possible to construct a process model au-tomatically, based directly on available data [50]. This way, the process model does not have to be created entirely by hand, reducing the potential for errors in this critical step in the simulation process. Moreover, using the data, the pro-cess model can be enhanced to show bottlenecks in the propro-cess, allowing these bottlenecks to be targeted in the simulation study.

Van der Aalst [50] describes process mining extensively in his book. Process min-ing works with event data, which can be acquired from an information system that supports the process. For example, data may be acquired from an electronic health record that logs all activities. The data in these event logs should at least consist of a case identifier, events that correspond to that case, and timestamps for those events. An example of an event log is provided in Table 4.1. Each row in the table corresponds to one event. The sequence of events belonging to a case is referred to as a trace. Event logs can contain more information, such as a cost, resources used, or a second timestamp for differentiating between beginning and end of an event.

Case identifier Activity Timestamp

1 A 28-01-2019 09:00 1 B 28-01-2019 10:00 1 C 30-01-2019 12:00 2 A 29-01-2019 14:00 2 C 30-01-2019 09:00 2 B 31-01-2019 12:00

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There are three main applications of process mining [50]. The first is process discovery, the construction of a process model based on event data. There are many different algorithms that can be used for process discovery. The second is conformance checking, where an existing model is compared to the event data to assess the conformance of the process to the model. The third is enhancement, where an existing process model is extended or improved by using the event data. In one type of enhancement, the process model is extended with performance data. For example, by showing waiting times and service times in the model, to assess performance.

To study the waiting times at the Maastro Clinic, it is essential to first analyze the process of delivering radiotherapy and its performance. Process mining pro-vides a way to automatically create a process model based on real event data. The process model can also be extended to show performance data, such as waiting times between events. As creating a process model is a critical step in the simu-lation process, we chose to use process mining to assist with this task. Moreover, enhancing the process model with performance data provides a way to identify parts of the process that form a bottleneck. Optimization experiments in the simulation can focus on these bottlenecks.

The goal of this study is to identify the current bottlenecks in the process of deliv-ering radiotherapy at the Maastro Clinic, decrease waiting times, and test patient capacity. By using computer simulation in combination with process mining this study expands on existing methodologies of studies found in the literature re-view of Chapter 3.

4.2 Setting and interviews

The Maastro Clinic is an independent radiotherapy clinic in Maastricht. It is lo-cated next to the Maastricht UMC+, an academic hospital. In addition to the primary location in Maastricht, the clinic has a secondary location in Venlo, with four linacs at the primary location, and two at the secondary location. The primary location offers brachytherapy, a form of radiotherapy where radiation sources are placed inside the body. A new proton therapy treatment room is present at the primary location as well.

Interviews were conducted at the Maastro Clinic and the radiotherapy depart-ment of the Erasmus MC. The Erasmus MC is a large academic medical center

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in Rotterdam. Its radiotherapy department is similar to the Maastro Clinic in the types of treatments they offer, and the number of linacs present at their pri-mary and secondary locations. The interviews served the purpose of developing a greater understanding of the process of delivering radiotherapy for construc-tion of the process model, creating a descripconstruc-tion of the process (Chapter 2), gath-ering information that might be missing from the dataset, and inquiring about perceived bottlenecks in the process.

Interview questions were created based on radiotherapy workflow overviews in literature [13–21], and assumptions about the required data for the simulation study. A semi-structured approach was used for the interviews. Questions were aimed at gaining a greater knowledge of the process of delivering radiotherapy and the workflow at that department, including planning methods and perceived bottlenecks. In the Maastro Clinic, a radiation oncologist and the team leader of administration participated in the interview. In the Erasmus MC, participants included a radiation therapist team leader, another radiation therapist, and a consultant business management.

4.2.1 Perceived bottlenecks

In the interviews, participants were asked if any bottlenecks in the process were known or suspected. In the Erasmus MC interview, every handover of work was named as a potential bottleneck. During the pretreatment phase, preparations require multiple members of staff to work on the treatment plan of a patient. At every handover there could be a waiting time for the work to be picked up again. In the Maastro Clinic, while they thought the workflow was very optimized in general, they indicated that there might still be room for improvement in waiting times between admission and first consultation, and between first consultation and imaging.

4.3 Process mining

Following the interviews, process mining was applied to data from the Maastro Clinic. The interviews provided insight into the process and suggested the pro-cess was linear, with no concurrent activities. This would result in a straightfor-ward process model. However, to validate the perception of the process from the

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interviews, process discovery was applied to the data. Moreover, enhancement of the process model with performance data may reveal bottlenecks that can be targeted in the simulation study. The process model and performance data from our process mining efforts will form the foundation for the simulation study.

4.3.1 Data

Data was retrieved from the electronic health record at the Maastro Clinic. It in-cluded the registration, appointment, and treatment preparation activities. The data covered a period of six months, from January 2019 to the end of June 2019. After an initial examination of the data from a period of one month, it was determined that a six month period would be sufficient. It was estimated that this would include enough patients that had a complete trajectory through the healthcare they received, from registration to treatment.

In the six month period, a total number of 1981 registrations took place, relating to 1827 different patients. Patient registrations were categorized in one of twelve healthcare paths. The largest number of patients were referred for palliative radiotherapy, followed by breast cancer and urological cancer.

4.3.2 Process mining tools

For process mining, the process mining toolkit ProM (version 6.9) [51] was used, as it is open source, well documented, targeted at researchers, and is the most commonly used tool for process mining research in healthcare [52, 53]. For pro-cess discovery, multiple algorithms are available, each using a different approach to discover a process model on the event log. Multiple algorithms were consid-ered: the alpha miner, the heuristics miner, fuzzy miner, inductive miner, and directly follows miner. The inductive miner and directly follows miner share a visual component that supports the replay of event data over the resulting pro-cess model, and is able to display performance indicators on the model.

The Directly Follows visual Miner [54] was selected for this study. The inter-views indicated that the process of delivering radiotherapy did not contain any concurrent activities. This allows the usage of this miner, as it does not sup-port concurrency in the process model. Imsup-portant for the selection of this miner was the ability to display performance data directly on the process model. This

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provides valuable insight into the performance of the process for the simulation study.

Some other factors further motivated the selection of the Directly Follows vi-sual Miner. The miner guarantees soundness of the resulting process model [55], meaning there is an option to complete the process from each state, and all ac-tivities in the process model are reachable in some way. Other miners, such as the heuristics miner or alpha miner do not guarantee soundness [56]. The alpha miner also has problems with noisy data, containing infrequent behavior that should not be in the process model [50]. Additionally, the Directly Follow visual Miner delivers process models that are easy to understand [55].

4.3.3 Filtering the data

Before the data could be used for process discovery, it had to be transformed to an event log format. Therefore, the data on registration, appointment, and treatment preparation was combined in a single table with the correct format. The resulting event log was immediately filtered to only include cases for which the registration data was present. As a result, cases that were registered before January 2019, and consequently had missing activities, were removed from the event log. Starting with this initial event log, further filtering was applied. In process mining, filtering is an iterative process. Based on initial findings with process discovery, the data is filtered further to adjust the scope of the process model [50]. In our approach, filtering was aimed at discovering a process model that displayed the relevant activities of delivering radiotherapy, discarding in-frequent activities, and selecting a start and end activity for the process model. Furthermore, some filtering was applied to improve the data quality of the pro-cess model.

The event log contained some traces that ended before any treatment was deliv-ered. Any patient that was registered late in the timeframe of our data will likely have appointments outside of the timeframe. Moreover, treatments that are can-celled may create the same issue. Therefore, data was filtered so that all traces had to have at least a registration event, a treatment preparation event, and a treatment event.

Some patients were admitted multiple times. This meant that some traces in the event log repeated the process. We were able to split those traces, so the resulting

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trajectory through the process of each admission could be included as a separate trace.

A few of the activities presented in the initial event log were duplicates. These were introduced when merging the appointment and treatment preparation data. For example, the CT scan is logged as both an appointment and treatment prepa-ration activity. The appointment data was kept, while the treatment prepaprepa-ration activity was discarded to remove the duplications. Similarly, some activities in the log were irrelevant variations of each other. For example, various types of CT scans were present in the log, and even a spelling difference for the same type of CT scan. These variations were renamed to an identical activity name.

To keep the scope of the process model manageable, infrequent or exceptional activities had be discarded. By experimenting with the frequency filters in the ProM toolkit and the filtering capabilities of the Directly Follows visual Miner, these activities were identified and filtered out. The event log also contained some activities that were not directly related to the delivery of radiotherapy, such as telephone consultations and appointments with the dietician or dental hygienist. Therefore, they were filtered out of the event log.

As the performance analysis was focused on the pretreatment phase, all events after the first radiation treatment were removed. This also provides a clear end point to the process model. Similarly, by filtering on registration as the starting event, a clear starting point was given to the process model.

By filtering, the number of traces in the event log was reduced from 1827 to 1208. In the initial event log the mean number of events per trace was 36, ranging from 1 to 190 events per trace. After filtering, the mean number of events per trace was 21, ranging from 5 to 67. For some patients, multiple treatment plans are made, which will result in traces with more events. The presence of a trace with only 5 events shows that some exceptional behavior is still present in the event log. However, with the filtered event log , it was found to not cause any issues for process discovery.

4.3.4 Discovered process model with performance data

The discovered process model, enhanced with performance data, is presented in Figure 4.1. The performance data was added by enabling the display of sojourn times in the Directly Follows visual Miner. This options adds the average time

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between activities to the process model. On each activity, the time between the completion of that activity and the completion of the previous activity is dis-played in days and hours.

The performance data shows that the longest interval is between registration and appointment with the physician assistant. The mean time between completion of those activities is 6 days, 18 hours, and 41 minutes. The second longest in-terval is found between the first consult with the radiation oncologist and the appointment for creation of a mold or mask.

One discrepancy to the interviews was found in the process model. In the in-terviews at the Maastro Clinic, it was indicated that the first appointment of a patient consisted of a visit to the physician assistant, followed by the first con-sultation with the radiation oncologist. However, the process model shows that, occasionally, the radiation oncologist is seen before the physician assistant. Because some activities were discarded while filtering the event log, the process model was discussed with the team leader of administration to ensure its validity. Moreover, it was clarified that if the physician assistant is not available right before the first consultation with the radiation oncologist, the physician assistant will see the patient after the radiation oncologist.

4.4 Simulation

Utilizing the process model and performance data from process mining, a simu-lation was developed. The simusimu-lation allows for experimentation with the pro-cess, with the goal to reduce waiting times and test patient capacity.

4.4.1 Development of the simulation model

The simulation model was developed in R using the package simmer. Simmer provides a generic framework for discrete event simulation in R [57]. Version 4.4.0 of simmer was used with R version 3.6.2, both released in December of 2019.

The simulation creates new patients and attributes them a type of tumor, which is used for assigning one of the radiation oncologists. Each patient follows the tra-jectory of delivering radiotherapy that is based on the process model discovered

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with process mining. After the patient received all their radiation treatments, they end this trajectory. The performance was measured by recording the flow time, the time interval between the creation of a patient and their first treatment session.

The simulated patients seize resources for each activity they go by in the trajec-tory. When a resource is currently unavailable, the patient will move to a queue. Once the resource becomes available, the activity will start and hold the patient during its service time, after which the patient continues along the trajectory. The arrival rate by which the simulation creates new patients was based on the data received from the Maastro Clinic. Similarly, the data provided the occur-rence of each type of tumor. Furthermore, along with information from the inter-views, the data was used to determine the service times for the various activities in the simulated trajectory, and the resources they used.

Each radiation oncologist was represented as a separate resource in the simula-tion model. This way, their individual availability could be implemented based on the schedules used at the Maastro Clinic. Moreover, this allowed for the as-signment of simulated patients to a radiation oncologist based on their type of tumor, as all radiation oncologists had their own specialty and only treated pa-tients with specific types of tumors.

The creation of simulated patients followed a Poisson arrival process. Service times were exponentially distributed, with a minimal service time equal to half of the average service time, resulting in a shifted exponential distribution. How-ever, the service times for appointments were deterministic. Using the Kendall notation for classifying queueing systems [27], this translates to M/M/c and M/D/c respectively, where c would be the number of number of servers avail-able for a specific task, which varies. The queueing discipline used was “first come, first served”. However, acute patients were simulated by attributing them a higher priority, making them move in front of regular patients in a queue. Delivering radiotherapy involves the management of many different resources. To manage the scope of the simulation model, some choices were made in the simulation design. Generally, making a simulation model excessively complex does not result in an increase in the quality of the results [58].

The Maastro Clinic has a primary location in Maastricht and secondary loca-tion in Venlo. The data showed that only 13.5% of all patients were seen at the

Reducing waiting time in a radiotherapy department using simulation and process mining

Reducing waiting time in a radiotherapy department

using simulation and process mining

Reducing waiting time in a radiotherapy department

using simulation and process mining

Abstract

Samenvatting

Contents

Chapter 1

General introduction

1.1

Waiting times and capacity in radiotherapy

1.2

Approach of this study

Chapter 2

Radiotherapy workflow

2.1

Regular patient flow

2.2

Deviations

Chapter 3

Radiotherapy in operations

research: a scoping review

3.1

Introduction

3.2

Preliminaries: operations research techniques

3.3

Methods

3.4

Results

3.5

Discussion

3.6

Conclusion

Chapter 4

Process mining and simulation of

a radiotherapy department

4.1

Introduction

4.2

Setting and interviews

4.3

Process mining

4.4

Simulation