Case Study: Extended Health Clinic

Submitted: 25 Sep 2017

Operations Research Topics: SimulationModelling

Application Areas: Healthcare

Contents

• Problem Description
• Problem Formulation
• Computational Model
• Results
• Conclusions

Problem Description

This case study extends the Simple Health Clinic – Scheduled Appointments model. The extensions are:

1. Walk-up patients are triaged before receiving treatment;
2. After being triaged, some walk-up patients need to have a test performed before seeing a doctor;
3. Appointment patients arrive at their appointment times +/- a few minutes;
4. The arrival rate of walk-up patients varies over the day.

The goal of this simulation study is to analyse the average time patients spend:

1. waiting for treatment; and
2. in the clinic;

and the average length of the patient queue (which informs waiting room size). This analysis will include a comparison of the walk-up vs scheduled patients.

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Problem Formulation

In order to formulate a simulation model we specify the following components:

1. Background – problem description
2. Objectives of the study
3. Expected benefits
4. The CM: inputs, outputs, content, assumptions, simplifications’
5. Experiments to run

Components 1(Background – problem description) and 2 (Objectives of the study) are given in the Problem Description section (see paragraph describing the goal of the simulation study to identify study objectives).

The Expected benefits (component 3) are a virtual environment for evaluating patient waiting times, total time patients spend in the clinic, and the number of patients waiting for treatment. This environment can be used to experiment with changes to the clinic, including a comparison of effects on the waiting times, queue length, etc for the walk-up vs the scheduled patients.

The CM content is specified using the following components:

1. Component List
2. Process flow diagram
3. Logic flow diagram
4. Activity cycle diagram

Component List

The components of the Extended Health Clinic model are:

• Walk-up patients with their (inter)arrival times
• Scheduled patients with their appointment times
• Triage nurses with their triage times
• Test nurses with their testing times
• Doctors with their treatment times
• Waiting room with its capacity

Process Flow Diagram

Patient Logic Flow Diagram		Doctor Logic Flow Diagrams
Nurse Logic Flow Diagrams

Activity Cycle Diagram

Once the content has been established (note this is usually an iterative process) we can identify the inputs and outputs: appointment times, interarrival times, triage times, test times, treatment times, waiting times for triage, testing, and treatment (i.e., Patient arrives to Nurse triages Patient, Nurse triages Patient to Nurse performs test on Patient, Nurse performs test on Patient to Doctor sees Patient, Nurse triages Patient to Doctor sees Patient, Patient arrives to Doctor sees Patient), total clinic time (Patient arrives to Outside), number in waiting room.

Assumptions are used to define stochasticity (e.g., Exponential interarrivals, Triangular treatment times) and the simplifications keep the system simple (e.g., single doctors and nurses on all day for triage, testing, and treatment, no registration, no prioritisation).

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Computational Model

Start with the Simple Health Clinic – Scheduled Appointments JaamSim model.

Select the PatientEntity and add a Test attribute to the AttributeDefinitionList by adding { Test 0} to the list.

Now add a distribution that determines if a Walk-Up patient needs a test or not. Add a DiscreteDistribution object from Model Palette > Probability Distributions. Name it TestDistribution and edit it so that 30% of Walk-Up patients require tests.

Object	Graphics	Key Inputs
TestDistribution	Position = 1 -2.5 0.0 m	UnitType = DimensionlessUnit, ValueList = 0 1, ProbabilityList = 0.7 0.3

Now select the AssignWalkup object and add { 'this.obj.Test = [TestDistribution].Value' } to AttributeAssignmentList.

Save your simulation.

Next, create two new servers (Process Flow > Server), one for triage and one for testing. Name then NurseTriage and NurseTest respectively and give them the nurse.png (icon made by Freepik from www.flaticon.com) graphic. Lay out NurseTriage (on the left), NurseTest (on the right), and TestDistribution (near NurseTest) as shown below:

Rename the ArriveToTreat EntityConveyor to be ArriveToTriage and change NextComponent to be NurseTriage. You can redirect the EntityConveyor by clicking on it, then Ctrl-clicking on its end point and dragging it to where you want it to be. Redirect ArriveToTriage as shown below:

Next, we need to add the branching for the potential test. Add a Branch object (Model Palette > Process Flow > Branch) and name it TestBranch. Now add 3 more EntityConveyors: TriageToDoctor, TriageToTest, TestToDoctor. TestBranch and the 3 conveyors are shown below (TriageToTest going horizontal left to right, TriageToDoctor diagonally down left, TestToDoctor diagonally down left).

Next, make sure that the flow of the patients through the triage and test conveyors and servers is set correctly. The TestBranch object uses the value of the entities' Test attribute with 1 added to it to transform it from a {0, 1} value to a {1, 2} value (JaamSim starts lists at 1 not 0), so a patient that doesn't need a test (Test = 0) goes to the first component in the list, i.e., TriageToDoctor conveyor.

Object	Key Inputs
ArriveToTriage	NextComponent = NurseTriage
NurseTriage	NextComponent = TestBranch
TestBranch	NextComponentList = TriageToDoctor TriageToTest, Choice = 'this.obj.Test + 1'
TriageToDoctor	NextComponent = Doctor, TravelTime = 2 min
TriageToTest	NextComponent = NurseTest, TravelTime = 2 min
NurseTest	NextComponent = TestToDoctor
TriageToDoctor	NextComponent = Doctor, TravelTime = 2 min

Save your simulation.

Now, add Queues for both triage and testing, set these queues as the wait queues for triage and testing. The treatment time is modelled by a triangular distribution with minimum 2 minutes, maximum 15 minutes and mode (most likely) 8 minutes, so add a TriangularDistribution called TriageDistribution with these parameters. The test time is modelled as a constant time of 10 minutes, so add this to the NurseTest's ServiceTime. You need to change the StateAssignment of NurseTriage and NurseTest to reflect these activities too.

Object	Key Inputs
NurseTriage	WaitQueue = TriageQueue, StateAssignment = Triage, ServiceTime = TriageDistribution
NurseTest	WaitQueue = TestQueue, StateAssignment = Test, ServiceTime = 10 min
TriageDistribution	UnitType = TimeUnit, MinValue = 2 min, MaxValue = 15 min, Mode = 8 min

Finally, you should change the StateAssignment of all your queues so that we can track the time spent waiting for various sets in the pathway. You also need to change the DefaultStateList of your patient entities.

Object	Key Inputs
WalkupQueue	StateAssignment = WaitTreat
AppointmentQueue	StateAssignment = WaitTreat
TriageQueue	StateAssignment = WaitTriage
TestQueue	StateAssignment = WaitTest
PatientEntity	DefaultStateList = { Arrive WaitTreat WaitTriage WaitTest Treat Triage Test Leave }

Save your simulation.

At this point you can run your simulation and ensure that your triage/test process does not cause any errors.

However, now that the PatientEntity has new states we need to modify and append our Statistics modules and Simulation output. Change the existing Statistics modules to gather all the time in the system and waiting times and change the outputs generated by the simulation.

Object	Key Inputs
TimeInSystem	SampleValue = 'this.obj.StateTimes([[Arrive]]) + this.obj.StateTimes([[WaitTriage]]) + this.obj.StateTimes([[Triage]]) + this.obj.StateTimes([[WaitTest]]) + this.obj.StateTimes([[Test]]) + this.obj.StateTimes([[WaitTreat]]) + this.obj.StateTimes([[Treat]]) + this.obj.StateTimes([[Leave]])'
WaitingTime	NextComponent = WaitingTriage SampleValue = 'this.obj.StateTimes([[WaitTriage]]) + this.obj.StateTimes([[WaitTest]]) + this.obj.StateTimes([[WaitTreat]])'
TimeInSystem2	SampleValue = 'this.obj.StateTimes([[Arrive]]) + this.obj.StateTimes([[WaitTreat]]) + this.obj.StateTimes([[Treat]]) + this.obj.StateTimes([[Leave]])'
WaitingTime2	NextComponent = WaitingTriage SampleValue = this.obj.StateTimes([[WaitTreat]])
WaitingTriage (New Statistics component)	UnitType = TimeUnit NextComponent = WaitingTest SampleValue = this.obj.StateTimes([[WaitTriage]])
WaitingTest (New Statistics component)	UnitType = TimeUnit NextComponent = WaitingTreat SampleValue = this.obj.StateTimes([[WaitTest]])
WaitingTreat (New Statistics component)	UnitType = TimeUnit NextComponent = PatientWalkupSink SampleValue = this.obj.StateTimes([[WaitTreat]])
Simulation	UnitTypeList = DimensionlessUnit TimeUnit TimeUnit TimeUnit TimeUnit TimeUnit DimensionlessUnit DimensionlessUnit TimeUnit TimeUnit DimensionlessUnit DimensionlessUnit RunOutputList = { [Simulation].RunIndex(1) } { [WaitingTriage].SampleAverage } { [WaitingTest].SampleAverage } { [WaitingTreat].SampleAverage } { [WaitingTime].SampleAverage } { [TimeInSystem].SampleAverage } { [WalkupQueue].QueueLengthAverage } { [Doctor].Utilisation } { [WaitingTime2].SampleAverage } { [TimeInSystem2].SampleAverage } { [AppointmentQueue].QueueLengthAverage } { '[Doctor2Appointment].Utilisation + [Doctor2Walkup].Utilisation' }

Save your simulation.

Run your simulation and use Lab3Analysis.R to look at the results from your simulation with the triage and tests added. The confidence intervals results should look as follows:

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Results

The results...

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Conclusions

In conclusion...

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