Simulation Model Outline

The idea behind this thesis is to model patient progression through the liver transplantation system. The intention is to find the most appropriate match between a donated liver and one of the patients on the waiting list, by examining their (individual) characteristics. We also wish to know the outcomes, with and without transplantation, that are experienced by each of the patients so that we may compare various matching policies and assess the overall utility of various policies (as discussed in Section 3.4.2).

3.5.1 DES Model Structure

Figure 3.4 below details the simulation model to be developed (Hepatica). The diagram captures the stages that a patient passes through from initial referral. It includes the patient flows after referral based on the stages outlined in Figure 1.4 (Section 1.3.3) and extended to include post transplant outcomes. Hepatica includes: (1) the referral stage, and (2) the assessment stage, which are reconsidered in Chapter 4 when the sub-models are created.

Methodology

Figure 3.4 A flow diagram to depict the process once a patient is diagnosed with ESLD.

The focus of Hepatica has been to incorporate the key stages of the process where the observed responses (as outlined in Section 3.4) of a particular policy need to be evaluated. This section outlines the sub-models developed to enable predictions at the various stages within Hepatica. The appropriate modelling techniques for each of the transitions and flows are explained in Section 3.6. Tables 3.5 to 3.7 summarise the scope of the model and the level of detail to be incorporated. Patient Referral To a Liver Unit Assessment At Liver Unit Death/ Removal Join the Waiting List Livers Donated Re-Listing Liver Allocated & Transplanted Death/ Graft failure Not Referred to Liver Unit Not assessed/assessed & not placed on list

Methodology

Table 3.5 Model Scope - Components included.

Component Justification

Patients Arrivals (ill will ESLD)

Determines the demand for transplantation and the patient flow rates through the transplantation process

Donors Arrivals Determines when a transplant may take place

Patient Referral to Liver Unit

A patient must be referred to a liver unit, as an initially step to obtaining a liver transplant. Determines patient flow through the system

Assessment Phase

A patient needs to pass the assessment phase (i.e., to be judged suitable for transplant) in order to be placed onto the WL and obtain a transplant. Determines patient flow through the system Waiting List/Queue for

Transplant

A transplant is allocated to patients that are on the liver transplant WL. Determines patient flow through the system

Allocation

The process by which it is decided who will receive a liver transplant. Determines patient flow through the system

Re-list post transplant Patients that also require transplant. Determines patient flow through the system

Death/Removal from WL

If a patient is removed or dies from the WL, then they are no longer waiting for a transplant. Determines patient flow through the system Death/Graft Failure

from transplant

Overall outcome. We know that these patients will no longer require another transplant. Determines patient flow through the system

Table 3.6 Model Scope - Components excluded.

Component Justification

Number of Liver Transplant Surgeons

Not relevant for the overall outcomes that are being evaluated

Number of Liver Transplant Units

Not relevant for the overall outcomes that are being evaluated

Government Campaigns

Have not affected donations significantly. But add to “What-If” scenarios by changing the supply

Opt-In/Opt-Out Not likely to change, however, added to “What-If”

Methodology

Table 3.7 Components - Level of Detail Included in Hepatica

Component Detail Comment

Patients

Patient inter- arrivals

Sets the patient flow into the system. Modelled as a distribution

Patient attributes

Helps to determine eventual outcomes. Modelled as several distributions

Donors

Donor inter- arrivals

Determines when a transplant may take places. Modelled as a distribution Donor

attributes

Helps to determine eventual outcomes. Modelled as several distributions Referral

Phase Process

Determines who is put forward for transplant. Represented by a set of rules Assessment

Phase Process

Determines who is put forward for transplant. Represented by a set of rules Waiting

list/Queue for Transplant

Queuing

Required to determine waiting times and determine the number and type of patients waiting for a transplant at any one point in time

Allocation Process Determines who is allocated a transplant.

Represented by a set of rules Re-list post

transplant Process

Determines who requires another transplant. Represented by a set of rules

Death or removal from waiting

list

Times

Determines the time at which a patient will die or be removed from the WL i.e., no longer requiring a transplant. Modelled as several distributions Death or graft failure from transplant Times

Determines the time at which a patient will die or suffer from graft failure and hence no longer require a liver transplantation. Modelled as several distributions

The key phases of the model as depicted in Figure 3.4, are:

(1) Arrivals (patient referrals to a liver unit and liver organs donated);

(2) Assessment Phase (the process by which it is determined whether a patient is suitable for transplant and hence whether they should join the waiting list or not); and

(3) Allocation/Transplant Phase (the process by which a donated liver is allocated to a patient so that the patient may have a transplant);

Methodology

(4) Outcomes (these are death or removal from the waiting list; death or graft failure or re-listing once transplanted).

To be able to capture these key phases, Hepatica must include the following components:

(1) Patient Generation and Patient Attribute Assignment;

(2) Donor Generation and Donor Attribute Assignment;

(3) Transplant Assessment Rules;

(4) Survival Time Generation {(1) the time from joining the waiting list to dying or being removed, (2) the time from receiving a transplant to dying or suffering from graft failure, (3) the time from receiving a transplant to being re-listed for another liver transplant operation};

(5) Maintain a list of candidates on the waiting list; and

(6) Transplant Allocation Rules.

Sub-models that capture these aspects are discussed in the next section.