Experimental Design

Two types of experimental design are commonly employed within simulation experiments; (1) full-factorial, and (2) fractional-factorial (Kelton and Barton

Methodology

2003; Law and Kelton 2000). However, neither of these approaches is appropriate within the context of this work. Assuming that each factor can take on one of two levels and there are k input factors, the full factorial approach identifies 2k different combinations of input factors. Within the context of this thesis we have initially defined 4 types of input factors (demand, supply, assessment rule, and allocation rule), which take on a varying number of levels (4, 4, 3, and 17, respectively). This implies a minimum10 of 4x4x3x17 = 816

experiments to perform under the full-factorial methodology. This is an extremely large number of experiments to perform and analyse. One approach to limit the number of experiments required is the fractional-factorial design. This approach performs a fraction of all the possible factor-combinations (Law and Kelton 2000), and the levels which are chosen to run are identified at random. This approach is appropriate where the levels are based on ordinal inputs (e.g., identifying the effect of employing 2, 3, 4, or 5 cashiers), but provides a non-intuitive means for this study, as many of the factors are not based on numerical aspects, for example, blood group or centre match. Therefore, a new experimental design, as described below, was developed to analyse which of the experimental factors (as outlined in Section 3.3) most improved the equity and utility measures.

Experimental Design Implemented

The experimental design implemented is as follows:

10 _{The number given is a minimum since several of the levels within the allocation factor could}

be combined to construct new levels, for example, L3 gives priority to patients with a compatible blood group and L6 to patients nationally, combining L3 and L6 would give a policy which gave

Methodology

(1) Run the base scenario which assumes the current assessment (A1) and allocation (L2) rules and constant future demand (D1) and supply (S1); (2) Run 23 other scenarios in which only one factor level change is made

(i.e., run the remaining scenarios outlined in Table 3.10);

(3) Analyse the results from steps (1) and (2) to identify (using methods outlined in Section 3.4.3) which of the scenarios in step (2) made improvements in the equity and/or utility measures, from the base scenario considered in step (1);

(4) Join up the allocation policies (where possible) found in (3) to create “alternative” allocation policies for investigation; and

(5) Run a full factorial experiment using the allocation factors identified in (3) and the most likely future demand and supply factors.

Methodology

Table 3.10 The Base Scenario and Scenarios where only One Factor Level is Changed.

Scenario Demand Supply Assessment Allocation

Base scenario D1 S1 A1 L2 L3 D1 S1 A1 L3 L4 D1 S1 A1 L4 L5 D1 S1 A1 L5 L6 D1 S1 A1 L6 L7 D1 S1 A1 L7 L8 D1 S1 A1 L8 L9 D1 S1 A1 L9 L10 D1 S1 A1 L10 L11 D1 S1 A1 L11 L12 D1 S1 A1 L12 L13 D1 S1 A1 L13 L14 D1 S1 A1 L14 L15 D1 S1 A1 L15 L16 D1 S1 A1 L16 L17 D1 S1 A1 L17 A2 D1 S1 A2 L2 A3 D1 S1 A3 L2 S2 D1 S2 A1 L2 S3 D1 S3 A1 L2 S4 D1 S4 A1 L2 D2 D2 S1 A1 L2 D3 D3 S1 A1 L2 D4 D4 S1 A1 L2 3.9 Summary

This chapter started by summarising the key reasons and objectives for modelling the UK Liver Transplant System. It outlined all the methods which are implemented in developing a model for capturing the assessment and allocation phases, in order to understand how changes within these phases affect the overall outcomes experienced by patients.

Methodology

Hepatica is also designed to incorporate the experimental factors (inputs) which capture future demand, future supply, alternative assessment rules and alternative allocation rules. These input factors are based on the likely or viable changes which may affect the UK system.

Hepatica allows the measurement of key equity and utility outputs. A methodology for the comparison of equity and utility outputs from the various scenarios (as defined by the input factors, Section 3.3) is constructed, to enable evaluation of any improvements made by the new scenarios (in particular, new assessment and allocation rules). The utility measures considered are:

– Life years in the system per patient; – Life years gained per transplant;

– The percentage of patients re-listed within 1 year of receiving a transplant; – The percentage of patients to experience death or graft failure within 1 year

of receiving a transplant; and

– The percentage of patients to experience death or removal from the waiting

list, and the number of livers wasted.

The level of equity within the system was also considered by looking at the outcomes that different patients experienced following their arrival onto the waiting list, and post-transplant.

This chapter also outlined the specific processes, tests and risk factors employed in developing the relevant sub-models. It also explained the techniques used to test the adequacy (i.e., goodness-of-fit) of the models developed.

Methodology

The experimental design used to run the various scenarios in Hepatica was also presented. Normal strategies, such as, full-factorial and fractional-factorial designs were explained not to be applicable in this study and therefore a new approach has been constructed.

Statistical Sub-Model Development