Development

The assessment outcome model attempts to capture the patient characteristics that influence which patients “join the waiting list”. Logistic regression was

identified as being the appropriate modelling technique to capture these outcomes (Section 3.2.3). The data required to create this sub-model are only held at individual liver units (Section 3.7.1); in this case the data used were obtained from Birmingham Liver Unit. Patients referred to a liver transplant unit with liver failure are placed on a national waiting list if deemed by their consultant to meet the assessment criteria (Section 1.3.4). The likelihood of a referred patient being placed on the waiting list is dependent on individual patient characteristics (e.g., age, liver disease, urgency, as summarised in Section 3.7.2). Table 4.2 summarises the data regarding these characteristics that were available for analysis.

The data was structured with an indicator that represented whether or not a particular patient had been placed onto the waiting list; this indicator represented the response variable of the logistic regression model. Of the 736 patients to be referred to Birmingham Liver Unit within the observation period, 62.4% were eventually placed on the waiting list.

Statistical Sub-Model Development

Table 4.2 Covariates considered in the Assessment Outcome Model.

Covariate Appropriate Values Discussion

Gender Male, Female. The prognosis for many diseases

varies by gender.

Age

Age in years. The UK Transplant guidelines determine the age of an adult as 17 for listing onto the waiting list. However, before the patients can be listed, they need to go through an assessment phase, hence 16 year olds are also considered in this part of the analysis.

Primary liver disease

Disease groups as outlined in Section A.1.2 (Appendix A).

The primary liver disease will influence prognosis and is also one of the variables by which

assessment and allocation decisions can be changed.

MELD score

Both as a continuous value based on the original score, and as a factor variable as explained in A.3 (Appendix A).

MELD score measures the severity of a chronic liver disease (Section 2.2.2).

Transplant urgency

Routine, Super Urgent.

Will influence how quickly a patient is assessed.

Model Development

Initially, a decision had to be made as to how to utilise the available MELD scores. Firstly, they are only applicable to chronic liver disease patients. Secondly, there is the option to either treat them as a single continuous variable, or to group the scores together to leave four factor variables (as explained in Section A.3, Appendix A). Three approaches were therefore trialled in modelling the outcome from referral, and these are summarised in Table 4.3. Appendix I reports on the details of the development of these models.

Statistical Sub-Model Development

Table 4.3 Approaches Analysed for the Assessment Outcome Model.

Approach Super Urgent/Acute

Patients

MELD Score as a independent variable

A Included when developing the logistic regression model

Excluded the MELD score in the analysis

B Excluded when developing the logistic regression model

Included the MELD score as a continuous variable

C Excluded when developing the logistic regression model

Included the MELD score as factor variables

Analysis of the data showed that 95.3% of all super urgent/acute patients were placed on the waiting list. For models B and C it was assumed that all super urgent/acute patients were listed onto the waiting list, and the MELD score is only used as a factor for the remaining patients who are suffering from chronic liver disease (since the score is not applicable to patients with super urgent or acute liver diseases).

Goodness-of-Fit

The goodness-of-fit tests used are summarised in Table 4.4. The percentage of correct classifications is defined as:

N b

a

(4.2)

where a = number of observed patients not listed & to have a calculated response value of “0” from the model,

b = number of observed patients listed & to have a calculated response value of “1” from the model,

Statistical Sub-Model Development

Table 4.4 Goodness-of-Fit Tests the Assessment Outcome Model.

A

pp

roac

h

Variables present in the final logistic model

A ll S up er U rge n t pati ents ass u m ed to be l ist ed?* C orr ec t cl as si fi cat ions (% ) C ox and Sn el l R 2 st at is ti c H os m er a nd L em es h ow t est (si g ni fi cance ) A Super Urgent/Acute Liver Disease

Unknown Liver Disease Cryptogenic Liver Disease

Alcoholic Liver Disease Hepatitis C

Age

No 69.0 (logistic model for all patients)

0.14 0.82

B Unknown Liver Disease Cryptogenic Liver Disease

Alcoholic Liver Disease Hepatitis C

Age

MELD score

Yes 66.2 (logistic model for routine patients) + 736 61 3 . 95  (super urgent cases) = 74.1 0.10 0.98

C Unknown Liver Disease Cryptogenic Liver Disease

Alcoholic Liver Disease Hepatitis C

Age

MELD group 2

Yes 66.2 (logistic model for routine patients) + 736 61 3 . 95  (super urgent cases) = 74.1 0.12 0.76

* when all super urgent patients are assumed to be listed, they were excluded from the development of the logistic regression model and the last two columns report statistics for just the logistic regression model which considered just the routine patients.