Development of a decision support tool for primary care management of patients with abnormal liver function tests without clinically apparent liver disease: a record-linkage population cohort study and decision analysis (ALFIE)

Epidemiology of liver disease in Tayside (ELDIT) database

The ELDIT project created a liver database in Tayside linking administrative clinical data with laboratory data. 16 Briefly, all electronic medical records (including laboratory tests) for Tayside were electronically linked with a unique identifier, the community health index (CHI). 15 The community health index is used for all health encounters in Tayside for the population registered with a general practice. The following independent data sources were record linked electronically, by means of the CHI, to maximise the accuracy of diagnosis and disease ascertainment:

• prescribing database: the HIC has person-specific dispensing information for the whole of Tayside17

• hospitalisation records: SMR (SMR1 – general admissions, SMR4 – alcohol-related psychiatric admissions and SMR6 – cancer admissions)

• death registry from the General Registry Office

• Carstairs categories for social deprivation based on the decennial census18

• endoscopy, regional biochemistry, pathology, irology and immunology databases.

Diagnostic algorithms for liver diseases have been created, and this database has already been used to assess the epidemiology and economic burden of viral hepatitis19 and other liver diseases.

The HIC prescription database is complete for all encashed prescriptions for the Tayside population from 1989 to 2003. The hospitalisation records (SMR) and mortality records are 100% complete for all admissions for Tayside residents. There were some gaps in the biochemistry database, as in the past, obscure databases were used in some peripheral hospitals and could not be recovered. However, this represented less than 1% of the total data on LFTs. Given that we had approximately 2 million tests after exclusions, bias due to missing tests would be minimal.

The ELDIT database, as described above, provided robust probabilities of outcomes. Costs of procedures were obtained from standard published values. The ELDIT database was updated to 2003, and this was funded by the British Liver Trust.

Prospective questionnaire data from patients undergoing ALFTs, as well as patients undergoing liver biopsy, provided utility-based quality of life measures in order to populate the decision trees. Other utility values were obtained from the literature and an expert panel of GPs and hepatologists.

Derivation of probabilities

Probabilities of outcome of liver disease or all cause mortality could be calculated using survival models such as the Cox proportional hazards regression model20 adjusting for confounders (such as age, sex, comorbidities, social deprivation), possibly incorporating time-dependent covariates and between-subject heterogeneity using frailty terms. 21 As deriving probabilities from the Cox model is not trivial, involving estimation of the baseline hazard, an alternative is the Weibull parametric regression model, which easily allows estimation of probability of outcome over any time period. The Weibull accelerated failure time model has been used to derive the Framingham coronary heart disease (CHD) risk equation22 and a CHD risk score for type 2 diabetes from Tayside data. 23 This gives greater flexibility in modelling over different time periods.

The main outcomes were:

• liver disease such as non-alcoholic fatty liver disease (NAFLD)

• liver disease mortality (yes/no)

• all cause mortality (yes/no).

The above models also allowed derivation of risks of outcomes stratified by factors entered in the regression model. For example, the risk of liver disease is clearly greater in patients with known alcohol abuse than in those without alcohol abuse. The following factors were entered in the regression models to assess their effect on risk and to estimate factor-specific risks:

• Age – derived from the first six digits of the patient identifier (CHI) (may be categorised as < 40 or 40+ depending on age distribution).

• Gender – derived from the ninth digit of the patient identifier (CHI).

• Pregnancy – from hospitalisation records (SMR2). This will, of course, exclude home births.

• Opioid abuse – a proxy measure will be obtained using methadone prescribing from the HIC prescription database.

• Alcohol dependence – we used hospitalisation records from SMR1 and SMR6, which include ICD-10 codes F10, X65 and T51. Y90 and Y91 may be used as supplementary information. This represented the more extreme end of alcohol abuse, demonstrating a weakness by missing others with mild or moderate alcohol abuse. On the other hand, this is also a strength, giving a clear definition and measures of the drivers of costs to the health service. The alternative of general practice notes would be prohibitively expensive and prone to classification error.

• Social deprivation – the Carstairs social deprivation score, assigned to postcodes for all residents of Tayside, is derived from the decennial census, incorporating the variables: housing density, car ownership, social class of the head of household and male unemployment. 18 Although social deprivation is a marker for cigarette smoking and comorbidity, we will also be able to assess the affect of individual comorbidities on risk.

• Diabetes defined from the Diabetes Audit and Research in Tayside, Scotland (DARTS) database, which is 97% sensitive for ascertainment of diabetes in the population. 24

• The Hearts database (sensitivity 95%), identifying those who have definite CHD (myocardial infarction or demonstrated coronary artery disease) in the Tayside population. 25

Other major comorbidities (see Appendix 3), such as respiratory disease, cerebrovascular disease, renal disease, ischaemic heart disease and cancers other than liver cancer, were defined by the SMR, which contains details of all hospital admissions, including ICD-9 and ICD-10 codes, for all Tayside residents, and is held in the HIC.

The HIC also contains the database of all encashed prescriptions in Tayside. This resource was used to create comorbidity variables such as:

• analgesics [non-steroidal inflammatory drugs (NSAIDs)]

• antibiotics

• lipid-lowering agents, such as statins.

Importantly, this resource allowed us to identify receipt of prescribed hepatotoxic drugs at the time of any ALFT.

Statistical analysis was performed on Statistical Analysis Software (SAS) version 8.0 (SAS Institute, Cary, NC). Decision analyses were performed in TreeAge Pro software, 2006 (TreeAge Software, Williamstown, MA). More details of the databases, methods and protocol are available from Donnan et al. 26

Study population

The study population was initially derived from a laboratory database which contained all electronically available LFT results from patients in the Tayside region of Scotland, UK during the 15-year period from 1989 to 2003. Tayside is a mixed urban/rural region characteristic of Scotland, with a population of approximately 429,000. Liver function tests included bilirubin, albumin, AP, GGT, ALT and AST. As many laboratories measure only either ALT or AST, these two tests were combined in this study and are referred to in all subsequent text as transaminases.

More details of the methods were described in Chapter 2. In brief, patients aged 16 and over, with no obvious clinical signs and symptoms of liver disease and with at least two initial LFTs referred from a Tayside GP between 1989 and 2003 were eligible for inclusion. Exclusion criteria detailed elsewhere ensured that the study population of patients had no clinically recognised liver disease at presentation in primary care (see Figure 1).

Databases

Data were extracted from the HIC, which is described in detail elsewhere. 26,27 The databases relevant to this study covered the entire study period and were used within procedures approved under the Data Protection Act and Caldicott Guardian.

All of the electronic databases described above were electronically linked with a unique identifier, the CHI. 27 The CHI is used for all health encounters in Tayside for the population registered with a general practice and is contained in all the databases described above.

Outcomes

The primary outcomes following the initial LFT results were:

• liver disease

• liver mortality

• all cause mortality.

For descriptive purposes, other outcomes including hospital admission, diagnosis of ischaemic heart disease (IHD), cancer, respiratory disease, diabetes and biliary disease were tabulated. The individual liver disease outcomes were also recorded by LFT and are listed in Appendix 4. Note that Gilbert’s disease is not included as a liver disease outcome.

Statistical analysis

For the baseline population, all LFTs were extracted and the numbers of patients plotted by year of first LFT. Normal, mildly elevated and severely elevated categories were defined for each test using regional laboratory standard cut-offs which vary by age and sex for some tests (see Table 1). Severely elevated was defined as 2.5 times the normal range. Baseline characteristics were tabulated by level of abnormality for each test. These characteristics were age, gender, Carstairs category, comorbidities during the period 1980 to study start (including cancer, diabetes, IHD, respiratory disease and biliary disease), alcohol dependency and drug misuse (from hospitalisations), methadone abuse, pregnancy and the use of statins, NSAIDs or antibiotics in the 3 months before LFTs.

Outcomes from the initial test results were also tabulated. Sensitivity, specificity, positive predictive values (PPVs) and negative predictive values (NPVs) of the LFTs to diagnose liver disease and to predict death (any cause and liver caused) were calculated over 1 and 5 years. As some patients did not have all their LFTs tested, liver disease diagnosis by LFT testing can be subject to selection bias. The predicted probability of testing for each LFT was found by fitting a logistic regression model adjusted for all the predictors mentioned above. 28,29 The probability of testing was then used to weight the logistic regression models for predicting outcome.

Survival analysis was conducted to investigate whether abnormality of an initial LFT had an effect on time to the specified outcomes, including all cause mortality, liver disease mortality and liver disease diagnosis. The starting point was taken as the date of the initial LFT test and the end point was 31 December 2003, date of outcome, emigration or death, whichever was earlier. All patients whose end point was not the outcome of interest were censored. Weibull regression models were fitted separately for each LFT by level of abnormality adjusted for the baseline characteristics. Initially, a univariate analysis was performed on each of these factors and those with a p-value > 0.3 were excluded from the stepwise regression technique. A multiple imputation technique was used to impute missing values for LFTs. 30 The proportional hazards assumption was checked and survival curves were plotted by initial LFT result. Analyses were performed using the SAS (version 8) software package.

Baseline characteristics

The mean age of patients with ALFTs was approximately 52 years, with the exception of albumin which had a mean age of 69 (compared with 53 for patients with normal albumin). Patients with abnormal AP were slightly younger (mean age 48 years). GGT was the only LFT measured more often in males than in females, and the only one to have noticeably higher prevalence of testing and abnormal tests in deprived areas (Table 2). Abnormal GGT groups also had the highest percentage of patients dependent on alcohol (15.3%), drugs (0.9%) and methadone (0.7%). Patients with abnormal albumin had much more comorbidity in comparison with the other LFTs (Table 2). The percentage of patients with an initial ALFT prescribed statins in the 3 months beforehand was less than in those with a normal LFT. The percentage of patients prescribed NSAIDs or antibiotics in the preceding 3 months was highest in those with lowered albumin (e.g. 14.3% versus 8.6% of those on antibiotics with normal albumin).

Outcomes

Table 3 contains the outcomes per 1000 patient-years (TPY) by initial LFT level. Low albumin was associated with much higher rates of mortality from any cause compared with the other LFTs, with rates of 166.3 TPY and 260.4 TPY for mildly and severely elevated respectively. Severe AP had the next highest death rate of 99.8 TPY. For liver-caused mortality, severely elevated GGT had the highest rate of 9.8 TPY followed by AP (8.43 TPY) and albumin (8.19 TPY). Albumin also had the highest rates for cancer death, and the rates of cancer diagnosis in those with a mild or severe albumin were 56.7 and 96.0 TPY respectively. Transaminase and GGT were most associated with liver diagnoses, with severely abnormal levels, having rates of 36.3 TPY and 41.0 TPY respectively. Rates of hospital admission after an abnormal albumin test were extremely high, with even a mildly lowered result having a rate of over 500 TPY.

Performance measures

For the outcomes of all cause mortality, liver mortality and liver disease diagnosis, GGT, weighted by predicted probability of testing, had the best sensitivity scores compared with the other LFTs, with scores of 0.769 and 0.714 for liver mortality over 1 year and 5 years respectively (Table 4). However, all the tests had generally low sensitivity. Albumin had the poorest sensitivity overall; however, its specificity was the highest (0.98 for liver disease diagnosis). Gamma-glutamyltransferase was the only LFT to have specificity scores below 0.90. All LFTs had NPVs of 0.99 or more for all outcomes except all cause mortality. However, all the tests had very low PPVs, between 0.002 and 0.052 for all outcomes except all cause mortality, for which albumin had the highest PPV (0.508 within 5 years).

Survival analysis

Liver disease diagnosis

All the LFTs were significantly predictive of liver disease even after adjusting for risk factors for liver damage (Table 5). Of the mildly elevated LFTs, transaminase had the highest HR of 4.23 (95% CI 3.55–5.04) (Figure 3a). All severely elevated LFTs had HRs over 8, with AP being the highest, followed by GGT and transaminase. Other factors predictive of liver disease were older age, Carstairs score, alcohol dependency, illicit drug use and methadone use. For the transaminase model, the HRs for the last three factors were 4.48 (95% CI 3.70–5.42), 2.25 (95% CI 1.51–3.36) and 4.52 (95% CI 3.07–6.65) respectively. Statin use was significantly associated with lower risk of liver disease for the bilirubin models, showing a 36% reduction in risk.

TABLE 5 - Weibull regression model results by level of initial LFT abnormality (vs normal) for time to liver disease, all cause mortality and liver disease mortality

AP, alkaline phosphatase; GGT, gamma-glutamyltransferase; HR, hazard ratio.

The missing data from transaminase and GGT were imputed using a multiple imputation method for the modelling.

Patients with severely elevated bilirubin were omitted from the population and thus this cohort is not in the survival model for bilirubin.

Weibull models were fitted separately for each LFT and were adjusted for all baseline factors described in the text. Gilbert’s syndrome is not classified as a liver disease outcome.

Variable	Liver disease	All cause mortality	Liver disease mortality
	HR (95% CI)	HR (95% CI)	HR (95% CI)
Albumin
Mildly lowered	3.41 (2.55–4.55)	2.65 (2.47–2.85)	7.38 (4.60–11.81)
Severely lowered	8.48 (5.04–14.28)	4.99 (4.26–5.84)	16.17 (6.41–40.81)
AP
Mildly elevated	2.91 (2.49–3.39)	1.80 (1.69–1.91)	3.81 (2.72–5.32)
Severely elevated	14.42 (10.20–20.37)	2.88 (2.44–3.40)	17.81 (9.20–34.49)
Transaminasea
Mildly elevated	4.23 (3.55–5.04)	1.35 (1.26–1.44)	5.41 (3.80–7.71)
Severely elevated	12.67 (9.74–16.47)	1.88 (1.58–2.23)	7.17 (3.75–13.70)
GGTa
Mildly elevated	2.54 (2.17–2.96)	1.56 (1.48–1.63)	4.89 (3.43–6.99)
Severely elevated	13.44 (10.71–16.87)	2.90 (2.61–3.23)	25.32 (15.27–41.97)
Bilirubinb
Mildly elevated	2.02 (1.68–2.44)	1.20 (1.12–1.29)	3.89 (2.76–5.48)

FIGURE 3.

Survival for (a) liver disease diagnosis in relation to transaminase level and (b) all cause mortality in relation to albumin severity.

Missing data methods

As mentioned in Chapter 3, there were some missing data for each LFT in the initial batch. Table 6 shows that only 8.83% of patients actually had all five LFTs on the first date of testing. This is due mainly to the fact that only 10.92% of patients were tested for GGT in the initial batch, and thus it had the largest amount of missing data (Table 6, column 2). The reason for this is most likely selective testing by the GP rather than actual missing or lost data. However, it is important to adjust the analysis for these missing data to reduce selection bias, as in a prospective study the protocol would be to test every patient with every LFT. Table 6 shows that albumin and AP have very small amounts of missing data (< 1%), bilirubin has more than 6% missing data and transaminase has more than 23% missing data. These, and GGT, can be allowed for using numerous methods of dealing with missing data. We shall discuss some of these methods in turn, starting with the most simple and concluding with the current ‘optimal’ method of multiple imputation.

Survival analysis methods

Survival analysis using regression methods allows one to measure the effect that covariates have on the hazard of a particular outcome (usually death) over time. Various methods exist for this analysis such as the common semi-parametric method, Cox proportional hazards. Unfortunately, the Cox model has become embedded in clinical survival analysis as it provides clinically meaningful HRs, even when simpler models provide a good fit. This report concentrates on use of the Weibull model, which, unlike the Cox model, is a fully parametric model and hence more concise in form. Parameters are also easily estimated using full maximum likelihood. It still allows derivation of the clinically useful HRs but also more easily allows derivation of probabilities over any time period. This model was also the final model used to derive probabilities of events in the Framingham Cohort study.

Survival analysis methods using categorical LFT results

Survival analysis using the Weibull regression method was conducted to investigate whether abnormality of an initial LFT (normal, mild, severe) was associated with time to outcomes including:

• liver disease diagnosis

• liver disease mortality

• all cause mortality.

The starting point was taken as the date of the initial batch of LFT tests and the end point was 31 December 2003, date of outcome, emigration or death, whichever was earlier. All patients whose end point was not the outcome of interest were censored. Initially, Weibull regression models were fitted separately for each LFT and the level of abnormality adjusted for the baseline characteristics. Levels of abnormality were taken as normal, mildly elevated and severely elevated as defined in Table 1 (for bilirubin the levels were only normal and mildly elevated as those with jaundice were excluded). Initially, a univariate analysis was performed on each of the baseline factors and those that had a p-value > 0.3 were excluded from further multivariate analysis including stepwise regression. Survival curves were plotted to display the survival functions by initial LFT result. The proportional hazards assumption was checked using plots of the log of the negative log of the survival function and by fitting log (time) by factor interactions to test for significance. Analyses were performed using the SAS (version 8) software package

The HRs are not outputted automatically in SAS for each parameter in the model. Only the parameter estimate is displayed with its 95% CIs, its standard error (SE) and its p-value. The HR was calculated using the following formula:

where β = parameter estimate and σ = scale parameter.

Hence, a negative coefficient for a factor represents increasing hazards with that factor.

If the hazard functions proved to be non-proportional, the survival plots and log of the negative log of the survival function plots helped inform the approximate time points at which the hazard functions became non-proportional. Further analyses were then conducted using models where the time was split into these different periods. Survival plots and log of the negative log plots were drawn again for each of these separate time models.

Missing data results

This section will discuss the results from the logistic regression modelling to predict outcome of LFT testing arising from the analysis to adjust for verification bias (see inverse weighting in the Methods section). From the survival analysis modelling, where LFT categories were used, three missing data methods were applied and these results are compared here for the transaminase and GGT models (the two tests with the most missing data).

Survival analysis using categorical LFT results

The survival analysis results where the LFT results have been grouped into normal, mildly elevated (or lowered for albumin) and severely elevated are presented in this section. The results are split into the following outcomes:

• first liver disease diagnosis

• liver mortality

• all cause mortality.

Liver disease diagnosis

All the LFTs were significantly predictive of liver disease even after adjusting for risk factors for liver damage. Of the mildly elevated LFTs, transaminase had the highest HR of 4.23 (95% CI 3.55–5.04). All severely elevated LFTs had HRs over 8, with AP being the highest followed by GGT and transaminase. Other factors predictive of liver disease were older age, Carstairs score, alcohol dependency, illicit drug use and methadone use. For the transaminase model the HRs for the last three factors were 4.48 (95% CI 3.70–5.42), 2.25 (95% CI 1.51–3.36) and 4.52 (95% CI 3.07–6.65) respectively. Statin use was significantly associated with lower risk of liver disease for the bilirubin models, showing a 36% reduction in risk.

The Kaplan–Meier plots for time to liver disease diagnosis by LFT category of result (normal, mildly elevated and severely elevated) are shown in Figure 4 for AP and transaminase. Severe AP can be seen to have high risk of liver disease, particularly in the first year.

FIGURE 4.

Time from first LFT to liver disease diagnosis by level of abnormality. (a) Alkaline phosphatase; (b) transaminase.

Liver disease mortality

Of the mildly ALFTs, low albumin had the highest HR for liver mortality of 7.38 (95% CI 4.60–11.81). Severely elevated GGT had the highest HR overall, with a value of 25.32 (95% CI 15.27–41.97), followed by AP and albumin. The only baseline factors which predicted liver disease mortality were gender, older age, Carstairs score (higher deprivation) and alcohol dependency. Alcohol dependency had HRs as high as 10.84 (95% CI 7.28–16.14) for the albumin-adjusted model. It was lowest for the GGT model, however, with a value of 3.92 (95% CI 2.73–5.61). Figure 5 shows the survival curves for albumin and GGT. Although the survival curves are very close together as a result of the low numbers of liver mortality, the HRs are large because of the flatness of the normal LFT curve.

FIGURE 5.

Survival from first LFT to liver mortality by level of abnormality. (a) Albumin; (b) gamma-glutamyltransferase.

All cause mortality

All LFTs had significantly high HRs for all cause mortality. Albumin had the largest HRs for mortality [4.99 (95% CI 4.26–5.84) for severely lowered]. For mildly lowered albumin the HR was more than 2.5 times that for normal albumin (see Figure 3b). GGT had similar HRs to AP, while transaminase had the lowest HRs for mortality. The baseline factors in the models predictive of death included gender, age, Carstairs score, IHD, renal disease, respiratory disease, diabetes, stroke, biliary cancer, all other cancers, statin use, NSAID and antibiotic use, alcohol dependency, drug dependency and methadone use. With the exception of biliary cancer, which had a typical HR of 15.70 (95% CI 5.06–48.71) (for the albumin-adjusted model), all HRs for these factors were less than 2. Statin use was associated with lower risk, with a typical HR of 0.56 (95% CI 0.49–0.65). Figure 6a demonstrates how serious an abnormal albumin is in relation to all cause mortality.

FIGURE 6.

Survival from first LFT to all cause mortality by level of abnormality. (a) Albumin; (b) alkaline phosphatase.

Assessment of proportionality

Figure 7 displays the log of the negative log of the survival function curves for initial transaminase to liver disease diagnosis and liver mortality by level of result. The plots look approximately parallel, although there are places of slight overlapping, particularly between the mildly elevated and severely elevated curves for liver mortality. Each plot shows steep curvature at initial testing, which suggests that survival differs during the first few months or so after initial testing compared with the rest of the study period. This was confirmed when tests for non-proportionality such as adding a log (time) by factor interaction term were statistically significant. Hence, because of the slight non-proportionality of the hazards in the first few months, it was decided to conduct separate analyses for different time points of the study period. The time periods chosen were day 0 to 3 months, 3 months to 1 year and 1 year to the end of the study. Any time period less than 3 months would result in very small numbers of events.

FIGURE 7.

Plots of the log of the negative log of the survival function against log of time for transaminase. (a) Liver disease diagnosis; (b) liver mortality.

Survival analysis using categorical LFT results by follow-up time period

The survival analysis conducted in the previous section was repeated for different time periods and for all outcomes. In the interests of brevity, the results are described only for the outcome of liver disease diagnosis, with multiple imputation of missing values. The significant factors associated with this outcome are shown in Appendix 8 for time periods of 0–3 months, 3 months to 1 year and 1 year to study end for each LFT.

Proportionality of hazards within separate time periods of follow-up

As a final check, the log of the negative log of the survival function curves for initial albumin were plotted within the three time periods. Figure 8 displays these for time to liver disease diagnosis. The plots look approximately parallel for the time periods of 0–3 months and 3 months to 1 year. As it probably does not make clinical sense to predict events such as mortality and diagnoses over long time periods, that is, more than 1 year after a single batch of LFTs, we concentrate on models using short time periods after LFTs, and these satisfy the model assumptions. Therefore, for the predictive model building using continuous LFT results described in Chapter 5, it was decided to use these shorter time periods. Models predicting events after 1 year could be constructed, but the assumptions of the models are not met and also are clinically less useful.

FIGURE 8.

Plots of the log of the negative log of the survival function against log of time to liver disease diagnosis for albumin-adjusted models at different time periods. (a) 0–3 months; (b) 3 months to 1 year; (c) 1 year and over.

Survival analysis methods

Survival analysis using regression methods allows one to measure the effect that covariates have on the hazard of a particular outcome (usually death) over time. As in previous chapters, this chapter concentrates on use of the Weibull model, which easily allows derivation of probabilities over any time period and is a fully parametric model.

Survival analysis using continuous LFT results

The modelling was repeated using the LFTs as continuous variables. This was implemented for a number of reasons:

• Cut-off points are somewhat arbitrary and may vary by location.

• Use of cut-off points reduces power.

• Using categorical factors increases the interaction terms and hence parameters to a large extent, especially with potential two-way, three-way and four-way interactions.

• In a clinical setting, using the whole scale gives more accurate estimates of probability of risk to inform decision making.

The categorical modelling allowed us to investigate graphically survival by degree of abnormality and proportional hazards. Prior to the modelling, transformations were calculated if the test results were not normally distributed. The significant LFTs from the models in Chapter 4 were entered into the Weibull models with all continuous LFT results. Any covariates which were non-significant were removed, and all other covariates which were non-significant in the previous models were entered one by one, in case they were significant when other LFTs were in the model. Looser exclusion criteria were placed on the continuous LFT results, with any LFT having a p-value of less than 0.3 being considered for inclusion in the model at this stage.

Model building with interaction terms

All two-way LFT interactions were entered into the models and the most non-significant terms were excluded. The model was then refitted and the process repeated until all the highest-order interactions were still significant at the 5% level. For each model, the Akaike’s information criterion (AIC) statistic was calculated. 35 This statistic is a measure of the goodness of fit of the model that penalises high parameter models and is calculated as:

where k = the number of parameters in the model.

With a large data set, it is likely that many spurious results could arise and use of AIC is considered equivalent to cross-validation methods. Akaike’s information criterion was also used to inform exclusion of model terms. If the difference in AIC between the model with a non-significant term included and the model without the term is greater than 4, then it was deemed a significant improvement in fit. If a situation arose where the significance of a term was borderline, e.g. p = 0.06, then AIC helped with the decision making process. All three-way interaction terms were also entered into the models and the exclusion process was repeated. The same was done for any four-way interactions between LFTs. The model with the lowest AIC was chosen as the best model thus far.

Following this process, interactions between the covariates and each other, and the covariates and the LFTs were also fitted one by one with any significant interactions kept in the model and any non-significant interactions excluded. Again, AIC was used to decide the optimal model.

Model assessment

Once the final models have been built they must be assessed to test that they are good at discriminating high from low risk and also are accurate in their predicted probabilities. Two types of analysis exist for this procedure – estimating discriminative ability (c-statistic) and testing calibration (Hosmer–Lemeshow test).

Calculating probabilities of risk

Once the models are derived, it is possible to calculate the probabilities of outcomes for hypothetical cases of patients. This is achieved by entering the various characteristics for each patient into the model. The values of each of these predictors for each patient (the Xs) are multiplied by their respective parameter estimates (βs) as in formula (1) below and added together to form the linear predictor. The result is subtracted from the log (time) and divided by the scale parameter (σ) to obtain U (2). The predicted probability is then calculated as in formula (3).

where k is the number of predictors.

95% CIs can be calculated for each probability of risk using the Delta method by multiplying the covariance matrix by a vector of first-order differentials of the parameter estimates. 22 The vector of first-order differentials is found to be:

Multiplication of (D′) × COV(X) × D results in the variance of U and so must be square rooted to give the standard deviation. The 95% CIs are then calculated as:

and therefore,

This process involves matrix multiplication and was implemented in PROC IML in SAS (version 9).

Final models

The final models arising are displayed in Tables 10–12 for liver disease diagnosis. The final models for liver mortality and all cause mortality are displayed in Appendix 9. These tables contain the model terms, the parameter estimates (or coefficients) with 95% CIs and the p-value.

Calibration

Liver disease diagnosis

Using the Grønnesby–Borgan method to calculate the goodness of fit of the model, the data was first of all split into percentiles of predicted probability according to the number of total events. These were calculated from baseline up to 3 months, 1 year and 4 years for comparison. The number of groups of risk was obtained using the suggestion of May and Hosmer39 as follows: as 172 patients were diagnosed with liver disease during the first 3 months of the study, when this figure was divided by 40 (and then rounded down to the nearest whole number), this implies that the data should be divided into quartiles of predicted probability. 39 The numbers of expected and observed events were then displayed in a bar chart for each quartile (Figure 10). The results of the goodness of fit test are shown in Table 13 as well as the comparison between each quartile and the 4th quartile. Using the –2 × log(likelihood ratio) goodness of fit test, the model shows significance (p = 0.01). From Figure 10 and the heterogeneity results (of each quartile versus the 4th quartile) in Table 13, it is clear that this lack of fit is due to the first quartile.

FIGURE 10.

Number of expected and observed liver disease events in the 3 months following LFTs.

TABLE 13 - Calibration statistics using the Grønnesby–Borgan method for various time points of the final liver disease diagnosis models

df, degrees of freedom.

χ² goodness of fit was calculated using –2 × log(likelihood ratio).

Time point	Group	χ2	df	p-value
3 months	All	10.82	3	0.01
	1	8.40	1	0.004
	2	0.50	1	0.48
	3	0.62	1	0.43
	4	–	–	–
1 year	All	6.67	3	0.08
	1	1.28	1	0.26
	2	0.05	1	0.82
	3	2.73	1	0.10
	4	–	–	–
4 years	All	15.31	9	0.08
	1	8.53	1	0.004
	2	9.00	1	0.003
	3	6.04	1	0.01
	4	7.47	1	0.006
	5	9.75	1	0.002
	6	9.51	1	0.002
	7	6.49	1	0.01
	8	8.92	1	0.003
	9	6.76	1	0.009
	10	–	–	–

For the final model predicting liver disease between 3 months and 1 year after initial LFTs, the data were again categorised into quartiles of predicted probability (167 events/40 = 4). Figure 11 shows the bar chart of expected and observed events for each quartile. The goodness of fit test for this model, however, was not significant (p = 0.08).

FIGURE 11.

Number of expected and observed liver disease events in the first year following LFTs.

The model predicting liver disease from 1 year after testing fitted the data reasonably well (p = 0.08). Predicted probabilities were calculated for the time point of 4 years, as the median follow-up time was 3.7 years. There were 752 events during this period and so the predicted probabilities were split into deciles of risk. The observed and expected events for each decile were plotted on a bar chart (Figure 12). Tests of heterogeneity were all significant for each decile versus the tenth decile of risk. This is perhaps more to do with the fit of the tenth decile than the others, as it is clear from the figure that this decile does not lie on the trend line of the previous nine deciles.

FIGURE 12.

Number of expected and observed liver disease events at year 4 following LFTs.

Liver disease mortality

The numbers of expected and observed deaths from liver disease within the first 3 months were displayed in a bar chart for each half of risk (Figure 13). Only two groups of risk were used, as only 20 events occurred in this time period, meaning that the minimum number of risk groups were to be used. The results of the goodness of fit test are shown in Table 14 and show good fit.

FIGURE 13.

Number of expected and observed liver mortality events in the 3 months following LFTs.

TABLE 14 - Calibration statistics using the Grønnesby–Borgan method for various time points of the final liver mortality models

df, degrees of freedom.

Test result differs from trend result because this used the Wald test.

χ² goodness of fit was calculated using –2 × log(likelihood ratio).

Time point from baseline	Group	χ2	df	p-value
3 months	Overall	1.19	1	0.28
	1st bitile	0.00	1	1.00a
	2nd bitile	–	–	–
4 years	Overall	11.82	4	0.02
	1st quintile	1.42	1	0.23
	2nd quintile	5.05	1	0.02
	3rd quintile	8.19	1	0.004
	4th quintile	6.24	1	0.01
	5th quintile	–	–	–

For the final model predicting liver mortality from 1 year after initial LFTs (at the time point of 4 years), the data were categorised into quintiles of predicted probability (as 211 events/40 = 5). Figure 14 shows the bar chart of expected and observed events for each quintile. The goodness of fit test for this model was significant (p = 0.02). From Figure 14 and the heterogeneity results in Table 14 it can be seen that there is overprediction at all quintiles.

FIGURE 14.

Number of expected and observed liver mortality events at year 4 following LFTs.

All cause mortality

There were 979 deaths during the first 3 months of the study, meaning that the predicted probabilities were categorised into deciles of risk. The numbers of expected and observed deaths within the first 3 months were displayed in a bar chart by decile of risk (Figure 15). The results of the goodness of fit test are shown in Table 15. From the figure, it looks as though the model fits the data well; however, the goodness of fit test is highly significant (p < 0.001) suggesting poor fit. Deciles 4–9 show significant differences from decile 10; this is due to overprediction by these deciles, while the others slightly underpredict. However, the visible difference is small.

FIGURE 15.

Number of expected and observed all cause mortality events in the 3 months following LFTs.

TABLE 15 - Calibration statistics using the Grønnesby–Borgan method for various time points of the final all cause mortality models

df, degrees of freedom.

χ² goodness of fit was calculated using –2 × log(likelihood ratio).

Time point from baseline	Group	χ2	df	p-value
3 months	Overall	40.49	9	< 0.001
	1st decile	0.23	1	0.63
	2nd decile	0.71	1	0.40
	3rd decile	1.71	1	0.19
	4th decile	5.65	1	0.02
	5th decile	11.86	1	< 0.001
	6th decile	16.36	1	< 0.001
	7th decile	11.82	1	< 0.001
	8th decile	8.06	1	0.005
	9th decile	8.64	1	0.003
	10th decile	–	–	–
1 year	Overall	24.03	9	0.004
	1st decile	2.94	1	0.09
	2nd decile	5.41	1	0.02
	3rd decile	4.46	1	0.03
	4th decile	3.83	1	0.05
	5th decile	8.67	1	0.003
	6th decile	15.64	1	< 0.001
	7th decile	2.07	1	0.15
	8th decile	8.18	1	0.004
	9th decile	3.88	1	0.05
	10th decile	–	–	–
4 years	Overall	33.06	9	< 0.001
	1st decile	0.17	1	0.68
	2nd decile	0.23	1	0.63
	3rd decile	1.20	1	0.27
	4th decile	3.97	1	0.05
	5th decile	6.34	1	0.01
	6th decile	2.20	1	0.14
	7th decile	0.82	1	0.37
	8th decile	0.00	1	0.99
	9th decile	1.01	1	0.32
	10th decile	–	–	–

The expected and observed deciles of risk of death during the period 3 months to 1 year following initial LFTs are displayed in Figure 16. A total of 1639 patients died during this period. As for the previous model, goodness of fit was poor (p = 0.004); however, this is not obvious from the graph. Heterogeneity was evident for the second, third, fifth, sixth and eighth deciles versus the tenth decile of risk.

FIGURE 16.

Number of expected and observed all cause mortality events in the first year following LFTs.

Similarly, a lack of fit is evident (p < 0.001) for the long-term model predicting death from 1 year onwards following the LFTs, with the fifth decile showing significant heterogeneity. Figure 17 illustrated clearly the overprediction of the model from the fifth decile onwards.

FIGURE 17.

Number of expected and observed all cause mortality events at year 4 following LFTs.

Discrimination

The discrimination statistics of each of the eight models are presented in Table 16. A model with an overall c-statistic greater than 0.7 is generally deemed good at assigning a greater predicted probability to someone who actually has the event and a smaller predicted probability to someone who does not have the event. With that in mind, the models predicting liver disease and all cause mortality during the first 3 months after LFTs have very good discriminatory power (c = 0.85 and 0.88 respectively). For the time period of 3 months to 1 year after LFTs the c-statistic is still acceptable for both outcomes, particularly all cause mortality. However, for the longer time period of 1 year to 15 years after initial LFTs the discrimination is poor.

Predicting probabilities for specific cases

Predictions based on the patients’ characteristics were derived from the liver disease diagnosis prediction models over a specified time period. From the factors listed in Table 10 the only characteristics required to enter the model predicting an event within 3 months are gender, age at baseline, Carstairs deprivation score, methadone dependency (yes/no) and the five LFT results.

Liver disease diagnosis within 3 months

Figure 18 is a plot of predicted probabilities of liver disease within 3 months for 16 different cases. The probabilities are for contrasting characteristics, i.e. the ages of 25 and 50 for males and females living in areas with Carstairs scores of –2 (reasonably affluent) and 4 (very deprived) and with methadone and non-methadone dependency. The example LFT results for these patients were 70 U/l for ALT, 230 U/l for AP, 95 U/l for GGT, 25 µmol/l for bilirubin and 40 g/l for albumin. It can be seen from Figure 16 that living in a deprived area increases the probability of liver disease, especially if the patient is a methadone user. Females have a greater probability of liver disease diagnosis within 3 months than males; e.g. a 25-year-old female methadone user living in a deprived area has a probability of 0.052, whereas a male with the same characteristics has a probability of 0.039. Fifty-year-olds have a lower probability of liver disease than 25-year-olds across all equivalent factors – even non-methadone users living in affluent areas; i.e. for males with these characteristics these probabilities are 0.012 and 0.014 respectively. However, the 95% CIs overlap, so these differences are not statistically significant.

FIGURE 18.

Probability (95% CI) of liver disease diagnosis within 3 months after initial LFTs for hypothetical patients. LFT results for these patients were 70 U/l for alanine transaminase, 230 U/l for alkaline phosphatase, 95 U/l for gamma-glutamyltransferase, 25 µmol/l for bilirubin and 40 g/l for albumin.

Liver disease within 1 year

The probability of liver disease diagnosis at 1 year can also be calculated using the model presented in Table 11. This model has some extra covariates to the one predicting for the first 3 months. These comprise history of gallbladder disorder (yes/no) and alcohol dependency (yes/no). Of the LFTs, bilirubin and AP were not included. A case example is a patient living in an area with a population mean Carstairs deprivation score (0.05) who is not a methadone user and does not have a history of gallbladder disorders. The LFT results of this patient were an ALT of 70 U/l (mildly elevated), a GGT of 200 µmol/l (mild, bordering on severely elevated) and a mildly lowered albumin of 30 g/l. Figure 19 shows the predicted probabilities of liver disease diagnosed at 1 year, broken down by gender, age (25/50) and alcohol dependency (yes/no). The probability for an alcohol-dependent patient can clearly be seen to be much higher than for a non-alcohol-dependent patient. For example, the probability of liver disease for a female aged 50 is doubled with alcohol dependency from 0.038 (95% CI 0.023–0.063) to 0.074 (95% CI 0.038–0.141). Also, females have higher risk than males over all combinations.

FIGURE 19.

Probability (95% CI) of liver disease diagnosis within 1 year after initial LFTs for hypothetical patients. The fixed characteristics of these patients are: Carstairs score (0.05), not a methadone user, no history of gallbladder disorders, an alanine transaminase of 70 U/l (mildly elevated), a gamma-glutamyltransferase of 200 µmol/l (mild, bordering on severely elevated) and a mildly lowered albumin of 30 g/l.

Systematic review of health-state utilities

Health-state utilities represent an individual’s preferred value for specific health states relative to full health, whether they are patients suffering from the condition in question, physicians or the general public. Estimates of utilities for various health states in liver disease are essential to assess cost-effectiveness/cost–utility of the management of liver disease. The health-related quality of life of chronic liver disease patients has been shown by various studies to be worse than that of healthy individuals. 42–45

Health-state utilities can be measured directly using methods such as the time-trade off (TTO) and the standard gamble (SG), and indirectly using health-state classification systems such as EQ-5D, SF-6D and health utility index (HUI); they can also be estimated by health-care experts. 46–50 Owing to the variation in utility assessment methods and states of disease, it is problematic to pool utility estimates from different studies. Methods of pooling include calculating the mean utility, stratifying by method and study population, and metaregression analysis. The last of these methods involves fitting a model with utility estimate as the outcome, adjusting for the various factors that influence the variation. This is superior to other methods as it allows us to assess the importance of these differences in study design. There is very little literature on meta-analysis of utilities and, as far as we know, none on liver disease utilities. 51–54

To derive estimates of health-state utilities for a decision analysis of the primary care management of patients with ALFTs without clinically apparent liver disease, we conducted a systematic review and metaregression of studies of health-state utilities in chronic liver disease. We also looked at the variation between the study designs used to measure utilities, including the methods used and the various states of disease.

Study searching

We conducted a search of the MEDLINE database from 1966 to September 2006, including key words and subject heading related to liver disease(s) and utility measuring tools. EMBASE and CINAHL were also searched, as was as the Cochrane Library. A manual search was also performed by examining the reference sections from papers we found which were relevant. We asked three international liver experts with experience in quality of life studies if they knew of any unpublished studies which measured utility in liver disease patients. Two replied.

The key words and subject headings used to find studies in MEDLINE, EMBASE and CINAHL, which measured health-state utilities using Ovid (September 2006) were:

1. Quality of life/

2. Liver Diseases/

3. Liver/

4. hepatitis.mp

5. cirrhosis.mp

6. utility$.mp

7. cost effective$.mp

8. Euroqol.mp

9. EQ-5D.mp

10. EQ5D.mp

11. SF-6D.mp

12. SF6D.mp

13. QWB.mp

14. Health Utilit$Index.mp

15. liver.mp

16. 2 or 3 or 4 or 5

17. 6 or 7

18. 1 and 16 and 17

19. 8 or 9 or 10 or 11 or 12 or 13 or 14

20. 15 and 19

21. 18 or 20

Study selection

All abstracts from the search were reviewed and the full text of any title or abstract which appeared to meet the inclusion criteria was retrieved. Any abstract that did not contain enough information to judge whether utilities were calculated were judged by a liver expert (JD) for exclusion or further investigation, i.e. retrieval of the full paper. The inclusion criteria were studies in English language journals of any design (i.e. case-control, randomised controlled trial, cohort, etc.) that have:

1. measured utility using health-state utility tools from liver disease patients, physicians or adults with no liver disease, or

2. estimated health-state utilities for various liver diseases by means of expert opinion.

Letters, comments, news articles and non-liver-related studies were excluded. In addition, studies were excluded if they obtained utility estimates from the literature, if there was not enough information on the derivation of the utility, if utility values were not reported or if the same population’s utilities were published twice.

Validity assessment

Another reviewer assessed the full papers independently and any disagreements about study inclusion were resolved by discussion if consensus could not be achieved. A reference management system (Reference Manager) was used to identify and extract duplicate studies.

Study characteristics

Each article that met the inclusion criteria was reviewed by an investigator who abstracted the following information: year of study, study population from whom utility was estimated (and its size), country of study, liver disease or disease state, utility estimation method, estimated utilities and variability of utility measurements. Outcomes were mean utilities (with SE or SD and/or 95% CIs) or median utilities (with IQR) for each liver disease or disease state.

Quantitative data synthesis

If at least three studies presented utilities for similar disease states within a specific liver disease then they were included in the metaregression model. 55,56 We fitted dummy variables in our model for utility tool used and disease state. The importance of each study was accounted for by weighting the model using the square of the SE. Where the SE was not published, we estimated it using other measures from the study, e.g. SD, sample size, CIs, etc., if possible. However, if any studies did not present data from which the SE could be calculated, or at least estimated, then they were excluded. Disease state names varied by study, so we grouped those that were close enough to be classified as the same, e.g. we grouped Child’s A from Younossi et al. 57 together with compensated cirrhosis. Approval was given to these groups of disease states by a liver expert (JD). A hierarchical model also allowed us to adjust our estimates for the random effects of utility within study. Akaike’s information criterion was used to judge the best model. Statistical analysis was conducted using Microsoft Excel and the SAS (version 8) software package.

Search results

From the Ovid MEDLINE search, 79 studies satisfied the above search criteria. EMBASE identified 169 studies, and CINAHL found only three studies. Five further studies were obtained by manual searching, and after duplicates were removed this left 217 articles. Figure 20 contains a flow diagram of exclusions. After the exclusion/inclusion criteria were applied, 30 studies were found to have measured utilities of liver diseases or disease states. The full list 50,57–85 is available as an appendix from the publication in Medical Decision Making (available at http://mdm.sagepub.com/supplemental/). 86 Table 17 lists all of the liver diseases and disease states for which utilities were found, and shows the number of studies by perspective and respondent type, and references the studies in which they appear. However, some of the studies had disease states which were unique to them, meaning that their utilities could not be grouped with utilities from other studies for the meta-analysis.

FIGURE 20.

Flow chart showing the exclusion path from the full search to the studies used in the meta-analysis.

Qualitative summary

The details of the 30 studies included in the systematic review can be found at www.sagepub.com/mdm. Of these studies, only one contained a TTO-estimated utility for hepatitis A virus (HAV) and this was estimated using a postal survey in non-HAV adults. 58 Four studies estimated utilities for hepatitis B virus (HBV) (all by an expert panel). These four studies measured utility by the following groups – treatment,59 severity of symptoms60 and stage of disease. 61,62 All four studies also used different tools, and only one had a large sample size (n = 128);60 the others had a sample size of between 4 and 7. Ten studies estimated utilities for hepatitis C virus (HCV) (six using patient respondents and four using expert panels). 50,57,61,63–69 Eight of these studies grouped utilities into stages of disease such as compensated cirrhosis and decompensated cirrhosis. However, there were still some differences, e.g. one study broke compensated cirrhosis down into compensated with normal or near-normal ALT, compensated with elevated ALT, compensated under treatment and compensated previously treated. 66

Two studies used up to four tools to estimate utilities for the same groups. 63,66 The degree of variation between the utility values of the different methods varied within stages of disease. For example, for mild/moderate chronic HCV the utilities ranged from 0.70 to 0.79,63 while for liver biopsy in cirrhotic patients they ranged from 0.51 to 0.83. 66 These large ranges in utilities were due mainly to the use of different methods, SG, TTO and visual analogue scale (VAS), with utilities derived from the VAS method generally being the smallest and those from the TTO and SG methods being the largest. In the one HCV study which used SG and TTO, the estimates were very close for most of the disease states in comparison with the VAS estimates, which were much lower. 66 Similar disease states between studies had similar utilities for the same method used. For example, two studies reported compensated cirrhosis in HCV patients using the VAS as having utilities of 0.65 and 0.66. Using the SG, the same two studies found utilities of 0.80 and 0.76. 63,66 Five studies used an expert panel or physicians to estimate the utilities, and only one of these had a large sample size (n = 113); the others had an average sample size of 6).

Five studies measured utilities for cirrhotic patients or chronic liver disease patients. 57,64,70–72 Of these, two also reported utilities for a subset of HCV patients (these were included in the above figures). Three studies used chronic liver disease patients to estimate utilities,57,64,71 one used an expert panel70 and one used both physicians and cirrhotic patients. 72 Again, patients were grouped into various stages of disease between studies, and all five studies used different utility measuring tools. Three studies used populations of liver transplant patients to estimate utilities for both pre and post liver transplants73–75 and three estimated utilities for post liver transplant only. 76–78 Three of these six studies found utilities for various time points after transplant73–75 and had the largest sample sizes (n > 180). One study grouped patients by number of transplant, Child–Pugh score and disease duration76 and another counted only transplants on children and categorised utility by age group (< 5 years and ≥ 5 years). 78 Interestingly, with the exception of the last study, all used the EQ-5D method to estimate utilities. It should be noted that six of the studies that had an HCV population also measured utilities for liver transplantation. No studies were found to have estimated utilities for alcohol-related liver diseases, primary biliary cirrhosis, autoimmune hepatitis or fatty liver disease. In addition to the liver disorders for which utilities were published (Table 17), other liver disease groups for which utilities were estimated included patients with colorectal liver metastases,79 candidates for liver transplant80 and patients with cirrhosis in conjunction with other comorbidities. 81 Psoriasis patients estimated utilities of ALFTs and biopsy,82 and patients with severe liver problems treated with a molecular adsorbent recirculating system (MARS) also estimated their utility. 83 Utilities for various complications of liver disease were also estimated including hepatic encephalopathy, ascites and varices. 57,72,84

Twenty-four of the 30 studies (http://mdm.sagepub.com/supplemental/) were not included in the metaregression; 18 were excluded because for each disease state within liver disease groups there were fewer than three studies; four were excluded because they did not have enough data to estimate the SE;50,64,65,85 one study used a child population78 and one study did not calculate an overall EQ-5D value. 71 Table 18 contains six studies, measuring 40 utilities for HCV states, which were included in the metaregression. 57,63,66–69 Two of these studies used the same population for the utility estimates; however, each study published results obtained using different tools. 67,68 Only HCV had enough studies and utilities to be considered for a metaregression analysis. The disease states included were moderate HCV, compensated cirrhosis, decompensated cirrhosis and post liver transplant. Where a study did not use the exact term ‘moderate HCV’, the closest state to it took its place, e.g. ‘mild/moderate HCV’ or ‘HCV with no cirrhosis’. 57,63 Standard errors were estimated for seven utilities as detailed in Table 18. Two of the studies were conducted in the US and two in Germany, while the others were carried out in the UK and Canada. The sample sizes per utility estimated ranged from 7 to 77.

Table 19 shows the number of each type of health-state utility tool (by perspective type, i.e. community or patient) used in all the studies shown in http://mdm.sagepub.com/supplemental/ and in those six used in the metaregression. The numbers are broken down further by the type of respondent. Seven different tools were used in studies included in the metaregression, the most frequently used being the VAS; this was used by nine of the studies identified in http://mdm.sagepub.com/supplemental/ and two in the metaregression. Six studies used the TTO overall, with one included in the metaregression, while four studies used the SG, with two included in the metaregression. The most popular indirect method was the EQ-5D with 10 of the studies identified in http://mdm.sagepub.com/supplemental/ (three used in the metaregression) utilising the tool. Eight of these studies used the UK tariff as the population norm and the other two used German and Canadian population norms. 63,83 The HUI versions 2 and 3 were the other two indirect methods used in the metaregression, and the TTO, SG and transformed VAS were the other direct methods. The transformed VAS is the SG-transformed visual analogue scale, which converts VAS scores to SG utilities [u = 1 – (1–v)2. 29]. 46 All of the direct utilities included in the metaregression were from patient respondents while all of the utilities from the classification systems were estimated from healthy subjects.

Quantitative summary

Twenty-three per cent of the utilities were measured using the EQ-5D method, 20% were estimated using the SG and 20% were estimated using the VAS. The results of the metaregression analysis are presented in Table 20. There was no significant difference between the utility of compensated cirrhosis in HCV compared with moderate HCV. However, decompensated cirrhosis in HCV had an estimated utility of 0.08 lower than that for moderate HCV (p < 0.001). Post liver transplant had an estimated utility of 0.04 lower than moderate HCV (p = 0.03). In comparison with the estimated utility using the EQ-5D assessment method, all except the VAS and the HUI3 had significantly higher utility scores. The highest utility was estimated from the transformed VAS, at 0.15 higher than the EQ-5D (p < 0.001). The TTO was next highest, with a utility of 0.12 higher than the EQ-5D (p < 0.001). The usual VAS method had the lowest utility, at 0.07 less than the EQ-5D (p < 0.001). HUI3 was the only assessment method to differ significantly from the EQ-5D.

The reference group for this model was moderate HCV using the EQ-5D method, which had an estimated utility of 0.75 and is the intercept in Table 20. To calculate the utility for any other disease state and method combination, the intercept is added to the corresponding parameter estimate. For example, the estimated pooled utility for decompensated cirrhosis in HCV using the TTO method is 0.79 (0.747 – 0.075 + 0.116). For compensated cirrhosis in HCV using the TTO, the estimate is 0.86 (0.747 + 0.001 + 0.116).

Another metaregression model was fitted as above but with country added. The only country to have utility estimates different from the reference country (the US) was the UK which lowered utility by 0.1 (p = 0.007). However, as only one utility in the model was estimated in the UK and the AIC was larger than in the previous model, we recommend that only the first model be considered robust.

Direct utility measuring methods

Indirect utility measuring methods

Scores derived from these quality of life measures have to be converted to a measure of utility through linkage with population preferences, and hence are indirect methods.

Clinical judgement

In this method a group of clinical experts are asked to assign utility values to a set of patient health states. These may be hospital specialists or primary care practitioners.

Anxiety measuring

In addition to measuring health-related quality of life, anxiety may be induced in the patient awaiting a definitive diagnosis or when contemplating an invasive procedure such as biopsy. Anxiety in both these scenarios was measured using a validated state–trait questionnaire.

Patient survey

Expert panel survey

A selection of 18 GPs were emailed and invited to join an expert panel to estimate the utilities of various liver diseases and disease states. They were selected from a database of GPs belonging to the Scottish Primary Care Research Network (SPCRN) research group. Twelve UK hepatologists were also invited, so that the differences in opinion between GPs and liver experts could be assessed. The questionnaire was emailed as an attachment and consisted of a table containing 30 liver diseases and disease states with space for the clinician to enter their estimate of the utility score for each, using their own judgement. Experts were also asked to give their confidence rating of their choice of utility on a scale from 1 to 5. A Delphi approach was taken, such that once the first round of questionnaires had been received, some basic descriptive statistics were calculated and the results and a second, similar, questionnaire were sent back to the experts. The results, combined with their own judgement, helped inform their decision for this second round, and allowed them to change it if they so wished. Of the 18 GPs and 12 hepatologists, nine and 10 respectively replied with their estimates for the first round. Of these, eight GPs and nine hepatologists successfully completed the second and final round. It should be noted that GPs were also asked to estimate the utilities of patients with ALFTs awaiting investigation and patients awaiting liver biopsy for comparison with patients’ estimates.

Patient survey

The characteristics and utility scores of the patients awaiting biopsy from Tayside and Nottingham were compared to check that there were no differences in these populations, so that their results could be combined. The only significant difference found was the proportion of males and females (p = 0.04), with 29% males from Tayside and 62% males from Nottingham. Of the utility scores and anxiety measures, only state–trait scores before biopsy were significantly different (higher in Nottingham; p = 0.03 for state and p = 0.01 for trait). As the utility scores were not significantly different between areas, it was decided to combine these for the liver biopsy group.

The characteristics of the two groups of patients are presented in Table 21. Comparison of the characteristics of patients with ALFTs and patients awaiting biopsy demonstrated that only having a degree was statistically significant (p = 0.02) using the Pearson’s chi-squared test. Forty-two per cent of patients with ALFTs had a degree compared with 22% of patients awaiting biopsy. Smoking status was almost significantly different between the two groups (p = 0.06; 15% of patients with ALFTs currently smoking and 27% of patients awaiting biopsy).

The comparisons of the two patient groups in terms of utility and anxiety scores are displayed in Table 22. The VAS score is significantly lower for the liver biopsy patients than for the ALFT patients (Figure 21). The state and trait parts of the state–trait anxiety scores before the consultation with the specialist are both significantly higher for the biopsy patients, indicating more anxiety (Figure 22). Although the utilities are also lower for the biopsy patients and the state–trait scores after consultation are higher, they are not significantly so. Figure 23 displays box plots of the EQ-5D and SF-6D estimated utilities by patient group. The state and trait sections of the anxiety measure before and after consultation were not significantly different for the biopsy patients (p = 0.08 and p = 0.41 for state and trait respectively, using the Wilcoxon signed rank test). However, they were significantly different for the ALFT patients (p = 0.001 and p = 0.04 for state and trait respectively), with lower anxiety after the consultation.

FIGURE 21.

Box plots of the VAS estimates for ALFT patients and liver biopsy patients.

FIGURE 22.

Box plots of the state–trait anxiety scores for ALFT patients and liver biopsy patients before and after consultation.

FIGURE 23.

Box plots of the EQ-5D and SF-6D utility scores for ALFT patients and liver biopsy patients.

The EQ-5D and SF-6D utilities were highly correlated for ALFT patients (ρ = 0.82, p < 0.001) and biopsy patients (ρ = 0.75, p < 0.001). The state part of the anxiety questionnaire before consultation was highly correlated with its score after for both ALFT patients (ρ = 0.62, p = 0.001) and biopsy patients (ρ = 0.61, p < 0.001). The same result was found for the trait part (ρ = 0.96, p < 0.001 for ALFT patients; ρ = 0.88, p < 0.001 and for liver biopsy patients).

Expert panel

The results of the first round of the questionnaire analysis are presented in Table 23 for the hepatologists. This is the table that was sent to the experts for the second round of the Delphi process. The results for the GPs are presented in Table 24. The final utility estimates from the second round are presented in Table 25. There were no significant differences between utilities from each round for both expert groups. There were, however, differences in confidence ratings. For hepatologists, confidence increased significantly for the hepatitis E utility estimate from a median of 2 to 3 out of 5 (p = 0.02). For the utility of non-alcoholic steatohepatitis (NASH), confidence increased from a median of 2.5 to 3 (p = 0.046). There were no significant differences in confidence between rounds for the GPs.

In a comparison of expert panels, there were significantly higher utilities (better quality of life) assigned by hepatologists compared with GPs for compensated cirrhosis, post liver transplant, primary biliary cirrhosis (PBC) and autoimmune hepatitis. On the other hand, GPs rated the following with higher utilities than hepatologists: alcoholic hepatitis, drug reaction causing jaundice and gallstones in common bile duct causing jaundice (see Table 25). There was a difference in confidence ratings between GPs (median = 2) and hepatologists (median = 3) for shock liver (p = 0.02).

Decision tree

A decision tree is a structure that models the pathway of a patient after a decision has been made at the root node (start of the tree) that in turn affects the treatment or investigations that the patient undergoes. From the root node there are two or more decisions which are taken. At the end of each decision there are further branches emanating which end at chance nodes. These branches are the outcomes of any tests or procedures that are followed on the way to the terminal node, which is the event of interest. Each branch (or action) from each chance node must therefore have a probability of occurring from the last chance node. These are called transition probabilities and are generally found from literature searches68,85 or through a combination of expert opinion and the literature. 62,84 In our study, we estimated probabilities directly from the population cohort. The terminal nodes are assigned values related to the outcome measure. For example, the values could be crude life expectancy or quality-adjusted life expectancy. 99 Often however, it is important to evaluate the optimal pathway of different treatments or procedures to minimise the cost while also maximising effectiveness. This is called a cost-effectiveness analysis and is a method commonly used by health economists and policy researchers. Effectiveness is often measured using years of life saved, but often the QALYs are used, these being the health-state utility value associated with the particular health state multiplied by the length of time in that state summed over all of the health states. This analysis is generally called cost–utility analysis.

The decision tree used in this study does not follow a patient having an initial batch of LFTs until death. This would involve a Markov model, which involves yearly (or monthly) cycles where each patient spends his or her time in a particular health state, which can change at each cycle, until death. In this study, we concentrated on the cost–utility of the decisions a GP has to make after a patient has initially ALFTs until a diagnosis is made. Figure 24 displays the decision tree designed for this analysis. The model was built with help from experts in primary care (FS), hepatology (JD, SR), biostatistics (PTD) and public health (PR). The numbers and probabilities displayed in Figure 24 are based on the whole population after multiple imputation had been utilised. Consequently, estimates of probabilities are adjusted to reduce selection bias, which is inevitable in observational data. The root node has patients with abnormal tests and there are three decisions a GP can make at this stage. These are to retest, refer to secondary care or do nothing. From the retest decision chance node, there are two possible pathways if the LFTs are normal or at least one is abnormal. If they are abnormal then they can be referred to secondary care where a diagnosis can be made (terminal nodes t1 and t2), or not referred within the year. For the latter case the terminal node would be undiagnosed liver disease (t3) or no undiagnosed liver disease (t4). If the retest is normal then it is assumed that they are not referred in that year and so their terminal nodes are of undiagnosed liver disease (t5) or no undiagnosed liver disease (t6). If the decision is taken to refer with no retests then the terminal nodes are liver disease (t7) and no liver disease (t8). If the GP decides to do nothing then the terminal nodes are taken as undiagnosed liver disease (t9) and no liver disease (t10).

FIGURE 24.

Decision tree structure with known numbers and probabilities of patients at each node from the Tayside historical cohort. Note: The terminal branches with ‘Liver disease unknown’ and ‘No liver disease unknown’ do not have probabilities assigned to them. These must be estimated and a sensitivity analysis must be performed for each.

The transition probabilities at each branch from the chance nodes are generally presented below each branch and should sum to 1 for each node. The costs and QALY values can be presented at the end of the terminal nodes, although these are not presented in Figure 24.

Transition probabilities

The probabilities at each of the branches emanating from the chance nodes of the tree must be calculated or estimated. Most of these were estimated from the study cohort. The biochemistry database contains all LFTs for the patients in this cohort, so it is possible to look at the retests and see whether these were taken in primary care (in which case the ‘retest’ decision arm would be taken) or secondary care (in which case the ‘refer’ decision arm would be taken). If no LFTs were taken again after 1 year then the patients would be in the ‘do nothing’ decision arm of the tree. The numbers of patients allocated to each arm were found in this way and are presented in Figure 24. For example, 3843 patients out of the 17,236 with ALFTs were retested within 1 year. The numbers of patients with abnormal or normal retests can then be added in the next pair of branches for the ‘retest’ decision arm. From this the probability can be calculated simply by dividing the number of patients with abnormal (or normal) retests by the number retested. It can be seen from Figure 24 that 66% of patients retested in primary care had abnormal results, so the probability is 0.66. By subtraction from 1, the probability of normal retests is 0.34. The next stage is to look at the third LFT batches to determine whether those patients with two ALFT batches were retested in secondary care within the year (i.e. referred). From the decision tree the probability of referral is 0.32. From these branches there is one more chance node leading to the terminal nodes of liver disease or no liver disease. The ELDIT database was used to find which of these patients were diagnosed within the year and which liver diseases were diagnosed. Of those patients retested in primary care and then referred, 9% were diagnosed with a liver disease within the year (this is the t1 branch). This meant that 91% were not diagnosed with liver disease. However, it should be noted that they could have been diagnosed with some other condition or could have died.

Where the GP decided to refer the patient to secondary care with no retest, 0.03 or 3% were diagnosed with liver disease within the year as registered in ELDIT (this is the t7 branch). Those patients who were retested with abnormal results and then not referred, those who were retested with normal results and those for whom the GP did nothing within the year all led to terminal nodes of undiagnosed liver disease and no undiagnosed liver disease. As these patients were not referred or retested again within the year it was not possible to estimate their probability of liver disease because it could be undiagnosed liver disease or no liver disease. Therefore, using the probabilities for the terminal branches that are already known, these undiagnosed probabilities were estimated using clinical judgement. The probabilities for these events will vary for each, as some patients have more severe results than others. For example, those patients with an abnormal retest who were not referred within the year would have a higher probability of liver disease than those who had normal retests. However, it would be assumed that they would still have a lower probability than those with abnormal retests who were referred (probability of liver disease = 0.09). Therefore for this group it was decided to allocate a probability of liver disease of 0.06. For the group of patients with normal retests it was decided to allocate a base probability of 0.02. This was the overall probability of liver disease diagnosis in the whole population. The patients who had no further investigations within the year were assigned a probability of 0.05. A sensitivity analysis was performed on these probabilities to examine the change if any in cost–utility.

Costs of tests and procedures

The various tests and procedures involved in the investigation of a patient to test for liver problems in general practice and secondary care were listed and validated by an expert hepatologist (JD). The costs of each of these were obtained from different sources and these are listed in Table 26. The cost of a GP consultation was obtained from the Unit Costs of Health and Social Care 2006 report of the Personal Social Services Research Unit (PSSRU). 100 This cost was £25 per surgery consultation lasting 10 minutes and included direct care staff costs and qualification costs. The same cost was obtained via email communication with the Healthcare Information Group, Information Services Division (ISD), who have access to the Scottish NHS costs book. The cost of taking the blood sample in primary care was also accounted for. It was assumed that a general practice nurse (including qualifications) took the sample, and this cost was found to be £9 per procedure from the PSSRU Unit Costs of Health and Social Care report. Costs of analysing the blood for LFT results were taken from Appendix 14 of an HTA report investigating the economics of hepatitis B treatment (the source was collaboration with hepatologists and specialist nurses at Southampton General Hospital Trust),101 and from the Department of Biochemical Medicine at Ninewells Hospital, Dundee. The difference in cost between the two sources was only 47p, with Ninewells being the cheapest. From the biochemistry data set it was possible to find the average number of LFT retests per patient in primary care to reflect the reality that it is unlikely that every patient will have only the one retest in primary care before being referred to secondary care. The costs of the remaining investigations were obtained from the Shepherd et al. HTA report. 101 These procedures were hepatitis B surface antigen tests, hepatitis C tests, antibody tests including antismooth muscle, antinuclear and antimitochondrial, an ultrasound scan of the liver and liver biopsy. The numbers of HBV, HCV and antibody tests were available for every patient in the population cohort from the ELDIT databases of virology and immunology laboratory results. The average number of these tests taken per patient during the year were used in the costs analysis (i.e. it was not simply assumed that each patient had one test each). Liver biopsies were also available from the ELDIT pathology data set and the average number per patient were also taken for the costs analysis. Ultrasound was the only test for which actual data were not available for the patients. However, a hepatologist (JD) assumed that every referral would automatically have an ultrasound and therefore this assumption was taken.

Health-state utilities

Health-state utilities have been discussed and estimated in detail in Chapter 7. The life-years spent in each health state of a decision model needs to be weighted by the quality of life of patients in that state. As the decision analysis model in this study occurs over only 1 year, the actual utility value itself can be used rather than multiplying it by the years spent in each health state to calculate QALYs, as in most studies. However, in this model, the patient moves through various health states over the year. For example, consider the pathway in Figure 26 leading to terminal node t1. The average time in days per patient spent in each health state from initial LFTs to retests to referral to liver disease diagnosis (via biopsy if taken) is shown in Figure 25 (also shown is time to a non-disease diagnosis t2). The health-state utilities differ for each of these health states and they are represented in the diagram as U₁ (for patients with ALFTs), U₂ (for patients waiting for biopsy) and U₃ (for patients with a diagnosis of liver disease till the end of the year). The overall utility for a patient in this cohort would be calculated by multiplying the days spent in each state by its respective utility. An adjustment has to be made to take account of those biopsied and those not biopsied. For example, the overall utility for a patient in this group was calculated as:

where B_t1 is the number of patients having a biopsy arm, and N_t1 is the number of patients in this arm of the tree.

FIGURE 25.

Diagram displaying average time in days between events to assist in utility calculation for the year. (a) Retested in primary care then referred; (b) referred from initial LFTs in primary care.

In this study B_t1 is 34 patients and N_t1 is 74. The utility values used for each of the three utilities mentioned above were taken from the systematic review in Chapter 6 and the patient survey of utility in Chapter 7. The values taken were 0.79 for ALFT patients, 0.73 for patients waiting liver biopsy and 0.67 for patients with diagnosed liver disease. This third utility was the value for Child’s B chronic liver disease from the study by Younossi et al. 57 The utility value for the event of no liver disease was estimated as a weighted average of well patients and patients with other disease. Therefore, an overall value of 0.8 was estimated for this outcome. The other utility values for the days with the terminal node events of undiagnosed liver disease and no undiagnosed liver disease were estimated by clinical experts. Some of these undiagnosed events were assumed to have varying utility values by decision arm since patients had normal LFT retests in one pathway while others had ALFT retests resulting in varying severity and thus utility of disease. For example, the utility value for the event of undiagnosed liver disease after an abnormal retest in primary care with no referral was estimated as 0.79, the same as that for patients with ALFTs awaiting further investigation. The same value was assigned to the alternative event of no undiagnosed liver disease. For patients with a normal retest in primary care the utility of undiagnosed liver disease was estimated as 0.85, better than those with abnormal retests. The utility for no undiagnosed liver disease in this arm was estimated as 0.95 as most would be assumed to be well. The overall utilities at each terminal node for each pathway are presented in Table 27. The utilities of patients who do not have further investigations were allocated a utility for undiagnosed liver disease of 0.67 and 0.90 for the alternative. Sensitivity analyses will be performed on these estimated utilities.

Cost–utility analysis

The decision tree model was used to estimate the patients’ QALY and health-care costs for each of the three decisions that a GP can make which may or may not lead to a diagnosis of liver disease. These decisions were compared using cost–utility analysis. The incremental cost–utility ratio (ICUR) was calculated, which compared the difference in each pair of decision costs divided by the difference in QALY. This is the same as measuring the extra costs needed for each additional unit of health gained for a more expensive but possibly more effective decision strategy. The cost–utility ratio is presented as cost in pounds per QALY saved.

Sensitivity analyses

Uncertainty in the parameters of a decision analysis model and how this uncertainty influences the results needs to be estimated. A one-way sensitivity analysis was performed on several variables, including the probabilities of undiagnosed disease and estimated utilities. This involves reanalysing the cost–utility using a range of values for these parameters. Two-way sensitivity analysis was also performed on those parameters which influenced the results of the one-way analysis. This examined the change in cost–utility by varying the values of two parameters at once.

Sensitivity analyses

The one-way sensitivity analysis of the probabilities (see Table 27) was performed for the values in the specified ranges. All values within the ranges of all the probabilities did not affect the cost–utility ratio, i.e. retesting still dominated referral. The results of some of the one-way sensitivity analyses are reported in Table 33. All parameters not shown in Table 33 are absent because the cost–utility ratio for referral was dominated by retesting for all sensitivity values. All of utility values entered into the one-way sensitivity analysis that were anywhere close to the baseline value retained the ICUR of referral dominated by retesting. One slight exception was the utility value for the referral with no liver disease pathway which caused the ICUR for referral to be dominated by retesting only until the value of 0.82. At a utility of 0.84, the ICUR was £5757 per QALY; however, this decreased to a value of £648 per QALY at a utility of 0.90. The only costing that had an effect on the ICUR was that for the same pathway – referral with no liver disease. At a costing of £100 the ICUR was still dominated by retesting, but at £75 referral overtook retesting as the best option, with an ICUR of £312 per QALY. However, the cost of a referral with its investigations is likely to be higher.

A two-way sensitivity analysis was performed on these two parameters of cost and utility for the pathway of referral with no resulting liver disease diagnosis, to look at where retesting has the best ICUR and where referral has the best ICUR. Figure 29 contains four plots of the net benefit adjusted for various amounts of willingness to pay (WTP). Net benefit measures the increase in utility of one decision over another. Willingness to pay is, of course, demonstrated from an NHS perspective. At smaller WTP amounts, referral is the most cost-effective choice for the lowest costs in the range and for any utility value of referral with resulting liver disease diagnosis. As the WTP increases, i.e. £5000/QALY, the referral option is more cost-effective for any cost with utilities in the range 0.85–0.9 for the referral with resulting liver disease diagnosis pathway. However, retesting is more cost-effective for all other combinations of cost and utility of referral with resulting liver disease diagnosis.

FIGURE 29.

Two-way sensitivity of cost and utility of referral with resulting liver disease diagnosis. (a) Willingness to pay (WTP) = £100/QALY; (b) WTP = £500/QALY; (c) WTP = £5000/QALY; (d) WTP = £25,000/QALY.

Results

The calculations of costs for each pathway of the decision tree and the mean cost per patient are presented in Tables 35–37. Table 38 shows the results of the baseline cost–utility analysis of the decision strategies available to a GP for patients in the top percentile of liver disease risk. As before, only the GP decisions of retest or refer are included in this analysis. Whereas before, retesting dominated the alternative strategy of referring, for these high-risk patients, neither dominated the other. Referral was less costly than retesting (by £11.20); retesting had a higher average utility, but by a small margin (0.001). As a result, the ICUR was £7588/QALY, meaning that to increase one QALY would cost £7588, by retesting. The cost and effectiveness relationship is plotted in Figure 31. The line connecting the two strategies means that neither is dominant over the other. Figure 32 shows the final decision tree model for this cohort.

FIGURE 31.

Cost (£) vs utility (quality-adjusted life-year) of the two decision choices for a GP.

FIGURE 32.

Decision tree model for patients in the top percentile of liver disease risk.

Sensitivity analyses

The results of the one-way sensitivity analysis of the probabilities listed in Table 34 are presented in Table 39. For the sensitivity of probabilities, referral was less costly than retesting for most of the ranges, although retesting had a higher average. The probability of liver disease following an abnormal retest and referral was 0.24 at baseline. At a value of 0.15, retesting actually dominated referral; however, for probability values of 0.17–0.27, neither dominated (although referral was less costly, meaning that ICURs existed for retesting and ranged from £102 per QALY to £56,383 per QALY) and from 0.29, referral dominated retesting. For probabilities of liver diseases following abnormal retests and no referral, the ICUR did not change from baseline value. For probabilities of liver disease following normal retests, referral was cheaper than retesting (and dominated from a value of 0.18 onwards). However, for probabilities near the baseline, the ICUR for retesting was reasonably cost-effective. Referral dominated retesting for the range 0.05–0.11 for the probability of liver disease following referral; however, at a value of 0.20, retesting dominated. For all the utility ranges, referral was the cheaper option and dominated retesting for most values less than the baseline. The costing for the pathway of abnormal retests, referral and liver disease diagnosis had a baseline value of £512. At a costing of £350–£400, referral was dominated by retesting; however, from £425–£700, referral was less costly, and the ICUR for retesting ranged from £478 to £20,728 per QALY. The baseline cost for the pathway of abnormal retests, referral and no liver disease diagnosed was estimated at £204 per patient. At a cost of £150, retesting dominated referral; however, for all other costings in the range of £175–£400, referral was less costly, and the ICUR for retesting ranged from £137 to £57,848 per QALY. Referral was cheaper for all the other ranges of the costs of the other pathways, apart from the upper end of the ranges for the costs of referral with liver disease (£430–£500) and referral with no liver disease (£175–£350) when retesting was dominant over referral.

TABLE 39 - One-way sensitivity analysis results of retest vs referral

This column is the ICUR of referral.

This column is the ICUR of retest.

Variable	Baseline value	Value	ICUR (£/QALY) for referrala	ICUR (£/QALY) for retestb
Probability
Abnormal retest, referral, liver disease	0.24	0.15	Dominated
		0.17		102
		0.21		2465
		0.27		56,383
		0.29–0.35		Dominated
Abnormal retest, no referral, liver disease	0.16	0.05–0.25		7588
Normal retest, liver disease	0.05	0.00		5285
		0.08		10,275
		0.16		184,244
		0.18–0.20		Dominated
Referral, liver disease	0.13	0.05–0.11		Dominated
		0.12		27,584
		0.19		62
		0.20	Dominated
Utility
Abnormal retest, referral, liver disease	0.65	0.5–0.62		Dominated
		0.64		39,934
		0.76		766
		0.90		357
Abnormal retest, referral, no liver disease	0.73	0.5–0.72		Dominated
		0.74		2129
		0.82		315
		0.90		170
Abnormal retest, no referral, liver disease	0.69	0.50–0.66		Dominated
		0.68		12,146
		0.80		1480
		0.90		855
Abnormal retest, no referral, no liver disease	0.69	0.50–0.68		Dominated
		0.70		2555
		0.80		335
		0.90		179
Normal retest, liver disease	0.79	0.5–0.6		Dominated
		0.62		102,720
		0.80		7196
		0.90		4745
Normal retest, no liver disease	0.87	0.70–0.86		Dominated
		0.88		3729
		0.95		818
Referral, liver disease	0.64	0.50		567
		0.56		939
		0.62		2739
		0.66–0.90		Dominated
Referral, no liver disease	0.74	0.50		53
		0.72		591
		0.76–0.90		Dominated
Cost (£)
Abnormal retest, referral, liver disease	512	350–400	Dominated
		425		478
		550		8578
		700		20,728
Abnormal retest, referral, no liver disease	204	150	Dominated
		175		137
		250		19,374
		400		57,848
Abnormal retest, no referral, liver disease	80	55		6634
		105		8510
Abnormal retest, no referral, no liver disease	80	55		2578
		105		12,429
Normal retest, liver disease	49	30		7486
		80		7758
Normal retest, no liver disease	49	30		5643
		80		10,819
Referral, liver disease	317	150		22,374
		290		9980
		395		685
		430–500	Dominated
Referral, no liver disease	139	50		60,364
		150		1119
		175–350	Dominated

A two-way sensitivity analysis was performed on the two parameters of cost for the pathway of referral with no resulting liver disease diagnosis and the probability of liver disease following referral. This was because the cost for this particular pathway changed to retesting being dominant over referral very close to the baseline cost at which referral was less costly. The probability of liver disease following referral should be accurate as it is based on actual observed data; however, at a probability of 0.20, retesting dominates referral and so is also close to the baseline probability of 0.13. Figure 33 contains three plots of the net monetary benefit adjusted for various amounts of WTP. At smaller WTP amounts, the referral option has the acceptable ICUR for the lowest costs in the range and for any probability of referral with liver disease diagnosis between 0.05 and 0.20 (Figure 33a). The baseline cost and probability are marked in the chart, and for this particular WTP they are within the referral strategy. As the WTP increases, i.e. £5000/QALY, the referral option is most cost-effective for low to mid costs and lower probabilities, and low costs and high probabilities (Figure 33b). At a high WTP of £25000/QALY, the referral option is cost-effective for low to high costs with low probabilities; however, retesting is better for mid to high probabilities at any cost and for low probabilities and high costs (Figure 33c). The baseline values for this WTP chart are clearly in the retesting strategy this time.

FIGURE 33.

Two-way sensitivity of cost of referral with no resulting liver disease and probability of referral with liver disease diagnosis. (a) Willingness to pay (WTP) = £500/QALY; (b) WTP = £5000/QALY; (c) WTP = £25,000/QALY. Note: The lines crossing on each chart are the baseline cost (£139.08) and probability used (0.13).