Assessing uncertainty in the burden of hepatitis C virus: Comparison of estimated disease burden and treatment costs in the UK

Summary Hepatitis C virus (HCV) is a major and growing public health concern. We need to know the expected health burden and treatment cost, and understand uncertainty in those estimates, to inform policymaking and future research. Two models that have been important in informing treatment guidelines and assessments of HCV burden were compared by simulating cohorts of individuals with chronic HCV infection initially aged 20, 35 and 50 years. One model predicts that health losses (measured in quality‐adjusted life‐years [QALYs]) and treatment costs decrease with increasing initial age of the patients, whilst the other model predicts that below 40 years, costs increase and QALY losses change little with age, and above 40 years, they decline with increasing age. Average per‐patient costs differ between the models by up to 38%, depending on the patients' initial age. One model predicts double the total number, and triple the peak annual incidence, of liver transplants compared to the other model. One model predicts 55%‐314% more deaths than the other, depending on the patients' initial age. The main sources of difference between the models are estimated progression rates between disease states and rates of health service utilization associated with different disease states and, in particular, the age dependency of these parameters. We conclude that decision‐makers need to be aware that uncertainties in the health burden and economic cost of HCV disease have important consequences for predictions of future need for care and cost‐effectiveness of interventions to avert HCV transmission, and further quantification is required to inform decisions.

informed UK guidance, 3 European recommendations 4 and an estimate of UK HCV burden, 5 and Harris et al.'s model 6 has informed an important review 7 and an analysis of treatment prioritization. 8 Here, we compare the two models in terms of estimated health detriment (quality-adjusted life-year [QALY] loss) and costs to the health service, using a model structure that can represent both models ( Figure 1).

| MATERIALS AND METHODS
We implemented Markov models of HCV progression in a cohort of chronically infected individuals, as described by Martin  Information. Individuals with mild chronic HCV may progress to moderate disease, cirrhosis, decompensated cirrhosis and hepatocellular carcinoma (HCC), whereas model A uses age-invariant annual probabilities of progression estimated by Shepherd et al, 9 and model B has age-dependent probabilities (Table S2). Individuals with mild disease, moderate disease and cirrhosis receive antiviral treatment of peginterferonα and ribavirin at fixed rates. Patients in whom sustained virologic response (SVR) does not occur are not eligible to receive further antiviral treatment.
Parameters specifying rates of progression and treatment are in Table S2, 2,6,10-12 with quality-of-life weights and costs in Table   S1. 2,13,14 Cost parameters, which we inflated to 2015-2016 UK pounds (GBP, £) using the hospital & community health services index, 15 not include a compartment for those being treated, it does account for the increased QALY losses and costs for those undergoing treatment. Treatment lasts between 12 and 48 weeks depending on the HCV genotype. A proportion of individuals in mild, moderate and cirrhosis states are treated each year, and therefore, we adjust the QALYs and costs for each of these states accordingly. Rates of age-dependent annual background mortality were obtained from life tables from the Office for National Statistics, 17 and quality-of-life norms by age were obtained from Kind et al 13 We considered cohorts of 1000 individuals aged 20, 35 and 50 years at the time of nascent chronic HCV infection, comparing the incidence of progression to various health states and the associated costs and QALY losses predicted by the two models, with results presented per person or per 1000 persons according to ease of reading. The analysis is from the perspective of the National Health Service (NHS) and considered the lifetime of the patient cohort.
Health utilities and costs were discounted at 3.5% p.a., as standard for the UK. 18 The division between HCV genotypes as described in the two models differs, with model A differentiating between genotype 1 and all other genotypes, and model B splitting the genotypes into categories of genotype 1, 4, 5, 6 and genotype 2, 3. To compensate for this, and to better compare between the two models, we split the populations into those who are, or are not, infected with HCV genotype 1 (Table S2).

| Effect of initial age on disease burden
The two models differ markedly in how initial age affects their Harris et al's model 6 ("model B" hereafter) predicts discounted costs increase with initial age below 40 years and then decline slightly ( Figure 2A), but that discounted QALY losses change little with initial age below 40 years and then decline ( Figure 2B).
Model A predicts higher discounted costs than model B except at initial ages >40 years but predicts lower discounted QALY losses except at initial ages <29 years. The age dependency of predicted discounted costs and QALY losses is much greater in model A than model B. As disease progression occurs over decades, discounting has an important effect on the net present value of costs and QALY losses, affecting not only the magnitude but also the effect of initial age: without discounting in both models, the costs and QALYs decline monotonically with increasing initial age, and model A predicts lower QALY losses for all but the very youngest initial ages ( Figure 2C,D).
The models differ markedly in the predicted costs, burden of illness (QALY loss) and the incidence of different stages of disease-both in terms of the timing of progression and the numbers of individuals affected, which will affect the need for particular types of care. We examine these differences below.

| Incidence of progression to disease states
In model A, the incidence of moderate disease is initially highest and declines monotonically over time, whereas in model B for those initially aged 20 and 35 years, the incidence fluctuates over time and is highest around 40 years of age (ie after 20 years in those initially aged 20 years and after 5 years in those initially aged 35 years), and for those initially aged 50 years, incidence is initially highest and then declines almost monotonically ( Figure 3).
There is a striking difference between the models regarding the incidence of cirrhosis and HCC ( Figure 3). Trends observed in model A are similar for all initial ages, with incidence of cirrhosis peaking at 7-8 cases per 1000 infections after roughly 20 years of infection. Incidence of HCC is low (1-2 cases per 1000 infections per year in all 3 cohorts).
In model B, the incidence of cirrhosis and HCC is much higher and has peaks occurring later (around 80 years of age for cirrhosis and a little older for HCC, regardless of initial age), and rates fluctuate over time due to patterns of age dependence. Both models predict similar incidence of mild SVR (ie successful treatment among those with mild chronic infection), and in both models, the incidence is initially maximal and then declines monotonically ( Figure 3). It should be noted however, that for model A at least, the decrease in SVR over time is a consequence of fewer individuals being in the mild disease state rather than the efficacy of treatment decreasing with age. Cumulative incidence reflects these results, peaking at

| Health detriment (QALY losses)
The average discounted QALY loss (due to morbidity and mortality) per chronic HCV infection estimated by model A is 4.9, 4.1 and 3.1 for those initially aged 20, 35 and 50 years, respectively ( Figure 2B, Mild and moderate disease stages account for 59%-72% of QALY losses in model A and 49%-65% in model B, with the proportion increasing with initial age in both models ( Figure 2B, Table 1). Up to half F I G U R E 2 A, Discounted (3.5% p.a.) cumulative costs, (B) discounted (3.5% p.a.) cumulative QALY losses, (C) undiscounted cumulative costs, (D) undiscounted cumulative QALY losses, over the lifetime of the patient by initial age of all discounted QALY losses in the models are due to mild disease (

| Costs
The cumulative discounted cost per chronic HCV infection declines with increasing initial age in model A (£19 200, £17 100 and £13 800 in those initially aged 20, 35 and 50 years, respectively), whereas in model B, costs increase slightly with initial age (£13 900, £15 100 and £15 300 in those initially aged 20, 35 and 50 years, respectively) ( Table 2). Temporal trends in discounted and undiscounted costs in the two models are shown in Figures S5-S8.  (Table S3). When using model B's unit costs in model A, the average discounted cost in persons initially aged 20, 35 and 50 years is £16 100, £14 400 and £11 700, respectively (Table S4). Note that the trends with initial age were unchanged in each model.
Mild and moderate disease stages account for only one-third of the total discounted cost in model A, whilst accounting for majority of the total cost (>57%) in model B (Table 2), particularly in the younger ages. If the unit costs from model A are used in model B (Table S3), then mild and moderate disease stages still account for more than half of the total cost, and if the unit costs from model B are applied to model A (Table S4), then mild and moderate stages account for ~40% of the total cost, which is still much less than in model B.
Costs due to mild disease decrease with increasing initial age in both models, but the proportion of total costs that they represent increases with initial age in model A whilst declining in model B (Table 2).
Costs due to moderate disease decrease with increasing initial age in model A and represent a slightly increasing proportion of total costs; in model B, these costs and the proportion of total costs that they represent both increase with increasing initial age ( Table 2). These patterns occur regardless of which set of unit costs is used ( Table 2, Tables   S3 and S4).
The average discounted costs per patient incurred due to cirrhosis, decompensated cirrhosis, HCC and liver transplantation decrease with increasing initial age in model A, as do the proportions of total discounted costs that they represent (Table 2)  QALY losses due to mortality are also shown. The percentage of the total QALY loss attributable to morbidity of each disease stage and mortality is also shown. Where applicable, the discount rate used is 3.5% p.a.

| DISCUSSION
There are important differences between the models that we com- Further studies of all of these are required, including analysis of potential synergistic effects 22 of combining HCV TasP with needle and syringe programmes (which reduce the infection risk of injecting) and opiate substitution therapy (which assist PWID in stopping injecting).
Use of transmission dynamic models to analyse surveillance data is important in assessing population-level impacts of interventions; 23 in the case of PWID, it is important to use models that account for the injecting network structure and dynamics. 21 In some marginalised populations, proactive "find and treat" services may be cost-effective or even cost-saving, as has been found for tuberculosis. 24 (DAAs), which are highly efficacious and well-tolerated but are also expensive, requires further study to determine how to use DAAs in a cost-effective manner. However, if the price paid for DAAs is too high, then this damages overall population health because the money could be used in another way to obtain a greater health gain.
In summary, this research has emphasised the uncertainty in the health burden and economic cost of HCV disease in the UK. The main source of uncertainty is progression rates between disease states and associated rates of health service utilization, particularly with regard to age dependency. In addition, the effects of other risk factors and comorbidities require quantification to improve information for planning and decision-making.
of the authors and not necessarily those of the Department of Health, EPSRC, MRC, NHS, NIHR or Public Health England.