**Speaker:** Susan Griffin and Neil Hawkins, Team for Economic Evaluation and Health Technology Assessment, Centre for Health Economics, Univerity of York

**Title:** Building a semi-Markov model in R: an example evaluation of antibiotic prophylaxis in HIV-infected children in Zambia.

**Abstract:** Cotrimoxazole (trimethoprim-suphamethoxazole) is a widely available, low cost antibiotic that is an effective treatment of, and prophylaxis against, common bacterial infections in HIV. However, no trials of cotrimoxazole prophylaxis in adults or children have been reported from areas with high levels of bacterial resistance such as Zambia. Children with HIV Antibiotic Prophylaxis (CHAP) was a randomized trial comparing daily cotrimoxazole with placebo in HIV-infected children aged 1-14 years in Zambia.

A decision-analytic model was constructed to estimate the lifetime cost and health outcomes of providing antibiotic prophylaxis to HIV-infected children in Zambia, using data from the CHAP trial. The model consisted of three live states described by CD4% (>16%, 8-15%, <7%) and a state for dead. The survival models used to estimate the probability of progressing between live states and to death indicated that these transitions were dependent on time in state and age at state entry.

In a simple four-state Markov model it would not be possible to incorporate time-dependent transition probabilities. In order to record the time spent in each state the model would have to be restructured to create tunnel states for each live state for each cycle of the model. The number of states required therefore expands from four (three live states and one dead) to S*n+1 where S is the number of live states and n is the number of cycles. With a time horizon of 20 years and a cycle length of 3 months such a model would require 241 states. Despite the complexity of the model, it was straightforward to implement it in the statistical programming language R.

Based on this HIV model, we will demonstrate that the use of R and similar programming languages, allows the implementation of more sophisticated models which more closely reflect the disease and treatment processes and so lead to more accurate decision making

**Speaker:** Mat Taylor, Senior Consultant, York Health Economics Consortium, University of York

**Title:** Accounting for Initial Disease Severity When Measuring Health Gains

**Abstract:** In current economic evaluation methods, 'QALYs gained' is used as a summary outcome. Under such methods, the value of a patient moving from a health state with utility 0.8 to full health (i.e. 1.0) is considered equivalent to a change from 0.3 to 0.5, since both show 'improvements' of 0.2. However, there is some evidence to suggest that the initial state may play an important role in the patient's own valuation of the health change. Specifically, it is likely that the more severe the initial state, the more a patient will value an 'equal' health gain.

Using experimental techniques, this study was able to show that the initial health state did influence the valuation of a specific health gain. Furthermore, a method was developed in order to quantify the effect of starting disease severity, and to develop a 'modified QALY gain' for use in health technology economic evaluation. The presentation outlines the background, experimental methods, results and practical uses of the proposed theory.

**Speakers/Co-authors:** **Presentation 1:** Laura Bojke, Karl Claxton, Yolanda Bravo, Team for Economic Evaluation and Health Technology Assessment, Centre for Health Economics, University of York.

**Title for presentation 1:** Using expert elicitation to resolve issues of structural uncertainty in decision analytic modelsPurpose: To demonstrate how formal elicitation methods can be used to parameterise structural uncertainties within decision analytic models and evaluate alternative methods to synthesise the information acquired through elicitation.

**Background:** Current methods to characterise structural uncertainty (scenario analysis and model averaging) fail to provide quantitative estimates of the scale of the uncertainty or inform the question of what further evidence would be needed to resolve them. A parameterisation of the structural uncertainty, and elicitation and synthesis of formal priors on these new model parameters is required. It is then possible to conduct expected value of information analysis and establish the value of acquiring further evidence to resolve structural uncertainty.

**Methods:** Structural uncertainties were identified in an existing probabilistic model of etanercept and infliximab for psoriatic arthritis. An interactive elicitation exercise was designed to: generate estimates of disease progression while responding to treatment and while relapsing; examine the extent of correlation between these two parameters and response to treatment; and calibrate expert judgement in subsequent synthesis. Fifteen experts completed the questionnaire. Alternative methods of synthesise were evaluated: scenarios using individual experts; random sampling across experts (linear pooling); and meta-analysis using fixed or random effects models. The resulting estimates of the structural parameters were applied to the model and the value of information associated with the structural uncertainties was calculated.

**Results:** Responses to the elicitation questions varied, reflecting different clinical opinion regarding treatment. Responses to the known parameter showed that experts assessments could be regarded as differentially weighted, with some experts providing more a more accurate response than others. When applied to the model, using expert’s assessment as individual scenarios produced 15 different sets of results and estimates of EVI which is of little value to decision makers. Sampling across experts generated the highest EVI (£ 12.6mil) compared to the random effects model method (£5.5mil) and fixed effects model method (£ 4mil). Tests for heterogeneity showed that a random effects model was more appropriate for pooling than a fixed effects model (chi-square = 31.07).

**Conclusions:** Parameterising structural uncertainty requires formal methods of elicitation which can capture correlation and assess the quality of responses. The appropriate synthesis of expert judgement is important so that the value of collecting further data to resolve structural uncertainties can be estimated.

**Speaker: Presentation 2:** John Paul Gosling, Department of Probability and Statistics, University of Sheffield

**Title for presentation 2:** Uncertainty in elicitation

**Abstract:** In the context of statistical analysis, elicitation is the process of translating someone's beliefs about some uncertain quantities into a probability distribution. The person's judgements about the quantities are usually fitted to some member of a convenient parametric family. This approach does not allow for the possibility that any number of distributions could fit the same judgements.

In this talk, elicitation of an expert's beliefs will be treated as any other inference problem: the facilitator of the elicitation exercise has prior beliefs about the form of the expert's density function, the facilitator elicits judgements about the density function, and the facilitator's beliefs about the expert's density function are updated in the light of these judgements. This will be motivated by a simple example of eliciting beliefs about the risk of yearly progres.

**Title:** The theory and the practice of modelling methods for evaluating screening: lessons from AMD

**Speaker:** Jon Karnon, Health Economics and Decision Science group, School of Health and Related Research, University of Sheffield

**Abstract:** Model-based cost-effectiveness analyses of adult screening programmes are generally more complex than model-based intervention analyses, which is primarily due to the need to model the preclinical, as well as the clinical, phases of a disease; and the interaction between a (possibly) repeated screening test. This seminar will summarise the findings of a recent review of methods for the model-based economic evaluation of screening programmes, and discuss these findings in the context of a subsequent applied evaluation of primary screening for age-related macular degeneration.

**Speaker:** Samer Kharroubi (CHEBS, University of Sheffield)

**Title:** Estimating utilities from individual health preference data: a nonparametric Bayesian method

**Abstract:** A fundamental benefit conferred by medical treatments is to increase the health related quality of life (HRQoL) experienced by patients. Various descriptive systems exist to define a patient's health state, and we address the problem of assigning a HRQoL value to any given state in such a descriptive system. Data derive from experiments in which individuals are asked to assign their personal values to a number of health states. We construct a Bayesian model that takes account of various important aspects of such data. Specifically, we allow for the repeated measures feature that each individual values several different states, and the fact that individuals vary markedly in their valuations, with some people consistently providing higher valuations than others. We model the relationship between HRQoL and health state nonparametrically. We illustrate our method using data from an experiment in which 611 individuals each valued up to 6 states in the descriptive system known as the SF-6D. Although the SF-6D distinguishes 18,000 different health states, only 249 of these were valued in this experiment. We provide posterior inference about the HRQoL values for all 18,000 states.

**Title:** Do patients value psychological outcomes and should they be incorporated into cost-effectiveness analysis?

**Speaker:** Gerry Richardson (TEEHTA, CHE)

**Abstract:** The optimal method of managing chronic health problems has been a longstanding problem for health services around the world. One method proposed to improve the management of chronic conditions is the implementation of interventions to promote self care. Not surprisingly, there has been much recent attention paid to interventions supporting self care in both published literature and policy documents. Recent studies have demonstrated that these interventions improve the self-efficacy of patients, defined as their confidence in their ability to manage their condition. While 'self-efficacy' is considered important by advocates of interventions to support self care it does not fit easily into cost-effectiveness analysis. (CEA) and we have no knowledge of whether self-efficacy is 'of value' per se, or indeed what that value might be. In contrast, though the QALY has a commonly expressed 'value', this may not incorporate all outcomes that are of interest. This leads to problems of interpretation as decision makers cannot assess the relative merits of self-efficacy compared to health related quality of life (HRQoL).This study uses a discrete choice experiment (DCE) to examine the relative values placed on HRQoL, self-efficacy, access to GPs and level of isolation; attributes that had previously been identified as important to consumers. This study design enables estimation of rates of substitution between, for example, self-efficacy and HRQoL. In principle, therefore, this technique allows the inclusion of outcomes outside those measured within the QALY into CEA.

**Title:** How cost-effective is screening for abdominal aortic aneurysms? A long-term perspective based on the MASS trial.

**Presenters:** Dr Lois Kim (MRC Biostatistics Unit, Cambridge)

**Abstract:** Screening for abdominal aortic aneurysms (AAA) has been investigated in a number of randomised trials that have consistently reported an AAA-related mortality benefit in the group invited to screening. Reliable estimates of long-term cost-effectiveness are now needed to inform policy decisions for AAA screening programmes. A Markov decision model for screening is described and extrapolated to 30 years. The strategy modelled involves a one-off scan at age 65, with annual and three-monthly follow-up scans for small and medium aneurysms respectively. Referral for elective surgery occurs at an aortic diameter of 5.5cm; without this elective intervention, aneurysms may rupture, requiring emergency surgery to prevent death. Model parameters are estimated from patient-level data from the UK Multi-centre Aneurysm Screening Study. Model structure is validated on this trial’s data, and input parameter uncertainty is addressed by probabilistic sensitivity analysis.

**Title:** Eliciting utilities through the standard gamble: some inconsistencies and some methods to overcome them.

**Presenter:** Prof. Jose-Luis Pinto, University Pompeu Fabra, Barcelona, Spain

**Abstract:** One of the most widely used methods to elicit utilities for health states is the Standard Gamble method. Using this method, utilities are usually estimated under two main assumptions: a) the QALY model holds, b) expected utility holds. We develop three methods based on the Standard Gamble procedure and two methods based on 'Double Gambles'. Under these two assumptions, the five methods should produce the same utilities for health states. We estimated the utility of some Euroqol health states using these five methods. Sixty students where interviewed on five different occasions. We used a different method in each interview. Utilities produce by each method were quite different. This clearly shows that one or the two assumptions used to estimate utilities are wrong. We show that by relaxing the QALY model utilities are still quite different. We then show that assuming that preferences are described by Prospect Theory and not by Expected Utility, utilities for health states are much closer although some inconsistencies remain. Our paper shows that the usual assumptions used to elicit utilities for health states might be producing biased utilities. We suggest that it would be better to estimate utilities using Prospect Theory or using Double Gambles.

## Who to contact

For more information on these seminars, contact:

Simon Walker

smw501@york.ac.uk

01904 321451