Department of Probability and Statistics
University of Sheffield

EPSRC CASE PhD Studentship

In collaboration with Novartis Pharma AG

Project title: Bayesian inference for health state utilities using pair-wise
comparison data (see below for description)

Supervised by Dr Jeremy Oakley (Probability and Statistics) and Professor
John Brazier (Health Economics and Decision Science)

REQUIREMENTS

Candidates should have, or should expect to obtain, a good first degree
(i.e. BSc/BA/MMath/MStat) or MSc (or equivalent) involving a substantial
proportion of statistics and mathematics. Some knowledge of Bayesian
statistics would be desirable, but training will be given as necessary.
The project will also involve a substantial computing element and experience
in a standard statistical computing environment will be an advantage.

ELIGIBILITY

The studentship is available to all EU nationals who are normally resident
within the UK. The studentship will cover all academic fees plus a
the standard EPSRC stipend (12,000GBP in 2005/6). In addition there is an
industrial contribution of 3,000GBP per year by Novartis. EU nationals who
are not resident in the UK may apply for a "fees-only" award.

APPLICATION PROCEDURE

Informal enquiries can be made to Jeremy Oakley, [log in to unmask],
tel: +44 (0) 114 222 3853 (direct line)

Applicants can submit a formal application by downloading an application
form from
http://www.sheffield.ac.uk/~gradsch/Recruitment/ApplicationForm/

Applications will be accepted until the studentship is filled. The
studentship will start on 19 September 2005.



PROJECT BACKGROUND

In the field of medical decision-making, increasing importance is being
given to the cost-effectiveness of treatments. Health-care providers have
limited financial resources, and need to consider carefully how these
resources should be allocated. In the UK, cost-effectiveness appraisals of
new treatments are frequently conducted for the National Institute of
Clinical Excellence (NICE).   When evaluating cost-effectiveness, it is
necessary to consider the value of any (health) outcome that may result from
the treatment in question. Additionally, different outcomes need to be
valued on a common scale, so that cost-effectiveness can then be compared
between any treatments for any conditions. Specifically, a utility function
is needed for all possible states of health that is representative of the
preferences of society as a whole.

To determine the ‘inputs’ for this utility function, various descriptive
schemes of health states have been proposed. For example, the EuroQoL
(EQ-5D) instrument defines a health state by five characteristics (mobility,
self-care, usual activities, pain/discomfort, anxiety/depression), with each
characteristic set at one of three levels of an ordinal scale. Surveys are
conducted to elicit utilities for a subset of the possible states, and
statistical models are then fitted to the resulting data so that the utility
for any health state can be estimated.
A substantial difficulty with this approach is in the actual elicitation of
a utility for any particular health state from a respondent. Two methods
used are the Time Trade-Off (TTO) approach and the Standard Gamble (SG). In
the TTO exercise, a respondent may be asked, for example, to consider how
many years of perfect health they consider to be equally preferable to
living in a state of moderate discomfort for 10 years. In the SG approach, a
respondent may be asked to provide a probability p such that living in a
state of moderate discomfort is equally preferable as a gamble involving
achieving perfect health with probability p and death with probability 1-p.
Clearly, although respondents in past surveys have been willing to answer
these questions, both questions are difficult to answer, and there is an
issue of how precise a value any respondent is capable of providing.

One possible solution to this problem is to give the respondents a much
simpler elicitation task, at the cost of a more complex subsequent
statistical analysis. Specifically, respondents can be asked simply to make
pair-wise comparisons (i.e. discrete choices) between different health
states, i.e., to state which of two particular health states they have a
preference for. Given pair-wise comparisons from a sample of respondents, it
is then possible to infer the relative quantitative preferences for the
population if one is willing to make assumptions about a latent population
mean utility function, and how individual’s utilities deviate
probabilistically from this population mean utility. Conventional approaches
assume that the population mean utility is a linear function of the
variables describing the health state, and that deviations from this mean
for individual respondents are given by a logistic distribution.

If decision-makers are to use utilities estimated from pair-wise
comparisons, it is essential that the uncertainty about population utilities
is understood, and the robustness of any decision to miss-specification of
the corresponding utilities investigated. In this project a fully Bayesian
approach will be developed for estimating and reporting uncertainty about
population utilities given pair-wise comparison data.