Economic evaluation of health
programmes
Department of Epidemiology, Biostatistics
and Occupational Health
Class no. 10: Cost-utility analysis – Part 3
Oct 6, 2008
Plan of class
More on expected utility theory
Methods for eliciting values or utilities
associated with health states (continued)
Axioms of von NeumannMorgenstern utility theory (1)
Axiom 1: (a) Preferences exist and (b) are
transitive.
Pair of risky prospects y and y’:
p=0.9
p=0.1
Win $1,000
Lose $100
p=0.7
p=0.3
Win $10,000
Lose $1000
Preferences exist: A person either prefers y to
y’, or y’ to y, or is indifferent between y and y’.
(Which would you prefer? Why?)
They are transitive: If 3 risky prospects y, y’ and
y’’, if y>y’ and y’>y’’, then y>y”
Axioms of von-Neumann
Morgenstern utility theory (2)
Axiom 2: Independence: Combining each of the
2 previous lotteries with an additional lottery r
in the same way should not affect your choice
between the 2 lotteries
Axiom of independence
p=0.9
p=0.6
p=0.4
p=0.1
Win $1,000
Lose $100
3rd lottery r (p, x1, x2)
Axiom: Choice between y and y’ unaffected by addition of
the same 3rd lottery with same probability of obtaining that
3rd lottery (say, p=0.9, x1=$5000, x2= - $1,000).
p=0.6
p=0.7
p=0.3
p=0.4
Win $10,000
Lose $100
3rd lottery r (p, x1, x2)
Axiom of continuity of
preferences
X
p
Alternative 1
Alternative 2
1-p
Z
Y
This axiom states that if Y is an outcome intermediate in
utility between X and Z, then there is some probability p at
which an individual will be indifferent between the lottery
that yields X or Z and the certain outcome Y
The point of these axioms
These axioms lead to the conclusion that
individuals maximize their expected utility.
Expected utility theory
Expected utility
theory implies that
the individual will
choose the gamble
with the highest
expected utility
p=0.9
Win $500
Lottery 1
p=0.1
p=0.7
Win $100
Win $400
Lottery 2
p=0.3
Win $200
EU (L1)= 0.9 x U(500) + 0.1 x U(100)
EU (L2)= 0.7 x U(400) + 0.3 x U(200)
Diminishing marginal utility of
money
U($)
$
Diminishing marginal utility of money gives us a simple way of
introducing risk aversion into EU calculation –actuarially fair
gamble less desirable than its certain monetary equivalent
Working through example
Suppose U(X)=X - 0.001 x X2. Then:
Winnings
500
400
200
100
Utility of winnings
250
240
160
90
Then:
EU(L1) = 0.9 x 250 + 0.1 x 90 = 225 + 9 = 234
EU (L2) = 0.7 x 240 + 0.3 x 160 = 168 + 48 = 216
Expected utility theory says rational individual will
choose L1
More on EU theory
Mathematically simple formula facilitates
analysis of complex decision problems
Widely used in spite of limitations
Time trade-off for temporary
health states
Alternative 1
Temporary state i for time t,
then healthy
Alternative 2
Temporary state j for time x < t,
then healthy
Vary x until respondent is indifferent between the alternatives
h(i) = 1 – (1-h(j)) x/t
Person Trade-Off
 If there are x people in adverse health
situation A and y people in adverse health
situation B, and you can only help (cure) one
group, which group would you choose?
• Vary the number of people in situation B until the
person is indifferent. Undesirability of health state
B relative to A is then x/y.
• Early study indicated same results as category
scaling
• Later work using PTO specifically reports
significant differences with the other methods
How do we evaluate
these methods?
 Practicality (related to acceptability – length,
complexity - how many people will complete
it?)
 Reliability (Test-retest or inter-rater reliability)
 Validity (What is gold standard? Theoretical
validity often invoked.)
VAS
Most practical and reliable, easy to use
and understand.
 But only weakly correlated with SG and TTO;
 appears to measure a “percentage of best
imaginable health state”, not a valuation of
that particular health state – a value, not a
utility
Could we measure it and then map to SG
or TTO utilities?
VAS vs SG
 Utilities =f(value, risk preference). Therefore,
risk-neutral individuals should give same
value to both. Several functions, have been
considered, including:
• U = Vb
• U = a + bV
• U=a + bV + cV2
 However, results are not consistent,
sometimes favoring power functions,
sometimes not.
VAS to TTO
 VAS to TTO:
• Again results are inconsistent.
 Conclusion: can’t really map VAS to either SG
or TTO
Standard gamble
 Practical, completion rates 80 – 95%.
 Reliable.
 Has element of choice under uncertainty –
 But is it really the relevant choice? Risk attitude is
known to vary depending on the circumstances, in
ways likely to differ from what is reflected in SG
questions.
 Also, people have difficulty with probabilities below
0.1 or above 0.9.
 So, not everyone agrees that this makes of SG
the “gold standard”.
TTO
 Practical and reliable, but assumes people willing
to trade-off constant proportion of remaining years
irrespective of remaining life expectancy. Yet:
• Some people unwilling to sacrifice any length of life
to be relieved of many health states; rate of
discounting may decrease with length of time (time
preference effects).
• Some health states may be perceived so negatively
by some that viewed as increasingly intolerable the
greater the duration of the negative health state
(duration effects)
Conclusion concerning SG,
TTO
Both can be viewed as providing
approximately correct, but somewhat
biased approximations to underlying
preferences.
PTO
Not often used.
Practicality not well assessed but appears
to require a fair amount of time.
Reliability unknown.
Validity: evidence that PTO may be better
at measuring social preferences – but that
is not necessarily what the other methods
want to measure!
On what basis should we
make these resource
allocation decisions? What
are we trying to maximize?
Welfarist vs non-welfarist
frameworks for thinking about
resource allocation
Welfarist resource allocation
 Social welfare is the sum of each individual’s
own utility, as assessed by themselves.
• Standard economic theory is welfarist: assumes
that individuals are the best judges of their own
welfare, expressed in terms of individual utility; and
that social welfare is the sum of individual utilities
– Analogous to the concept of consumer sovereignty: we
do not question peoples’ individual preferences
– Perspective tends to lead to a more market-oriented,
libertarian economic and social policy
Non-welfarist, or “extrawelfarist”
• Individuals are not necessarily the best judges of
their own welfare;
• Social welfare is not simply the sum of individual
utilities.
• Practically this means that we give the public at
large the authority to determine whether a certain
allocation of resources is better than another.
• Can you think of some examples?
Who should provide
preferences?
(Welfarist: individuals affected; nonwelfarist: the public, who are taxpayers)
Affects results – greater knowledge of
health state, and especially direct
experience, yields higher ratings of quality
of life usually. Example:
– Patients with colostomies: 0.92
– General public evaluation of colostomies: 0.8.
Why are there discrepancies?
• Poor descriptions of health states
• Changing standards/psychological
adaptation
• Adaptation
Patient experience vs public
preferences
Patient experience
For:
Know own health state
Their well-being at stake
Public preferences
For:
Veil of ignorance : No vested interest
Public funding like insurance
Against:
Against:
Possibility of strategic responses
Little knowledge
Infeasible or unethical in some cases
Does public want to provide this input?
Adaptation leads to underestimation of
need
Are preferences elicited or
constructed?
 Cognitive tasks very demanding (many
characteristics for a health state, many health
states to compare)
 3 successive interviews using VAS and SG –
1/3 of people changed their preferences over
time, saying they re-thought their initial
position
 Somewhat contradicts assumption that
preferences exist initially
Conclusions
 Inconsistent opinions concerning SG vs TTO
 Need to move towards better-informed
preferences from general public
 If one adopts “extra-welfarist” position, then
PTO, informing people well, may be a good
solution