Economic evaluation of health programmes

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Economic evaluation of health programmes

• Department of Epidemiology, Biostatistics and
  Occupational Health
• Class no. 10 Cost-utility analysis Part 3
• Oct 6, 2008

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Plan of class

• More on expected utility theory
• Methods for eliciting values or utilities
  associated with health states (continued)

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Axioms of von Neumann- Morgenstern utility theory
(1)
Axiom 1 (a) Preferences exist and (b) are
transitive. Pair of risky prospects y and y
Win 1,000
Win 10,000
p0.9
p0.7
p0.1
p0.3
Lose 100
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 ygty and ygty, then ygty
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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
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Axiom of independence
Win 1,000
p0.9
p0.6
p0.1
Lose 100
3rd lottery r (p, x1, x2)
p0.4
Axiom Choice between y and y unaffected by
addition of the same 3rd lottery with same
probability of obtaining that 3rd lottery (say,
p0.9, x15000, x2 - 1,000).
Win 10,000
p0.7
p0.6
p0.3
Lose 100
3rd lottery r (p, x1, x2)
p0.4
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Axiom of continuity of preferences
X
p
Alternative 1
Z
1-p
Y
Alternative 2
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
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The point of these axioms

• These axioms lead to the conclusion that
  individuals maximize their expected utility.

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Expected utility theory
Win 500
Expected utility theory implies that the
individual will choose the gamble with the
highest expected utility
p0.9
Lottery 1
p0.1
Win 100
Win 400
p0.7
Lottery 2
p0.3
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)
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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
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Working through example

• Suppose U(X)X - 0.001 x X2. Then

Winnings Utility of winnings
500 250
400 240
200 160
100 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
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More on EU theory

• Mathematically simple formula facilitates
  analysis of complex decision problems
• Widely used in spite of limitations

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Time trade-off for temporary health states
Temporary state i for time t, then healthy
Alternative 1
Temporary state j for time x lt t, then healthy
Alternative 2
Vary x until respondent is indifferent between
the alternatives
h(i) 1 (1-h(j)) x/t
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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

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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.)

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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?

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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
• Ua bV cV2
• However, results are not consistent, sometimes
  favoring power functions, sometimes not.

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VAS to TTO

• VAS to TTO
• Again results are inconsistent.
• Conclusion cant really map VAS to either SG or
  TTO

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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.

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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)

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Conclusion concerning SG, TTO

• Both can be viewed as providing approximately
  correct, but somewhat biased approximations to
  underlying preferences.

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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!

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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
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Welfarist resource allocation

• Social welfare is the sum of each individuals
  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

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Non-welfarist, or extra-welfarist

• 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?

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Who should provide preferences?

• (Welfarist individuals affected non-welfarist
  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.

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Why are there discrepancies?

• Poor descriptions of health states
• Changing standards/psychological adaptation
• Adaptation

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Patient experience vs public preferences
Patient experience Public preferences
For Know own health state Their well-being at stake For Veil of ignorance No vested interest Public funding like insurance
Against Possibility of strategic responses Infeasible or unethical in some cases Adaptation leads to underestimation of need Against Little knowledge Does public want to provide this input?
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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

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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