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 theoryMethods for eliciting values or utilities

associated with health states (continued)

Axioms of von Neumann- Morgenstern utility theory (1)

Win $1,000

Lose $100

p=0.9

p=0.1

Win $10,000

Lose $1000

p=0.7

p=0.3

Axiom 1: (a) Preferences exist and (b) are transitive.Pair of risky prospects y and y’:

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 independenceWin $1,000

Lose $100

p=0.9

p=0.1

Win $10,000

Lose $100

p=0.7

p=0.3

p=0.6

p=0.4

p=0.6

p=0.4

3rd lottery r (p, x1, x2)

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).

Axiom of continuity of preferences

X

Z

p

1-pAlternative 1

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

Y

The point of these axioms

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

Expected utility theory

Win $500

Win $100

p=0.9

p=0.1

Win $400

Win $200

p=0.7

p=0.3

Expected utility theory implies that the individual will choose the gamble with the highest expected utility

EU (L1)= 0.9 x U(500) + 0.1 x U(100)EU (L2)= 0.7 x U(400) + 0.3 x U(200)

Lottery 1

Lottery 2

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 Utility of winnings

500 250400 240200 160100 90

Then: EU(L1) = 0.9 x 250 + 0.1 x 90 = 225 + 9 = 234EU (L2) = 0.7 x 240 + 0.3 x 160 = 168 + 48 = 216Expected 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

Temporary state i for time t, then healthy

Temporary state j for time x < t, then healthy

Alternative 2

Alternative 1

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 “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?

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.

Why are there discrepancies?

• Poor descriptions of health states• Changing standards/psychological

adaptation• Adaptation

Patient experience vs public preferences

Patient experience Public preferencesFor: Know own health stateTheir well-being at stake

For:Veil of ignorance : No vested interestPublic funding like insurance

Against:Possibility of strategic responsesInfeasible or unethical in some casesAdaptation leads to underestimation of need

Against:Little knowledgeDoes public want to provide this input?

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