Economic evaluation of health programmes

1. Economic evaluation of health programmes Department of Epidemiology, Biostatistics and Occupational Health Class no. 10: Cost-utility analysis – Part 3 Oct 6, 2008

2. Plan of class • More on expected utility theory • Methods for eliciting values or utilities associated with health states (continued)

3. 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 p=0.9 p=0.7 p=0.1 p=0.3 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 y>y’ and y’>y’’, then y>y”

4. 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

5. Axiom of independence Win $1,000 p=0.9 p=0.6 p=0.1 Lose $100 3rd lottery r (p, x1, x2) p=0.4 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). Win $10,000 p=0.7 p=0.6 p=0.3 Lose $100 3rd lottery r (p, x1, x2) p=0.4

6. Axiom of continuity of preferences X p Alternative 1 1-p Z 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

7. The point of these axioms • These axioms lead to the conclusion that individuals maximize their expected utility.

8. Expected utility theory Expected utility theory implies that the individual will choose the gamble with the highest expected utility Win $500 p=0.9 Lottery 1 p=0.1 Win $100 Win $400 p=0.7 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)

9. 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

10. Working through example • Suppose U(X)=X - 0.001 x X2. Then: 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

11. More on EU theory • Mathematically simple formula facilitates analysis of complex decision problems • Widely used in spite of limitations

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

13. 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

14. 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.)

15. 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?

16. 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.

17. VAS to TTO • VAS to TTO: • Again results are inconsistent. • Conclusion: can’t really map VAS to either SG or TTO

18. 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”.

19. 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)

20. Conclusion concerning SG, TTO • Both can be viewed as providing approximately correct, but somewhat biased approximations to underlying preferences.

21. 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!

22. 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

23. 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

24. 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?

25. 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.

26. Why are there discrepancies? • Poor descriptions of health states • Changing standards/psychological adaptation • Adaptation

27. Patient experience vs public preferences

28. 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

29. 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