20 times 80 is enough

1. 20 times 80 is enough Ben van Hout Julius Center for Health Sciences and Primary Care

2. Contents • Introductionary remarks • Valueing health states • The classic approach • The Bayesian approach • A comparison • How further • Concluding remarks

3. Uncertainty surrounding costs and effects

4. EuroQol

5. EQ-5D Index

6. Valueing health states • Populations from the general public are asked to attain values to health states which are described in terms of scores on different dimensions • EQ-5D • 5 dimensions • 3 scores per dimension • Not all health states are valued • There is an underlying structure

7. What do we want? • To compare the results from different therapies • Using data from RCT’s • Using models • Using valuations from the general public • Medians • Which may be country specific

8. Among the numerous problems • Each country starts its own valuation study withouth learning from the other countries • Utility estimates are hardly ever surrounded with uncertainty margins • Especially when collected alongside trials

9. The MVH-study • 3395 respondents • 41 health states + 11111 + unconsious • rescaled • 15 states per respondent • Mostly about 800 respondents per state • A few with 1300 • 3333 for all • Inconsistents taken out • 39868 valuations

10. The 3074 clean repondents (36369 clean data-points)

11. A typical good health state

12. A typical bad health state

13. A typical health state

14. Mean values + 95% confidence intervals

15. The classic appproach (EQ-5D)

16. Linear model; middle level = 2

17. Linear model; middle level is free

18. Linear Model, middle level free + n3 term

19. Uncertainties surrounding the model estimates

20. Observations + model estimates with 95% confidence limits

21. Let’s go Bayesian • The confidence intervals of my predictions of the average values are sometimes out of the range defeined by the confidence intervals of my observed average values • Wouldn’t it be nice if we would also acknowldege that we are uncertain about our model? • Samer Kharroubi, Tony O’Hagan and John Brazier

22. The Kharroubi approach • The function is unknown and is a random function • The expected values of the function are described by a linear model • Look at all valuations as random variables following a large 243-dimensional multinomial distribution with correlations that decrease with the distance between the states • Respondents may differ by a parameter α.

23. The Kharroubi approach • Succesfull in describing the SF-6D • Unsuccessful in working with 40,000 data-points • So, • A random sample of 38*80 points • Estimate • Predict 3 remaining points • Compare with classical approach

24. Within a few minutes

25. And while waiting the results • What if I don’t use all the data, but just the averages • And play around with a classical Bayesian alternative

26. Parameter estimates

27. Estimates based on averages (including 95% confidence intervals)

28. Standard Bayesian

29. Parameter estimates

30. Aren’t you neglecting something? • Standard Bayesian approach using WinBugs σ= 0.52 (in comparison to 0.59 following classical approach) • We know the uncertainties surrounding the observed average values • We can include those in WinBugs

31. Partly promising Bayesian

32. Hey, there is Samer • Relatively very good fit, but not as good as mine • But much better than mine without the dummies and the n3 • My predictions are better

33. A comparison • The Bayesian approach is - off course - more intuitive • It seems much more flexible in a natural way • It may take ways more computer-time • It may not handle large data-sets very well • I hope to be more convinced at the end of this week

34. How further • A better inclusion of the uncertainties surrounding the averages • Can’t Samer work with 41 data-points? • Using the first data-set as prior to the next • Designing a next country specific study

35. Concluding remarks • Bayesian analysis makes one feel good • Samer for president • I’m almost convinced