20 times 80 is enough Ben van Hout 10/4/19 Julius Center for Health Sciences and Primary Care

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

Uncertainty surrounding costs and effects

EuroQol

EQ-5D Index

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

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

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

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

The 3074 clean repondents (36369 clean data-points)

A typical good health state

A typical bad health state

A typical health state

Mean values + 95% confidence intervals

The classic appproach (EQ-5D)

Linear model; middle level = 2

Linear model; middle level is free

Linear Model, middle level free + n3 term

Uncertainties surrounding the model estimates

Observations + model estimates with 95% confidence limits

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

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.

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

Within a few minutes

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

Parameter estimates all data average estimate se Constant 15.65 0.47 15.38 0.43 B1 -1.49 0.16 -1.58 0.14 B2 -1.33 0.15 -1.28 B3 -0.35 0.17 -0.29 B4 -2.02 -1.92 0.13 B5 -1.29 -1.20 D1 0.88 0.21 0.92 0.20 D2 0.22 0.23 0.12 S3 0.53 0.44 S4 D5 0.56 0.59 N3 -2.80 0.37 -3.03 0.35

Estimates based on averages (including 95% confidence intervals)

Standard Bayesian

Parameter estimates Bayesian Classical estimate se Constant 16.16 0.41 15.38 0.43 B1 -1.62 0.14 -1.58 B2 -1.21 -1.28 B3 -0.59 0.15 -0.29 0.16 B4 -2.08 0.13 -1.92 B5 -1.37 -1.20 D1 0.88 0.18 0.92 0.20 D2 0.12 0.21 S3 0.19 0.44 S4 0.84 0.22 D5 0.60 0.59 N3 -2.31 0.34 -3.03 0.35

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

Partly promising Bayesian

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

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

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

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