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20 times 80 is enough Ben van Hout 17/7/16 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 fl 10.000 difference in costs fl 7.500 fl 5.000 fl 2.500 fl 0 fl 2.500fl 5.000fl 7.500fl 10.000-1,00 -0,80 -0,60 -0,40 -0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 difference in event free survival 1 0.8 0.6 0.4 0.2 0 €0 € 20,000 € 40,000 € 60,000 € 80,000 € 100,000 EuroQol EQ-5D Index MACCE Free Survival 100% 90% 80% 70% 60% 50% 0 200 400 600 800 1000 1200 Days since random ization Q5D-index SA not w orking Q5D-index CABG not w orking MACCE Free Survival 100% 90% 80% 70% 60% 50% 0 200 400 600 800 1000 Days since random ization Q5D-index SA w orking Q5D-index CABG not w orking 1200 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) 10 8 6 4 2 0 -2 -4 -6 -8 -10 1 229 457 685 913 1141 1369 1597 1825 2053 2281 2509 2737 2965 10 8 6 4 2 0 -2 -4 -6 -8 -10 1 229 457 685 913 1141 1369 1597 1825 2053 2281 2509 2737 2965 A typical good health state 700 600 500 400 300 200 Std. Dev = 3,00 100 Mean = 8,2 N = 1318,00 0 -10,0 -6,0 -8,0 TTO11112 -2,0 -4,0 2,0 0,0 6,0 4,0 10,0 8,0 A typical bad health state 100 80 60 40 20 Std. Dev = 4,95 Mean = -3,8 N = 844,00 0 -10,0 -6,0 -8,0 TTO33323 -2,0 -4,0 2,0 0,0 6,0 4,0 10,0 8,0 A typical health state 100 80 60 40 20 Std. Dev = 6,01 Mean = 1,3 N = 842,00 0 -10,0 -6,0 -8,0 TTO32211 -2,0 -4,0 2,0 0,0 6,0 4,0 10,0 8,0 Mean values + 95% confidence intervals The classic appproach (EQ-5D) U f ( x) e U o 1 x1 2 x 2 3 x 3 4 x 4 5 x 5 e e n(0, ) U f ( x) e 11 U o i xi e i 1 e n(0, ) Linear model; middle level = 2 10 8 6 2 0 -2 -6 -8 21111 11211 11121 12111 11112 12211 12121 11122 22112 22121 21222 11312 12222 22122 21312 22222 11113 13212 13311 12223 11131 21323 32211 23321 21232 22323 22331 33212 11133 21133 23313 23232 33321 22233 32313 32223 13332 32232 32331 33232 33323 33333 -4 Observed lower upper predicted 4 Linear model; middle level is free 10 8 6 2 0 -2 -6 -8 21111 11211 11121 12111 11112 12211 12121 11122 22112 22121 21222 11312 12222 22122 21312 22222 11113 13212 13311 12223 11131 21323 32211 23321 21232 22323 22331 33212 11133 21133 23313 23232 33321 22233 32313 32223 13332 32232 32331 33232 33323 33333 -4 Observed lower upper predicted 4 Linear Model, middle level free + n3 term Uncertainties surrounding the model estimates 2 x ' n( x ' , x ' ( x ' x ) x ) 1 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 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 0.14 B3 -0.35 0.17 -0.29 0.16 B4 -2.02 0.14 -1.92 0.13 B5 -1.29 0.15 -1.20 0.14 D1 0.88 0.21 0.92 0.20 D2 0.22 0.23 0.12 0.21 S3 0.53 0.23 0.44 0.21 S4 0.88 0.23 0.88 0.22 D5 0.56 0.22 0.59 0.21 N3 -2.80 0.37 -3.03 0.35 Estimates based on averages (including 95% confidence intervals) Standard Bayesian Yi N ( i , ) 11 i o i xij j 1 (0.001,0.001) I N ( i ; I ) I N (0.001;0.001) i (0.001,0.001) Parameter estimates Bayesian Classical estimate se estimate se Constant 16.16 0.41 15.38 0.43 B1 -1.62 0.14 -1.58 0.14 B2 -1.21 0.14 -1.28 0.14 B3 -0.59 0.15 -0.29 0.16 B4 -2.08 0.13 -1.92 0.13 B5 -1.37 0.13 -1.20 0.14 D1 0.88 0.18 0.92 0.20 D2 0.18 0.20 0.12 0.21 S3 0.19 0.20 0.44 0.21 S4 0.84 0.20 0.88 0.22 D5 0.60 0.20 0.59 0.21 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 Yi N ( i , 1 1 i ) Yi N ( i , ) 11 11 i o i xij i j 1 (0.001,0.001) i o i xij (0.001,0.001) I N ( i ; I ) I N (0.001;0.001) i (0.001,0.001) j 1 i N (0, 1 ) i I N ( i ; I ) I N (0.001;0.001) i (0.001,0.001) 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