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Use of Bayesian Methods for Markov Modelling in Cost Effectiveness Analysis: An application to taxane use in advanced breast cancer. Nicola Cooper, Keith Abrams, Alex Sutton, David Turner, Paul Lambert Department of Epidemiology & Public Health, University of Leicester, UK. OBJECTIVE. - PowerPoint PPT Presentation
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Use of Bayesian Methods for Markov Modelling in Cost Effectiveness
Analysis: An application to taxane use in
advanced breast cancerNicola Cooper, Keith Abrams,
Alex Sutton, David Turner, Paul LambertDepartment of Epidemiology & Public Health,
University of Leicester, UK
OBJECTIVE
•To demonstrate how CE decision analysis may be implemented from a Bayesian perspective, using MCMC simulation methods.
•Illustrative example: CE analysis of taxane use for the second-line treatment of advanced breast cancer compared to conventional treatment
•To demonstrate how CE decision analysis may be implemented from a Bayesian perspective, using MCMC simulation methods.
•Illustrative example: CE analysis of taxane use for the second-line treatment of advanced breast cancer compared to conventional treatment
OUTLINE
•Decision-Analytical Model
•Transition Probabilities
•Model Evaluation Methods
•Model Results
•Summary & Conclusions
•Decision-Analytical Model
•Transition Probabilities
•Model Evaluation Methods
•Model Results
•Summary & Conclusions
MODEL
• 4 Stage stochastic Markov Model
• 4 Health states• Response
• Stable
• Progressive
• Death
• Cycle length = 3 weeks (35 cycles)
• Maximum of 7 treatment sessions
• 4 Stage stochastic Markov Model
• 4 Health states• Response
• Stable
• Progressive
• Death
• Cycle length = 3 weeks (35 cycles)
• Maximum of 7 treatment sessions
MODEL cont.Stages 1 & 2(cycles 1 to 3)
Stage 3(cycles 4 to 7)
Stage 4(cycles 8 to 35)
Treatment cycles
Post -Treatment
cycles
In 2nd line treatment
Respond Stable Progressive Dead
Respond Stable Progressive Dead
Respond Stable Progressive Dead
1) Pooled estimates
Odds - log scale.1 .25 1 5
Combined
Bonneterre
Sjostrom
Nabholtz
Chan
mu.rsprtD sample: 12001
-5.0 0.0 5.0
0.0 0.5 1.0 1.5 2.0
In 2nd line
treatment
Respond Stable Progressive Dead
TRANSITION PROBABILITIES
3) Transformation of distribution to transition probability
2) Distribution
4) Application to model
(i) time variables:
(ii) prob. variables:
j
ttP j)],(1ln[exp1
0
jjo ttP /1)],(1[1
•Stochastic Markov Models:
–Classical Model - Monte Carlo (MC) simulation model (EXCEL)
–Bayesian Model - Markov Chain Monte Carlo (MCMC) simulation model (WinBUGS)
•Stochastic Markov Models:
–Classical Model - Monte Carlo (MC) simulation model (EXCEL)
–Bayesian Model - Markov Chain Monte Carlo (MCMC) simulation model (WinBUGS)
MODEL EVALUATION
Docetaxel
Doxorubicin
RESULTS
Stable
Progressive
Respond
Death
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102
Number of weeks
Pe
rce
nta
ge
of co
ho
rt
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102
Number of weeks
Pe
rce
nta
ge
of co
ho
rt
CE PLANE (MC)
Classical (MC) Simulations
-£4,000
-£2,000
£0
£2,000
£4,000
£6,000
£8,000
£10,000
-0.50 -0.40 -0.30 -0.20 -0.10 - 0.10 0.20 0.30 0.40 0.50
Incremental utility
Inc
rem
en
tal
co
st
Doxorubicin dominates
Docetaxel more effective but more costly
Docetaxel less costly but less
effective
Docetaxel dominates
Bayesian (MCMC) Simulations
-£4,000
-£2,000
£0
£2,000
£4,000
£6,000
£8,000
£10,000
-0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50
Incremental utility
Inc
rem
en
tal
co
st
Doxorubicin dominates
Docetaxel more effective but more costly
Docetaxel less costly but less
effective
Docetaxel dominates
CE PLANE (MCMC)
RESULTS
ΔE
ΔC (ICER) Ratio CE lIncrementa
ΔCΔERC (INB)Benefit Net lIncrementa
Incremental Costs
C = CT – CC
Incremental Utilities
E = UT – UC
Classical (MC) model £5,295 (£3,321 to £7,228) 0.044 (-0.10 to 0.19)
Bayesian (MCMC) model £4,529 (£1,415 to £7,458)
0.034 (-0.20 to 0.24)
INB CURVES
-£6,000
-£4,000
-£2,000
£0
£2,000
£4,000
£6,000
£8,000£
0
£5
0,0
00
£1
00
,00
0
£1
50
,00
0
£2
00
,00
0
£2
50
,00
0
Willingness to Pay, Rc
Va
lue
of
ne
t b
en
efi
t
Classical (MC) modelBayesian (MCMC) model
NET BENEFIT (cont.)
-£40,000
-£30,000
-£20,000
-£10,000
£0
£10,000
£20,000
£30,000
£40,000
£0
£5
0,0
00
£1
00
,00
0
£1
50
,00
0
£2
00
,00
0
£2
50
,00
0
Willingness to Pay, Rc
Va
lue
of
ne
t b
en
efi
t
Classical (MC) modelupper limitlower limit
NET BENEFIT (cont.)
-£40,000
-£30,000
-£20,000
-£10,000
£0
£10,000
£20,000
£30,000
£40,000
£0
£5
0,0
00
£1
00
,00
0
£1
50
,00
0
£2
00
,00
0
£2
50
,00
0
Willingness to Pay, Rc
Va
lue
of
ne
t b
en
efi
t
Classical (MC) modelBayesian (MCMC) modelupper classicallower classicalupper Bayesianlower Bayesian
CONCLUSIONS
Advantages of the Bayesian approach compared to equivalent Classical approach
(i) Incorporation of greater parameter uncertainty
(ii)Ability to make direct probability statements & thus direct answers to the question of interest
(iii)Incorporation of expert opinion either directly or regarding the relative credibility of different data sources
Advantages of the Bayesian approach compared to equivalent Classical approach
(i) Incorporation of greater parameter uncertainty
(ii)Ability to make direct probability statements & thus direct answers to the question of interest
(iii)Incorporation of expert opinion either directly or regarding the relative credibility of different data sources
ACCEPTABILITY CURVE
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0£
0
£5
0,0
00
£1
00
,00
0
£1
50
,00
0
£2
00
,00
0
£2
50
,00
0
£3
00
,00
0
£3
50
,00
0
£4
00
,00
0
£4
50
,00
0
£5
00
,00
0
Willingness to Pay, Rc
Pro
ba
bil
ity
Co
st
Eff
ec
tiv
e
Classical (MC) model
Bayesian (MCMC) model
FURTHER WORK
•Sensitivity analysis–One / multi-way analysis
–Choice of prior distributions
–MCMC convergence
•Simple versus Complex Markov model–Time dependent variables
–Two-way pathways
(e.g. stable to response to stable)
•Sensitivity analysis–One / multi-way analysis
–Choice of prior distributions
–MCMC convergence
•Simple versus Complex Markov model–Time dependent variables
–Two-way pathways
(e.g. stable to response to stable)
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