Utilizzo dei modelli decisionali per la valutazione economica
Gianluca Baio
University College LondonDepartment of Statistical Science
[email protected]://www.ucl.ac.uk/statistics/research/statistics-health-economics/
http://www.statistica.it/gianlucahttps://github.com/giabaio
IX Congresso Nazionale BIASParma
Friday, 29 September 2017
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 1 / 39
Outline
1. Health economic evaluation– What is it?– How does it work?
2. Statistical modelling– Individual-level vs aggregated data– The importance of being a Bayesian
3. Economic modelling & Decision analysis– Relevant quantities– Criteria for decision making
4. Uncertainty analysis– Rationale & main ideas– Value of information (hints)
5. Conclusions
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 2 / 39
Outline
1. Health economic evaluation– What is it?– How does it work?
2. Statistical modelling– Individual-level vs aggregated data– The importance of being a Bayesian
3. Economic modelling & Decision analysis– Relevant quantities– Criteria for decision making
4. Uncertainty analysis– Rationale & main ideas– Value of information (hints)
5. Conclusions
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 2 / 39
Outline
1. Health economic evaluation– What is it?– How does it work?
2. Statistical modelling– Individual-level vs aggregated data– The importance of being a Bayesian
3. Economic modelling & Decision analysis– Relevant quantities– Criteria for decision making
4. Uncertainty analysis– Rationale & main ideas– Value of information (hints)
5. Conclusions
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 2 / 39
Outline
1. Health economic evaluation– What is it?– How does it work?
2. Statistical modelling– Individual-level vs aggregated data– The importance of being a Bayesian
3. Economic modelling & Decision analysis– Relevant quantities– Criteria for decision making
4. Uncertainty analysis– Rationale & main ideas– Value of information (hints)
5. Conclusions
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 2 / 39
Outline
1. Health economic evaluation– What is it?– How does it work?
2. Statistical modelling– Individual-level vs aggregated data– The importance of being a Bayesian
3. Economic modelling & Decision analysis– Relevant quantities– Criteria for decision making
4. Uncertainty analysis– Rationale & main ideas– Value of information (hints)
5. Conclusions
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 2 / 39
Health technology assessment (HTA)
Objective: Combine costs & benefits of a given intervention into a rational scheme forallocating resources
Statisticalmodel
Economicmodel
Decisionanalysis
Uncertaintyanalysis
• Estimates relevant populationparameters θ
• Varies with the type ofavailable data (& statisticalapproach!)
• Combines the parameters to obtaina population average measure forcosts and clinical benefits
• Varies with the type of availabledata & statistical model used
• Summarises the economic modelby computing suitable measures of“cost-effectiveness”
• Dictates the best course ofactions, given current evidence
• Standardised process
• Assesses the impact of uncertainty (eg inparameters or model structure) on theeconomic results
• Mandatory in many jurisdictions (includingNICE, in the UK)
• Fundamentally Bayesian!
∆e = fe(θ)
∆c = fc(θ)
. . .
ICER = g(∆e,∆c)
EIB = h(∆e,∆c; k)
. . .
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 3 / 39
Health technology assessment (HTA)
Objective: Combine costs & benefits of a given intervention into a rational scheme forallocating resources
Statisticalmodel
Economicmodel
Decisionanalysis
Uncertaintyanalysis
• Estimates relevant populationparameters θ
• Varies with the type ofavailable data (& statisticalapproach!)
• Combines the parameters to obtaina population average measure forcosts and clinical benefits
• Varies with the type of availabledata & statistical model used
• Summarises the economic modelby computing suitable measures of“cost-effectiveness”
• Dictates the best course ofactions, given current evidence
• Standardised process
• Assesses the impact of uncertainty (eg inparameters or model structure) on theeconomic results
• Mandatory in many jurisdictions (includingNICE, in the UK)
• Fundamentally Bayesian!
∆e = fe(θ)
∆c = fc(θ)
. . .
ICER = g(∆e,∆c)
EIB = h(∆e,∆c; k)
. . .
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 3 / 39
Health technology assessment (HTA)
Objective: Combine costs & benefits of a given intervention into a rational scheme forallocating resources
Statisticalmodel
Economicmodel
Decisionanalysis
Uncertaintyanalysis
• Estimates relevant populationparameters θ
• Varies with the type ofavailable data (& statisticalapproach!)
• Combines the parameters to obtaina population average measure forcosts and clinical benefits
• Varies with the type of availabledata & statistical model used
• Summarises the economic modelby computing suitable measures of“cost-effectiveness”
• Dictates the best course ofactions, given current evidence
• Standardised process
• Assesses the impact of uncertainty (eg inparameters or model structure) on theeconomic results
• Mandatory in many jurisdictions (includingNICE, in the UK)
• Fundamentally Bayesian!
∆e = fe(θ)
∆c = fc(θ)
. . .
ICER = g(∆e,∆c)
EIB = h(∆e,∆c; k)
. . .
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 3 / 39
Health technology assessment (HTA)
Objective: Combine costs & benefits of a given intervention into a rational scheme forallocating resources
Statisticalmodel
Economicmodel
Decisionanalysis
Uncertaintyanalysis
• Estimates relevant populationparameters θ
• Varies with the type ofavailable data (& statisticalapproach!)
• Combines the parameters to obtaina population average measure forcosts and clinical benefits
• Varies with the type of availabledata & statistical model used
• Summarises the economic modelby computing suitable measures of“cost-effectiveness”
• Dictates the best course ofactions, given current evidence
• Standardised process
• Assesses the impact of uncertainty (eg inparameters or model structure) on theeconomic results
• Mandatory in many jurisdictions (includingNICE, in the UK)
• Fundamentally Bayesian!
∆e = fe(θ)
∆c = fc(θ)
. . .
ICER = g(∆e,∆c)
EIB = h(∆e,∆c; k)
. . .
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 3 / 39
Health technology assessment (HTA)
Objective: Combine costs & benefits of a given intervention into a rational scheme forallocating resources
Statisticalmodel
Economicmodel
Decisionanalysis
Uncertaintyanalysis
• Estimates relevant populationparameters θ
• Varies with the type ofavailable data (& statisticalapproach!)
• Combines the parameters to obtaina population average measure forcosts and clinical benefits
• Varies with the type of availabledata & statistical model used
• Summarises the economic modelby computing suitable measures of“cost-effectiveness”
• Dictates the best course ofactions, given current evidence
• Standardised process
• Assesses the impact of uncertainty (eg inparameters or model structure) on theeconomic results
• Mandatory in many jurisdictions (includingNICE, in the UK)
• Fundamentally Bayesian!
∆e = fe(θ)
∆c = fc(θ)
. . .
ICER = g(∆e,∆c)
EIB = h(∆e,∆c; k)
. . .
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 3 / 39
1. (“Standard”) Statistical modelling — Individual level data
• The available data usually look something like this:
Demographics HRQL data Resource use dataID Trt Sex Age . . . u0 u1 . . . uJ c0 c1 . . . cJ
1 1 M 23 . . . 0.32 0.66 . . . 0.44 103 241 . . . 802 1 M 21 . . . 0.12 0.16 . . . 0.38 1 204 1 808 . . . 8773 2 F 19 . . . 0.49 0.55 . . . 0.88 16 12 . . . 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
and the typical analysis is based on the following steps:
1 Compute individual QALYs and total costs as
ei =J∑j=1
(uij + uij−1)δj
2and ci =
J∑j=0
cij ,[
with: δj =Timej − Timej−1
Unit of time
]
2 (Often implicitly) assume normality and linearity and model independently individualQALYs and total costs by controlling for baseline values
ei = αe0 + αe1u0i + αe2Trti + εei [+ . . .], εei ∼ Normal(0, σe)
ci = αc0 + αc1c0i + αc2Trti + εci [+ . . .], εci ∼ Normal(0, σc)
3 Estimate population average cost and effectiveness differentials and use bootstrap toquantify uncertainty
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 4 / 39
1. (“Standard”) Statistical modelling — Individual level data
• The available data usually look something like this:
Demographics HRQL data Resource use dataID Trt Sex Age . . . u0 u1 . . . uJ c0 c1 . . . cJ
1 1 M 23 . . . 0.32 0.66 . . . 0.44 103 241 . . . 802 1 M 21 . . . 0.12 0.16 . . . 0.38 1 204 1 808 . . . 8773 2 F 19 . . . 0.49 0.55 . . . 0.88 16 12 . . . 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
and the typical analysis is based on the following steps:
1 Compute individual QALYs and total costs as
ei =J∑j=1
(uij + uij−1)δj
2and ci =
J∑j=0
cij ,[
with: δj =Timej − Timej−1
Unit of time
]
Time (years)
Qu
alit
y o
f lif
e (
sca
le 0
-1)
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
δj
uij+uij−12
QALYi = “Area under the curve”
2 (Often implicitly) assume normality and linearity and model independently individualQALYs and total costs by controlling for baseline values
ei = αe0 + αe1u0i + αe2Trti + εei [+ . . .], εei ∼ Normal(0, σe)
ci = αc0 + αc1c0i + αc2Trti + εci [+ . . .], εci ∼ Normal(0, σc)
3 Estimate population average cost and effectiveness differentials and use bootstrap toquantify uncertainty
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 4 / 39
1. (“Standard”) Statistical modelling — Individual level data
• The available data usually look something like this:
Demographics HRQL data Resource use dataID Trt Sex Age . . . u0 u1 . . . uJ c0 c1 . . . cJ
1 1 M 23 . . . 0.32 0.66 . . . 0.44 103 241 . . . 802 1 M 21 . . . 0.12 0.16 . . . 0.38 1 204 1 808 . . . 8773 2 F 19 . . . 0.49 0.55 . . . 0.88 16 12 . . . 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
and the typical analysis is based on the following steps:
1 Compute individual QALYs and total costs as
ei =J∑j=1
(uij + uij−1)δj
2and ci =
J∑j=0
cij ,[
with: δj =Timej − Timej−1
Unit of time
]
2 (Often implicitly) assume normality and linearity and model independently individualQALYs and total costs by controlling for baseline values
ei = αe0 + αe1u0i + αe2Trti + εei [+ . . .], εei ∼ Normal(0, σe)
ci = αc0 + αc1c0i + αc2Trti + εci [+ . . .], εci ∼ Normal(0, σc)
3 Estimate population average cost and effectiveness differentials and use bootstrap toquantify uncertainty
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 4 / 39
1. (“Standard”) Statistical modelling — Individual level data
• The available data usually look something like this:
Demographics HRQL data Resource use dataID Trt Sex Age . . . u0 u1 . . . uJ c0 c1 . . . cJ
1 1 M 23 . . . 0.32 0.66 . . . 0.44 103 241 . . . 802 1 M 21 . . . 0.12 0.16 . . . 0.38 1 204 1 808 . . . 8773 2 F 19 . . . 0.49 0.55 . . . 0.88 16 12 . . . 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
and the typical analysis is based on the following steps:
1 Compute individual QALYs and total costs as
ei =J∑j=1
(uij + uij−1)δj
2and ci =
J∑j=0
cij ,[
with: δj =Timej − Timej−1
Unit of time
]
2 (Often implicitly) assume normality and linearity and model independently individualQALYs and total costs by controlling for baseline values
ei = αe0 + αe1u0i + αe2Trti + εei [+ . . .], εei ∼ Normal(0, σe)
ci = αc0 + αc1c0i + αc2Trti + εci [+ . . .], εci ∼ Normal(0, σc)
3 Estimate population average cost and effectiveness differentials and use bootstrap toquantify uncertainty
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 4 / 39
1. (“Standard”) Statistical modelling — Aggregated data
1 Build a population level model (eg decision tree/Markov model)
NStandard/new
treatment
N − SEtNo side effects
(1− πt)
SEtBlood-related
side effects(πt)
AtAmbulatory care
(γ)
SEt −AtHospital admission
(1− γ)
et = 0, ct = cdrugt + camb
et = 0, ct = cdrugt + chosp
et = 1, ct = cdrugt
Economic outcomes
NB: in this case, the “data” are typically represented by summary statistics for theparameters of interest θ = (πt, γ, ...)
2 Use point estimates for the parameters to build the “base-case” (average) evaluation
3 Use resampling methods (eg bootstrap) to propage uncertainty in the pointestimates and perform uncertainty analysis
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 5 / 39
1. (“Standard”) Statistical modelling — Aggregated data
1 Build a population level model (eg decision tree/Markov model)
NStandard/new
treatment
N − SEtNo side effects
(1− πt)
SEtBlood-related
side effects(πt)
AtAmbulatory care
(γ)
SEt −AtHospital admission
(1− γ)
et = 0, ct = cdrugt + camb
et = 0, ct = cdrugt + chosp
et = 1, ct = cdrugt
Economic outcomes
NB: in this case, the “data” are typically represented by summary statistics for theparameters of interest θ = (πt, γ, ...)
2 Use point estimates for the parameters to build the “base-case” (average) evaluation
3 Use resampling methods (eg bootstrap) to propage uncertainty in the pointestimates and perform uncertainty analysis
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 5 / 39
1. (“Standard”) Statistical modelling — Aggregated data
1 Build a population level model (eg decision tree/Markov model)
NStandard/new
treatment
N − SEtNo side effects
(1− πt)
SEtBlood-related
side effects(πt)
AtAmbulatory care
(γ)
SEt −AtHospital admission
(1− γ)
et = 0, ct = cdrugt + camb
et = 0, ct = cdrugt + chosp
et = 1, ct = cdrugt
Economic outcomes
NB: in this case, the “data” are typically represented by summary statistics for theparameters of interest θ = (πt, γ, ...)
2 Use point estimates for the parameters to build the “base-case” (average) evaluation
3 Use resampling methods (eg bootstrap) to propage uncertainty in the pointestimates and perform uncertainty analysis
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 5 / 39
“Standard” approach to HTA — “Two-stage”
Statisticalmodel
Economicmodel
Decisionanalysis
Uncertaintyanalysis
• Estimates relevant populationparameters θ
• Varies with the type ofavailable data (& statisticalapproach!)
• Combines the parameters to obtaina population average measure forcosts and clinical benefits
• Varies with the type of availabledata & statistical model used
• Summarises the economic model bycomputing suitable measures of“cost-effectiveness”
• Dictates the best course of actions,given current evidence
• Standardised process
• Assesses the impact of uncertainty (egin parameters or model structure) onthe economic results
• Mandatory in many jurisdictions(including NICE, in the UK)
• Fundamentally Bayesian!
1. Estimation (base-case)
θ
yp(y | θ)
θ̂ = f(Y )
“Two-stage approach” (Spiegelhalter, Abrams & Myles, 2004)
2. Probabilistic sensitivity analysis
⇒
θp(θ) ! g(θ̂)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 6 / 39
“Standard” approach to HTA — “Two-stage”
Statisticalmodel
Economicmodel
Decisionanalysis
Uncertaintyanalysis
• Estimates relevant populationparameters θ
• Varies with the type ofavailable data (& statisticalapproach!)
• Combines the parameters to obtaina population average measure forcosts and clinical benefits
• Varies with the type of availabledata & statistical model used
• Summarises the economic model bycomputing suitable measures of“cost-effectiveness”
• Dictates the best course of actions,given current evidence
• Standardised process
• Assesses the impact of uncertainty (egin parameters or model structure) onthe economic results
• Mandatory in many jurisdictions(including NICE, in the UK)
• Fundamentally Bayesian!
1. Estimation (base-case)
θ
yp(y | θ)
θ̂ = f(Y )
“Two-stage approach” (Spiegelhalter, Abrams & Myles, 2004)
2. Probabilistic sensitivity analysis
⇒
θp(θ) ! g(θ̂)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 6 / 39
2./3. Economic modelling+Decision analysis — base-case scenario
Cost-effectiveness plane
Effectiveness differential
Cos
t diff
eren
tial
∆e
∆c
∆e = E[e | θ̂1]︸ ︷︷ ︸µ̂e1
− E[e | θ̂0]︸ ︷︷ ︸µ̂e0
∆c = E[c | θ̂1]︸ ︷︷ ︸µ̂c1
− E[c | θ̂0]︸ ︷︷ ︸µ̂c0
ICER =E[∆c]
E[∆e]=µ̂c1 − µ̂c0µ̂e1 − µ̂e0
= Cost per outcome
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 7 / 39
2./3./4. Economic modelling+Decision analysis+Uncertainty analysis
Cost-effectiveness plane
∆e
∆c
Effectiveness differential
Cos
t diff
eren
tial
∆e = E[e | θ1]︸ ︷︷ ︸µe1
− E[e | θ0]︸ ︷︷ ︸µe0
∆c = E[c | θ1]︸ ︷︷ ︸µc1
− E[c | θ0]︸ ︷︷ ︸µc0
•
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 7 / 39
What’s wrong with this?...
• Potential correlation between costs & clinical benefits [Both ILD and ALD]
– Strong positive correlation — effective treatments are innovative and result fromintensive and lengthy research ⇒ are associated with higher unit costs
– Negative correlation — more effective treatments may reduce total care pathway costse.g. by reducing hospitalisations, side effects, etc.
– Because of the way in which standard models are set up, bootstrapping generally onlyapproximates the underlying level of correlation — MCMC does a better job!
• Joint/marginal normality not realistic [Mainly ILD]
– Costs usually skewed and benefits may be bounded in [0; 1]– Can use transformation (e.g. logs) — but care is needed when back transforming to
the natural scale– Should use more suitable models (e.g. Beta, Gamma or log-Normal) — generally
easier under a Bayesian framework
• Particularly as the focus is on decision-making (rather than just inference), we needto use all available evidence to fully characterise current uncertainty on the modelparameters and outcomes [Mainly ALD]
– A Bayesian approach is helpful in combining different sources of information– Propagating uncertainty is a fundamentally Bayesian operation!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 8 / 39
What’s wrong with this?...
• Potential correlation between costs & clinical benefits [Both ILD and ALD]
– Strong positive correlation — effective treatments are innovative and result fromintensive and lengthy research ⇒ are associated with higher unit costs
– Negative correlation — more effective treatments may reduce total care pathway costse.g. by reducing hospitalisations, side effects, etc.
– Because of the way in which standard models are set up, bootstrapping generally onlyapproximates the underlying level of correlation — MCMC does a better job!
• Joint/marginal normality not realistic [Mainly ILD]
– Costs usually skewed and benefits may be bounded in [0; 1]– Can use transformation (e.g. logs) — but care is needed when back transforming to
the natural scale– Should use more suitable models (e.g. Beta, Gamma or log-Normal) — generally
easier under a Bayesian framework
• Particularly as the focus is on decision-making (rather than just inference), we needto use all available evidence to fully characterise current uncertainty on the modelparameters and outcomes [Mainly ALD]
– A Bayesian approach is helpful in combining different sources of information– Propagating uncertainty is a fundamentally Bayesian operation!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 8 / 39
What’s wrong with this?...
• Potential correlation between costs & clinical benefits [Both ILD and ALD]
– Strong positive correlation — effective treatments are innovative and result fromintensive and lengthy research ⇒ are associated with higher unit costs
– Negative correlation — more effective treatments may reduce total care pathway costse.g. by reducing hospitalisations, side effects, etc.
– Because of the way in which standard models are set up, bootstrapping generally onlyapproximates the underlying level of correlation — MCMC does a better job!
• Joint/marginal normality not realistic [Mainly ILD]
– Costs usually skewed and benefits may be bounded in [0; 1]– Can use transformation (e.g. logs) — but care is needed when back transforming to
the natural scale– Should use more suitable models (e.g. Beta, Gamma or log-Normal) — generally
easier under a Bayesian framework
• Particularly as the focus is on decision-making (rather than just inference), we needto use all available evidence to fully characterise current uncertainty on the modelparameters and outcomes [Mainly ALD]
– A Bayesian approach is helpful in combining different sources of information– Propagating uncertainty is a fundamentally Bayesian operation!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 8 / 39
Why does it matter?
Example: survival analysis in health economic evaluation
• Survival data are often the main outcome in clinical studies relevant for HTA– Cancer drugs (progression-free/overall survival time): ≈ 40% of NICE appraisals!– Need to extrapolate, for economic modelling purposes. BUT: Limited follow up from
trials, not consistent with time horizon of economic model
●
time
Sur
viva
l
as.factor(arm)=0as.factor(arm)=1
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 9 / 39
Why does it matter? Median survival time
Example: survival analysis in health economic evaluation
• Survival data are often the main outcome in clinical studies relevant for HTA– Cancer drugs (progression-free/overall survival time): ≈ 40% of NICE appraisals!– Need to extrapolate, for economic modelling purposes. BUT: Limited follow up from
trials, not consistent with time horizon of economic model
●
time
Sur
viva
l
as.factor(arm)=0as.factor(arm)=1
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0 Kaplan Meier
Weibull
● ●8.33
11.54
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 9 / 39
Why does it matter? Mean survival time
Example: survival analysis in health economic evaluation
• Survival data are often the main outcome in clinical studies relevant for HTA– Cancer drugs (progression-free/overall survival time): ≈ 40% of NICE appraisals!– Need to extrapolate, for economic modelling purposes. BUT: Limited follow up from
trials, not consistent with time horizon of economic model
●
time
Sur
viva
l
as.factor(arm)=0as.factor(arm)=1
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0 Kaplan Meier
Weibull
9.0910.34
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 9 / 39
Why does it matter?
Example: survival analysis in health economic evaluation
• Survival data are often the main outcome in clinical studies relevant for HTA– Cancer drugs (progression-free/overall survival time): ≈ 40% of NICE appraisals!– Need to extrapolate, for economic modelling purposes. BUT: Limited follow up from
trials, not consistent with time horizon of economic model
• When there is strong correlation among the survival parameters, the results ofuncertainty analysis may be (strongly) biased under a more simplisticfrequentist model
– This matters most in health economics, because this bias carries over the economicmodelling, optimal decision making and assessment of the impact of parametricuncertainty!
• For more complex models, MLE-based estimates may fail to converge– This may be an issue for multi-parameter models, where limited data (not compounded
by relevant prior information) are not enough to fit all the model parameters– NB: you would normally need to fit more complex models for cases where the survival
curves are “strange” and so the usual parametric models fail to provide sufficient fit
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 9 / 39
Why does it matter?
Example: survival analysis in health economic evaluation
• Survival data are often the main outcome in clinical studies relevant for HTA– Cancer drugs (progression-free/overall survival time): ≈ 40% of NICE appraisals!– Need to extrapolate, for economic modelling purposes. BUT: Limited follow up from
trials, not consistent with time horizon of economic model
Model fit for the Generalised F model , obtained using Flexsurvreg(Maximum Likelihood Estimate). Running time: 1.157 seconds
mean se L95% U95%mu 2.29139696 0.0798508 2.13489e+00 2.44790e+00sigma 0.58729598 0.0725044 4.61076e-01 7.48069e-01Q 0.84874994 0.2506424 3.57500e-01 1.34000e+00P 0.00268265 0.0902210 6.33197e-32 1.13655e+26as.factor(arm)1 0.34645851 0.0877892 1.74395e-01 5.18522e-01
Model fit for the Generalised F model , obtained using Stan(Bayesian inference via Hamiltonian Monte Carlo). Running time: 26.692 seconds
mean se L95% U95%mu 2.256760 0.3455163 0.0897086 0.0865904sigma 0.507861 0.0762112 0.3608566 0.6582047Q 0.700062 0.3358360 0.0786118 1.3880582P 1.131968 0.5837460 0.3908284 2.6342762as.factor(arm)1 0.345516 0.0865904 0.1745665 0.5176818
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 9 / 39
Bayesian modelling
Existing knowledge• Population registries
• Observational studies
• Small/pilot RCTs
• Expert optionsp(θ)
0.0 0.2 0.4 0.6 0.8 1.0
theta
Prior
Encode the assumption that a drug has a response rate between 20 and 60%
Current data
• Large(r) scale RCT
• Observational study
• Relevant summaries
p(y | θ)
Updated knowledge
p(θ | y)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 10 / 39
Bayesian modelling
Existing knowledge• Population registries
• Observational studies
• Small/pilot RCTs
• Expert optionsp(θ)
Current data
• Large(r) scale RCT
• Observational study
• Relevant summariesp(y | θ)
0.0 0.2 0.4 0.6 0.8 1.0
theta
LikelihoodPrior
Observe a study with 150 responders out of 200 patients given the drug
Updated knowledge
p(θ | y)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 10 / 39
Bayesian modelling
Existing knowledge• Population registries
• Observational studies
• Small/pilot RCTs
• Expert optionsp(θ)
Current data
• Large(r) scale RCT
• Observational study
• Relevant summariesp(y | θ)Updated knowledge
p(θ | y)
0.0 0.2 0.4 0.6 0.8 1.0
theta
Posterior
LikelihoodPrior
Update knowledge to describe revised “state of science”
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 10 / 39
Bayesian HTA in action — Decision analytic models (influenza)
Yes(p1)
Cost with NIs +cost influenza
Yes Influenza?
No(1 − p1)
Cost with NIs
Prophylactic NIs?
Yes(p0)
Cost influenza
No Influenza?
No(1 − p0)
Cost with no NIsµe1 = −lp1
µe0 = −lp0
µc1 =(cNI + cInf
)p1 + cNI (1− p1)
µc0 =(cNI + cInf
)p0 + cNI (1− p0)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 11 / 39
Bayesian HTA in action — Decision analytic models (influenza)
xh
βh mh
γh
µγ σ2γ
p0
Module 1: Influenza incidence
• H studies reporting number ofpatients who get influenza (xh) inthe sample (mh)
• βh = population probability ofinfluenza (from study h)
logit(βh) = γh ∼ Normal(µγ , σγ)
• µγ ∼ Normal(0, v) = pooledaverage probability of infection (onlogit scale!)
⇒ p0 =exp(µγ)
[1 + exp(µγ)]
p1
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 11 / 39
Bayesian HTA in action — Decision analytic models (influenza)
xh
βh mh
γh
µγ σ2γ
p0
r(0)s
π(0)s n(0)
s
r(1)s
π(1)s n(1)
s
αs δs
µδ σ2δ
ρ
Module 2: Prophylaxis effectiveness
• S studies reporting number of
infected patients r(t)s in a sample
made of n(t)s subjects
• π(t)s = study- and
treatment-specific chance ofcontracting influenza
logit(π(0)s
)= αs ∼ Normal(0, 10)
logit(π(1)s
)= αs + δs
δs ∼ Normal(µδ, σδ) =study-specific treatment effect
• µδ ∼ Normal(0, v) = pooledlog-odds ratio of influenza giventreatment ⇒ ρ = exp(µδ)
p1
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 11 / 39
Bayesian HTA in action — Decision analytic models (influenza)
xh
βh mh
γh
µγ σ2γ
p0
r(0)s
π(0)s n(0)
s
r(1)s
π(1)s n(1)
s
αs δs
µδ σ2δ
ρ
p1Can combine modules 1 and 2
p1 =ρp0/(1− p0)
1 + ρp0/(1− p0)
h = 1, . . . , H s = 1, . . . , S
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 11 / 39
Bayesian HTA in action — Decision analytic models (influenza)
Inference for Bugs model at "EvSynth.txt",Current: 2 chains , each with 10000 iterations (first 9500 discarded), n.thin = 20Cumulative: n.sims = 1000 iterations saved
mean sd 2.5% 25% 50% 75% 97.5% Rhat n.effp0 = p1 0.059 0.023 0.024 0.045 0.056 0.071 0.113 1.004 460p1 = p2 0.013 0.008 0.004 0.008 0.012 0.016 0.031 1.006 440
...µc0 = mu.c[1] 20.000 0.412 19.360 19.730 19.940 20.190 20.971 1.001 1000µc1 = mu.c[2] 19.226 0.142 19.070 19.140 19.200 19.280 19.550 1.011 1000µe0 = mu.e[1] -0.489 0.203 -1.004 -0.589 -0.461 -0.353 -0.178 1.003 510µe1 = mu.e[2] -0.111 0.070 -0.267 -0.134 -0.097 -0.068 -0.030 1.009 970
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mu.e[1]
mu.
e[2]
−1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 0.0
−1.
0−
0.8
−0.
6−
0.4
−0.
20.
0
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mu.c[1]
mu.
c[2]
19 20 21 22 23
19.0
19.5
20.0
20.5
21.0
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 12 / 39
Bayesian approach to HTA
Statisticalmodel
Economicmodel
Decisionanalysis
Uncertaintyanalysis
• Estimates relevant populationparameters θ
• Varies with the type ofavailable data (& statisticalapproach!)
• Combines the parameters to obtaina population average measure forcosts and clinical benefits
• Varies with the type of availabledata & statistical model used
• Summarises the economic model bycomputing suitable measures of“cost-effectiveness”
• Dictates the best course of actions,given current evidence
• Standardised process
• Assesses the impact of uncertainty (egin parameters or model structure) onthe economic results
• Mandatory in many jurisdictions(including NICE, in the UK)
• Fundamentally Bayesian!
Estimation & PSA (one stage)
θ
yp(y | θ)
p(θ) p(θ | y)
“Integrated approach” Spiegelhalter, Abrams & Myles (2004)Baio, Berardi & Heath (2017)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 13 / 39
Bayesian approach to HTA [p(θ | y) vs gi(θi)]
Parameters Model structure Decision analysis
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 1.5 2.0
0.0 0.2 0.4 0.6 0.8 1.0
0 2000 6000 10000
π0
ρ
γ
chosp
Old chemotherapy
A0Ambulatory care
(γ)99K camb
SE0Blood-relatedside effects
(π0)
H0Hospital admission
(1 − γ)99Kchosp
cdrug0 L99N
Standardtreatment
A0Ambulatory care
(γ)99K camb
N − SE0No side effects
(1 − π0)
H0Hospital admission
(1 − γ)99Kchosp
New chemotherapy
A1Ambulatory care
(γ)99K camb
SE1Blood-relatedside effects(π1 = π0ρ)
H1Hospital admission
(1 − γ)99Kchosp
cdrug1 L99NNew
treatment
A1Ambulatory care
(γ)99K camb
N − SE1No side effects
(1 − π1)
H1Hospital admission
(1 − γ)99Kchosp
Old chemotherapyBenefits Costs
743.1 656 644.6
New chemotherapyBenefits Costs
743.1 656 644.6
ICER =276 468.6
58.3
ICER = 6 497.1
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 14 / 39
Bayesian approach to HTA [p(θ | y) vs gi(θi)]
Parameters Model structure Decision analysis
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 1.5 2.0
0.0 0.2 0.4 0.6 0.8 1.0
0 2000 6000 10000
π0
ρ
γ
chosp
x
x
x
x
Old chemotherapy
A0Ambulatory care
(γ)99K camb
SE0Blood-relatedside effects
(π0)
H0Hospital admission
(1 − γ)99Kchosp
cdrug0 L99N
Standardtreatment
A0Ambulatory care
(γ)99K camb
N − SE0No side effects
(1 − π0)
H0Hospital admission
(1 − γ)99Kchosp
New chemotherapy
A1Ambulatory care
(γ)99K camb
SE1Blood-relatedside effects(π1 = π0ρ)
H1Hospital admission
(1 − γ)99Kchosp
cdrug1 L99NNew
treatment
A1Ambulatory care
(γ)99K camb
N − SE1No side effects
(1 − π1)
H1Hospital admission
(1 − γ)99Kchosp
Old chemotherapyBenefits Costs
741 670 382.1
743.1 656 644.6
New chemotherapyBenefits Costs
732 1 131 978
743.1 656 644.6
ICER =276 468.6
58.3
ICER = 6 497.1
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 14 / 39
Bayesian approach to HTA [p(θ | y) vs gi(θi)]
Parameters Model structure Decision analysis
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 1.5 2.0
0.0 0.2 0.4 0.6 0.8 1.0
0 2000 6000 10000
π0
ρ
γ
chosp
x
x
x
x
Old chemotherapy
A0Ambulatory care
(γ)99K camb
SE0Blood-relatedside effects
(π0)
H0Hospital admission
(1 − γ)99Kchosp
cdrug0 L99N
Standardtreatment
A0Ambulatory care
(γ)99K camb
N − SE0No side effects
(1 − π0)
H0Hospital admission
(1 − γ)99Kchosp
New chemotherapy
A1Ambulatory care
(γ)99K camb
SE1Blood-relatedside effects(π1 = π0ρ)
H1Hospital admission
(1 − γ)99Kchosp
cdrug1 L99NNew
treatment
A1Ambulatory care
(γ)99K camb
N − SE1No side effects
(1 − π1)
H1Hospital admission
(1 − γ)99Kchosp
Old chemotherapyBenefits Costs
741 670 382.1699 871 273.3
New chemotherapyBenefits Costs
732 1 131 978664 1 325 654
ICER =276 468.6
58.3
ICER = 6 497.1
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 14 / 39
Bayesian approach to HTA [p(θ | y) vs gi(θi)]
Parameters Model structure Decision analysis
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.5 1.0 1.5 2.0
0.0 0.2 0.4 0.6 0.8 1.0
0 2000 6000 10000
π0
ρ
γ
chosp
x
x
x
x
Old chemotherapy
A0Ambulatory care
(γ)99K camb
SE0Blood-relatedside effects
(π0)
H0Hospital admission
(1 − γ)99Kchosp
cdrug0 L99N
Standardtreatment
A0Ambulatory care
(γ)99K camb
N − SE0No side effects
(1 − π0)
H0Hospital admission
(1 − γ)99Kchosp
New chemotherapy
A1Ambulatory care
(γ)99K camb
SE1Blood-relatedside effects(π1 = π0ρ)
H1Hospital admission
(1 − γ)99Kchosp
cdrug1 L99NNew
treatment
A1Ambulatory care
(γ)99K camb
N − SE1No side effects
(1 − π1)
H1Hospital admission
(1 − γ)99Kchosp
Old chemotherapyBenefits Costs
741 670 382.1699 871 273.3. . . . . .726 425 822.2
716.2 790 381.2
New chemotherapyBenefits Costs
732 1 131 978664 1 325 654. . . . . .811 766 411.4
774.5 1 066 849.8
ICER =276 468.6
58.3
ICER = 6 497.1
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 14 / 39
2. Economic modelling
Cost-effectiveness plane
Effectiveness differential
Cos
t diff
eren
tial
∆e
∆c
∆e = E[e | θ1]︸ ︷︷ ︸µe1
− E[e | θ0]︸ ︷︷ ︸µe0
∆c = E[c | θ1]︸ ︷︷ ︸µc1
− E[c | θ0]︸ ︷︷ ︸µc0
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 15 / 39
3. Decision analysis
Cost-effectiveness plane∆e = E[e | θ1]︸ ︷︷ ︸
µe1
− E[e | θ0]︸ ︷︷ ︸µe0
∆c = E[c | θ1]︸ ︷︷ ︸µc1
− E[c | θ0]︸ ︷︷ ︸µc0
Effectiveness differential
Cos
t diff
eren
tial
∆e
∆c
ICER =E[∆c]
E[∆e]=
E[µc1]− E[µc0]
E[µe1]− E[µe0]
= Cost per outcome
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 15 / 39
3./4. Decision analysis+Uncertainty analysis
Cost effectiveness plane
New Chemotherapy vs Old Chemotherapy
Effectiveness differential
Cost diffe
rential
−200 −100 0 100 200
−200000
0200000
600000
• ICER=6497.10
k = 1000
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 15 / 39
3./4. Decision analysis+Uncertainty analysis
Cost effectiveness plane
New Chemotherapy vs Old Chemotherapy
Effectiveness differential
Cost diffe
rential
−200 −100 0 100 200
−200000
0200000
600000
• ICER=6497.10
k = 25000
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 15 / 39
4. Uncertainty analysis — Cost-effectiveness acceptability curve
0 10000 20000 30000 40000 50000
0.0
0.2
0.4
0.6
0.8
1.0
Cost EffectivenessAcceptability Curve
Willingness to pay
Pro
babi
lity
of c
ost e
ffect
iven
ess
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 16 / 39
Advanced decision modelling 1. Multiparameter evidence synthesis
• Unusual for a policy question to be informed by a single study– Must use all available and relevant evidence
• Multiparameter evidence synthesis (often called Network Meta-Analysis)– Learning about more than one quantity from combination of direct and indirect
evidence
• Simplest example:– New treatment C: been trialled against old treatment B, but not to A– For health economic evaluation need to compare A/B/C together– ⇒ Learn about C/A effect from C/B and B/A trial data
• Also called mixed treatment comparisons– since can also “mix” direct and indirect data on same comparison
• Common in UK health technology assessment, but require some statistical skills
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 17 / 39
Smoking cessation trial data: network meta-analysis
Comparison A: No intervention B: Self-help C: Individual counselling D: Group counselling Baseline treatment
AB79/702 77/694 A18/671 21/535 A8/116 19/149 A
AC
75/731 363/714 A2/106 9/205 A58/549 237/1561 A0/33 9/48 A3/100 31/98 A1/31 26/95 A6/39 17/77 A64/642 107/761 A5/62 8/90 A20/234 34/237 A95/1107 143/1031 A15/187 36/504 A78/584 73/675 A69/1177 54/888 A
ACD 9/140 23/140 10/138 A
AD 0/20 9/20 A
BC 20/49 16/43 B
BCD 11/78 12/85 29/170 B
BD 7/66 32/127 B
CD12/76 20/74 C9/55 3/26 C
• 24 trials; outcome: successfully quit smoking by 6-12 months
• Network of comparisons involving 4 interventions
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 18 / 39
Network of comparisons: smoking cessation
A: Nointervention
D: Groupcounselling
B: Self-help
C: Individualcounselling
2 trials15 trials
3 trials
2 trials
4 trials
1 trial
N=12846
N=2867
N=318
N=255
N=441
N=764
• All comparisons haveat least one trial withdirect data
• We wish to enhancedirect with indirectevidence
• e.g. A-D comparison(2 direct trials)improved by includingA-C, C-D trials
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 19 / 39
Networks with missing direct comparisons
Treatment A
Treatment D
Treatment B
Treatment C
2 trials15 trials
3 trials
2 trials
?
?
• In other applications,might want to learnabout comparisonswith no direct trialevidence
• e.g. how much betterthan current treatmentC is new treatment D?
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 19 / 39
Results: Comparing direct and mixed evidence
Direct-only odds ratios (CIs) from classical analysis of pooled individual data
• Precision of D/A estimate improvedby indirect C/A, C/D data
• Strong direct data for othercomparisons, so not improved byindirect evidence
• C/B estimate from one direct study→ pulled towards much biggerindirect C/A, B/A data
– Evidence of heterogeneity —should consider “random effect”modelling. . .
Odds ratio
●
●
●
●
●
●
0 1 2 3 4 5
●
●
●
●
●
●
Pooled N
B: Self−help / A: None
C: Individual / A: None
D: Group / A: None
C: Individual / B: Self−help
D: Group / B: Self−help
D: Group / C: Individual
2867
12846
318
255
441
764
Fixed effects mixedFixed effects direct
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 20 / 39
Advanced decision modelling 2. Markov models
• Assess long-term cost-effectiveness based only on short-term data
• State-transition (usually Markov) models for clinical histories– Commonly implemented in Excel, or specialized software (e.g. TreeAge)
• Assume a set of S “clinically relevant” states– Exhaustive and mutually exclusive
• The structure (links among nodes) describes the dynamics of disease history– Arrows connecting two states encode the assumption that a transition from the one
where the arrow originates to the one reached by it is possible– Absence of an arrow between two states implies that the transition from one to the
other is not allowed by our model
• From one period to the next, subjects can move among the states according to therules specified by the arrows
• Movements occur according to suitable transition probabilities
πj = πj−1Λj
where– πj is the vector of probabilities for each state at time j– Λj = [Λj;s,s′ ] is a transition matrix describing the probability of moving from state s
to state s′ at time j
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 21 / 39
Advanced decision modelling 2. Markov models
• Assess long-term cost-effectiveness based only on short-term data
• State-transition (usually Markov) models for clinical histories– Commonly implemented in Excel, or specialized software (e.g. TreeAge)
• Assume a set of S “clinically relevant” states– Exhaustive and mutually exclusive
• The structure (links among nodes) describes the dynamics of disease history– Arrows connecting two states encode the assumption that a transition from the one
where the arrow originates to the one reached by it is possible– Absence of an arrow between two states implies that the transition from one to the
other is not allowed by our model
• From one period to the next, subjects can move among the states according to therules specified by the arrows
• Movements occur according to suitable transition probabilities
πj = πj−1Λj
where– πj is the vector of probabilities for each state at time j– Λj = [Λj;s,s′ ] is a transition matrix describing the probability of moving from state s
to state s′ at time j
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 21 / 39
Advanced decision modelling 2. Markov models
• Assess long-term cost-effectiveness based only on short-term data
• State-transition (usually Markov) models for clinical histories– Commonly implemented in Excel, or specialized software (e.g. TreeAge)
• Assume a set of S “clinically relevant” states– Exhaustive and mutually exclusive
• The structure (links among nodes) describes the dynamics of disease history– Arrows connecting two states encode the assumption that a transition from the one
where the arrow originates to the one reached by it is possible– Absence of an arrow between two states implies that the transition from one to the
other is not allowed by our model
• From one period to the next, subjects can move among the states according to therules specified by the arrows
• Movements occur according to suitable transition probabilities
πj = πj−1Λj
where– πj is the vector of probabilities for each state at time j– Λj = [Λj;s,s′ ] is a transition matrix describing the probability of moving from state s
to state s′ at time j
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 21 / 39
Advanced decision modelling 2. Markov models
1. Define a structure
Disease
In health Death
Recoveryxyyxxyyxxyyxxyyxxyyxyyxx
xyyxxyyxxyyxxyyxxyyxyyxx
xyyx
xy
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 22 / 39
Advanced decision modelling 2. Markov models
2. Estimate the transition probabilities
Disease
In health Death
Recovery
λ22
λ11
λ12 λ24
λ14λ44
λ23λ31 λ34
xyyxxyyxxyyxxyyxxyyxyyxx
xyyxxyyxxyyxxyyxxyyxyyxx
xyyx
xy
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 22 / 39
Advanced decision modelling 2. Markov models
3. Run the simulation: time j = 0
Disease
In health Death
Recovery
λ22
λ11
λ12 λ24
λ14λ44
λ23λ31 λ34
xyyxxyyxxyyxxyyxxyyxyyxx
xyyxxyyxxyyxxyyxxyyxyyxx
xyyx
xy
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 22 / 39
Advanced decision modelling 2. Markov models
3. Run the simulation: time j = 1
Disease
In health Death
Recovery
λ22
λ11
λ12 λ24
λ14λ44
λ23λ31 λ34
xyyxxyyxxyyxxyyxxyxyyxyx
xyyxxyyxxyyxxyyxxyyxyx
xyy
xy
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 22 / 39
Advanced decision modelling 2. Markov models
3. Run the simulation: time j = 2
Disease
In health Death
Recovery
λ22
λ11
λ12 λ24
λ14λ44
λ23λ31 λ34
xyyxxyyxxyyxxyyxxyxyyxyx
xyyxxyyxxyyxxyyxxyyxyx
xyxy
x
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 22 / 39
Advanced decision modelling 2. Markov models
3. Run the simulation: time j = 3
Disease
In health Death
Recovery
λ22
λ11
λ12 λ24
λ14λ44
λ23λ31 λ34
xyyxxyyxxyyxxyyxxyxyyxyx
xyyxxyyxxyyxxyyxxyyxyx
xyx
xx
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 22 / 39
Advanced decision modelling 2. Markov models
3. Run the simulation: time j = J
Disease
In health Death
Recovery
λ22
λ11
λ12 λ24
λ14λ44
λ23λ31 λ34
xyyxxyyxxyyxxyyxxyxyyxyx
xyyxxyyxxyyxxyyxxyyxyyxx
xyx
xx
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 22 / 39
Advanced decision modelling 2. Markov models
• MMs are very popular in modelling non-communicable diseases (eg cancer)
• Usually, they are run using (yet again...) a “hybrid” approach
1 Estimate relevant parameters (eg based on survival analysis), using proper statisticalsoftware (Stata, SAS, R,. . . )
2 Import/copy table of results in an Excel spreadsheet3 Use methods to approximate correlation across survival parameters (eg Cholesky
decomposition)4 Simulate a large number of survival curves (based on parameters simulations)5 Use the survival curves to determine the transition probabilities in the Markov model
• This is often a recipe for disaster!– Correlation among survival parameters crucial — need to properly account for that!– Mixing fdifferent software not always ideal– Programming Excel for MMs can be easy (for very simple models), but can become
highly inefficient!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 23 / 39
Advanced decision modelling 2. Markov models
• MMs are very popular in modelling non-communicable diseases (eg cancer)
• Usually, they are run using (yet again...) a “hybrid” approach1 Estimate relevant parameters (eg based on survival analysis), using proper statistical
software (Stata, SAS, R,. . . )
2 Import/copy table of results in an Excel spreadsheet3 Use methods to approximate correlation across survival parameters (eg Cholesky
decomposition)4 Simulate a large number of survival curves (based on parameters simulations)5 Use the survival curves to determine the transition probabilities in the Markov model
• This is often a recipe for disaster!– Correlation among survival parameters crucial — need to properly account for that!– Mixing fdifferent software not always ideal– Programming Excel for MMs can be easy (for very simple models), but can become
highly inefficient!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 23 / 39
Advanced decision modelling 2. Markov models
• MMs are very popular in modelling non-communicable diseases (eg cancer)
• Usually, they are run using (yet again...) a “hybrid” approach1 Estimate relevant parameters (eg based on survival analysis), using proper statistical
software (Stata, SAS, R,. . . )2 Import/copy table of results in an Excel spreadsheet
3 Use methods to approximate correlation across survival parameters (eg Choleskydecomposition)
4 Simulate a large number of survival curves (based on parameters simulations)5 Use the survival curves to determine the transition probabilities in the Markov model
• This is often a recipe for disaster!– Correlation among survival parameters crucial — need to properly account for that!– Mixing fdifferent software not always ideal– Programming Excel for MMs can be easy (for very simple models), but can become
highly inefficient!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 23 / 39
Advanced decision modelling 2. Markov models
• MMs are very popular in modelling non-communicable diseases (eg cancer)
• Usually, they are run using (yet again...) a “hybrid” approach1 Estimate relevant parameters (eg based on survival analysis), using proper statistical
software (Stata, SAS, R,. . . )2 Import/copy table of results in an Excel spreadsheet3 Use methods to approximate correlation across survival parameters (eg Cholesky
decomposition)
4 Simulate a large number of survival curves (based on parameters simulations)5 Use the survival curves to determine the transition probabilities in the Markov model
• This is often a recipe for disaster!– Correlation among survival parameters crucial — need to properly account for that!– Mixing fdifferent software not always ideal– Programming Excel for MMs can be easy (for very simple models), but can become
highly inefficient!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 23 / 39
Advanced decision modelling 2. Markov models
• MMs are very popular in modelling non-communicable diseases (eg cancer)
• Usually, they are run using (yet again...) a “hybrid” approach1 Estimate relevant parameters (eg based on survival analysis), using proper statistical
software (Stata, SAS, R,. . . )2 Import/copy table of results in an Excel spreadsheet3 Use methods to approximate correlation across survival parameters (eg Cholesky
decomposition)4 Simulate a large number of survival curves (based on parameters simulations)
5 Use the survival curves to determine the transition probabilities in the Markov model
• This is often a recipe for disaster!– Correlation among survival parameters crucial — need to properly account for that!– Mixing fdifferent software not always ideal– Programming Excel for MMs can be easy (for very simple models), but can become
highly inefficient!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 23 / 39
Advanced decision modelling 2. Markov models
• MMs are very popular in modelling non-communicable diseases (eg cancer)
• Usually, they are run using (yet again...) a “hybrid” approach1 Estimate relevant parameters (eg based on survival analysis), using proper statistical
software (Stata, SAS, R,. . . )2 Import/copy table of results in an Excel spreadsheet3 Use methods to approximate correlation across survival parameters (eg Cholesky
decomposition)4 Simulate a large number of survival curves (based on parameters simulations)5 Use the survival curves to determine the transition probabilities in the Markov model
• This is often a recipe for disaster!– Correlation among survival parameters crucial — need to properly account for that!– Mixing fdifferent software not always ideal– Programming Excel for MMs can be easy (for very simple models), but can become
highly inefficient!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 23 / 39
Advanced decision modelling 2. Markov models
• MMs are very popular in modelling non-communicable diseases (eg cancer)
• Usually, they are run using (yet again...) a “hybrid” approach1 Estimate relevant parameters (eg based on survival analysis), using proper statistical
software (Stata, SAS, R,. . . )2 Import/copy table of results in an Excel spreadsheet3 Use methods to approximate correlation across survival parameters (eg Cholesky
decomposition)4 Simulate a large number of survival curves (based on parameters simulations)5 Use the survival curves to determine the transition probabilities in the Markov model
• This is often a recipe for disaster!– Correlation among survival parameters crucial — need to properly account for that!– Mixing fdifferent software not always ideal– Programming Excel for MMs can be easy (for very simple models), but can become
highly inefficient!
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 23 / 39
Uncertainty analysis — beyond the CEAC
• Decision models usually contain a very large number of parameters — so it’simportant to fully assess the resulting uncertainty in the decision-making process
• BUT: the CEAC only deals with the probability of making the “right decision”
• But it does not account for the payoff/penalty associated with making the“wrong” one!
• Example 1: Intervention t = 1 is the most cost-effective, given current evidence– Pr(t = 1 is cost-effective) = 0.51– If we get it wrong: Increase in costs = £3
If we get it wrong: Decrease in effectiveness = 0.000001 QALYs– Large uncertainty/negligible consequences ⇒ can afford uncertainty
• Example 2: Intervention t = 1 is the most cost-effective, given current evidence– Pr(t = 1 is cost-effective) = 0.999– If we get it wrong: Increase in costs = £1 000 000 000
If we get it wrong: Decrease in effectiveness = 999999 QALYs– Tiny uncertainty/dire consequences ⇒ probably should think about it...
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 24 / 39
Uncertainty analysis — beyond the CEAC
• Decision models usually contain a very large number of parameters — so it’simportant to fully assess the resulting uncertainty in the decision-making process
• BUT: the CEAC only deals with the probability of making the “right decision”
• But it does not account for the payoff/penalty associated with making the“wrong” one!
• Example 1: Intervention t = 1 is the most cost-effective, given current evidence– Pr(t = 1 is cost-effective) = 0.51– If we get it wrong: Increase in costs = £3
If we get it wrong: Decrease in effectiveness = 0.000001 QALYs– Large uncertainty/negligible consequences ⇒ can afford uncertainty
• Example 2: Intervention t = 1 is the most cost-effective, given current evidence– Pr(t = 1 is cost-effective) = 0.999– If we get it wrong: Increase in costs = £1 000 000 000
If we get it wrong: Decrease in effectiveness = 999999 QALYs– Tiny uncertainty/dire consequences ⇒ probably should think about it...
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 24 / 39
Uncertainty analysis — beyond the CEAC
• Decision models usually contain a very large number of parameters — so it’simportant to fully assess the resulting uncertainty in the decision-making process
• BUT: the CEAC only deals with the probability of making the “right decision”
• But it does not account for the payoff/penalty associated with making the“wrong” one!
• Example 1: Intervention t = 1 is the most cost-effective, given current evidence– Pr(t = 1 is cost-effective) = 0.51– If we get it wrong: Increase in costs = £3
If we get it wrong: Decrease in effectiveness = 0.000001 QALYs– Large uncertainty/negligible consequences ⇒ can afford uncertainty
• Example 2: Intervention t = 1 is the most cost-effective, given current evidence– Pr(t = 1 is cost-effective) = 0.999– If we get it wrong: Increase in costs = £1 000 000 000
If we get it wrong: Decrease in effectiveness = 999999 QALYs– Tiny uncertainty/dire consequences ⇒ probably should think about it...
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 24 / 39
The rationale for PSA / research prioritisation
do not gather
additional data
keep
t = 0
switch to
t = 1
y
y
temporarily keep
t = 0 & gather
additional data
E
z
z
switch to
t = 1
keep
t = 0
D
u(y)
u(y)
u(z)
u(z)
decisions
random events
sampling costs
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 25 / 39
The rationale for PSA / research prioritisation
do not gather
additional data
keep
t = 0
switch to
t = 1
y
y
temporarily keep
t = 0 & gather
additional data
E
z
z
switch to
t = 1
keep
t = 0
D
u(y)
u(y)
u(z)
u(z)
decisions
random events
sampling costs
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 25 / 39
The rationale for PSA / research prioritisation
do not gather
additional data
keep
t = 0
switch to
t = 1
y
y
temporarily keep
t = 0 & gather
additional data
E
z
z
switch to
t = 1
keep
t = 0
D
u(y)
u(y)
u(z)
u(z)
decisions
random events
sampling costs
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 25 / 39
4. Uncertainty analysis Expected Value of Perfect Information
Parameters simulations Expected utility Maximum OpportunityIter/n π0 ρ . . . γ NB0(θ) NB1(θ) net benefit loss
1 0.365 0.076 . . . 0.162 19 214 751 19 647 706 19 647 706 0
2 0.421 0.024 . . . 0.134 17 165 526 17 163 407 17 165 526 2 119.3
3 0.125 0.017 . . . 0.149 18 710 928 16 458 433 18 710 928 2 252 495.5
4 0.117 0.073 . . . 0.120 16 991 321 18 497 648 18 497 648 0
5 0.481 0.008 . . . 0.191 19 772 898 18 662 329 19 772 898 1 110 569.3
6 0.163 0.127 . . . 0.004 17 106 136 18 983 331 18 983 331 0
. . . . . . . . . . . .
1000 0.354 0.067 . . . 0.117 18 043 921 16 470 805 18 043 921 1 573 116.0
Average 18 659 238 19 515 004 19 741 589 226 585
• Characterise uncertainty in the model parameters– In a full Bayesian setting, these are draws from the joint posterior distribution of θ– In a frequentist setting, these are typically Monte Carlo draws from a set of univariate
distributions that describe some level of uncertainty around MLEs (two-step/hybrid)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 26 / 39
4. Uncertainty analysis Expected Value of Perfect Information
Parameters simulations Expected utility Maximum OpportunityIter/n π0 ρ . . . γ NB0(θ) NB1(θ) net benefit loss
1 0.365 0.076 . . . 0.162 19 214 751 19 647 706 19 647 706 0
2 0.421 0.024 . . . 0.134 17 165 526 17 163 407 17 165 526 2 119.3
3 0.125 0.017 . . . 0.149 18 710 928 16 458 433 18 710 928 2 252 495.5
4 0.117 0.073 . . . 0.120 16 991 321 18 497 648 18 497 648 0
5 0.481 0.008 . . . 0.191 19 772 898 18 662 329 19 772 898 1 110 569.3
6 0.163 0.127 . . . 0.004 17 106 136 18 983 331 18 983 331 0
. . . . . . . . . . . .
1000 0.354 0.067 . . . 0.117 18 043 921 16 470 805 18 043 921 1 573 116.0
Average 18 659 238 19 515 004 19 741 589 226 585
• Uncertainty in the parameters induces a distribution of decisions– Typically based on the net benefits: NBt(θ) = kµet − µct– In each parameters configuration can identify the optimal strategy
• Averaging over the uncertainty in θ provides the overall optimal decision, givencurrent uncertainty (= choose the intervention associated with highestexpected utility)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 26 / 39
4. Uncertainty analysis Expected Value of Perfect Information
Parameters simulations Expected utility Maximum OpportunityIter/n π0 ρ . . . γ NB0(θ) NB1(θ) net benefit loss
1 0.365 0.076 . . . 0.162 19 214 751 19 647 706 19 647 706 0
2 0.421 0.024 . . . 0.134 17 165 526 17 163 407 17 165 526 2 119.3
3 0.125 0.017 . . . 0.149 18 710 928 16 458 433 18 710 928 2 252 495.5
4 0.117 0.073 . . . 0.120 16 991 321 18 497 648 18 497 648 0
5 0.481 0.008 . . . 0.191 19 772 898 18 662 329 19 772 898 1 110 569.3
6 0.163 0.127 . . . 0.004 17 106 136 18 983 331 18 983 331 0
. . . . . . . . . . . .
1000 0.354 0.067 . . . 0.117 18 043 921 16 470 805 18 043 921 1 573 116.0
Average 18 659 238 19 515 004 19 741 589 226 585
• Summarise uncertainty in the decision, eg via the Expected Value of “Perfect”Information (EVPI)
– Defined as the average Opportunity Loss– Can also be computed as the difference between the average maximum expected
utility under “perfect” information and the maximum expected utility overall —in formula:
EVPI = Eθ
[maxt
NBt(θ)
]−max
tEθ [NBt(θ)]
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 26 / 39
4. Uncertainty analysis Expected Value of Partial Perfect Information
• θ = all the model parameters; can be split into two subsets– The “parameters of interest” φ, e.g. prevalence of a disease, HRQL measures, length
of stay in hospital, ...– The “remaining parameters” ψ, e.g. cost of treatment with other established
medications,
• We are interested in quantifying the value of gaining more information on φ, whileleaving the current level of uncertainty on ψ unchanged
• In formulæ:– First, consider the expected utility (EU) if we were able to learn φ but not ψ– If we knew φ perfectly, best decision = the maximum of this EU– Of course we cannot learn φ perfectly, so take the expected value– And compare this with the maximum expected utility overall– This is the EVPPI!
EVPPI = Eφ
[maxt
Eψ|φ [NBt(θ)]
]−max
tEθ [NBt(θ)]
• That’s the difficult part!
– Can do nested Monte Carlo, but takes forever to get accurate results– Recent methods based on Gaussian Process regression very efficient
Strong et al (2014)Heath et al (2016)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 27 / 39
4. Uncertainty analysis Expected Value of Partial Perfect Information
• θ = all the model parameters; can be split into two subsets– The “parameters of interest” φ, e.g. prevalence of a disease, HRQL measures, length
of stay in hospital, ...– The “remaining parameters” ψ, e.g. cost of treatment with other established
medications,
• We are interested in quantifying the value of gaining more information on φ, whileleaving the current level of uncertainty on ψ unchanged
• In formulæ:– First, consider the expected utility (EU) if we were able to learn φ but not ψ
– If we knew φ perfectly, best decision = the maximum of this EU– Of course we cannot learn φ perfectly, so take the expected value– And compare this with the maximum expected utility overall– This is the EVPPI!
EVPPI = Eφ
[maxt
Eψ|φ [NBt(θ)]
]−max
tEθ [NBt(θ)]
• That’s the difficult part!
– Can do nested Monte Carlo, but takes forever to get accurate results– Recent methods based on Gaussian Process regression very efficient
Strong et al (2014)Heath et al (2016)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 27 / 39
4. Uncertainty analysis Expected Value of Partial Perfect Information
• θ = all the model parameters; can be split into two subsets– The “parameters of interest” φ, e.g. prevalence of a disease, HRQL measures, length
of stay in hospital, ...– The “remaining parameters” ψ, e.g. cost of treatment with other established
medications,
• We are interested in quantifying the value of gaining more information on φ, whileleaving the current level of uncertainty on ψ unchanged
• In formulæ:– First, consider the expected utility (EU) if we were able to learn φ but not ψ
– If we knew φ perfectly, best decision = the maximum of this EU– Of course we cannot learn φ perfectly, so take the expected value– And compare this with the maximum expected utility overall– This is the EVPPI!
EVPPI = Eφ
[maxt
Eψ|φ [NBt(θ)]
]−max
tEθ [NBt(θ)]
• That’s the difficult part!
– Can do nested Monte Carlo, but takes forever to get accurate results– Recent methods based on Gaussian Process regression very efficient
Strong et al (2014)Heath et al (2016)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 27 / 39
4. Uncertainty analysis Expected Value of Partial Perfect Information
• θ = all the model parameters; can be split into two subsets– The “parameters of interest” φ, e.g. prevalence of a disease, HRQL measures, length
of stay in hospital, ...– The “remaining parameters” ψ, e.g. cost of treatment with other established
medications,
• We are interested in quantifying the value of gaining more information on φ, whileleaving the current level of uncertainty on ψ unchanged
• In formulæ:– First, consider the expected utility (EU) if we were able to learn φ but not ψ– If we knew φ perfectly, best decision = the maximum of this EU
– Of course we cannot learn φ perfectly, so take the expected value– And compare this with the maximum expected utility overall– This is the EVPPI!
EVPPI = Eφ
[maxt
Eψ|φ [NBt(θ)]
]−max
tEθ [NBt(θ)]
• That’s the difficult part!
– Can do nested Monte Carlo, but takes forever to get accurate results– Recent methods based on Gaussian Process regression very efficient
Strong et al (2014)Heath et al (2016)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 27 / 39
4. Uncertainty analysis Expected Value of Partial Perfect Information
• θ = all the model parameters; can be split into two subsets– The “parameters of interest” φ, e.g. prevalence of a disease, HRQL measures, length
of stay in hospital, ...– The “remaining parameters” ψ, e.g. cost of treatment with other established
medications,
• We are interested in quantifying the value of gaining more information on φ, whileleaving the current level of uncertainty on ψ unchanged
• In formulæ:– First, consider the expected utility (EU) if we were able to learn φ but not ψ– If we knew φ perfectly, best decision = the maximum of this EU– Of course we cannot learn φ perfectly, so take the expected value
– And compare this with the maximum expected utility overall– This is the EVPPI!
EVPPI = Eφ
[maxt
Eψ|φ [NBt(θ)]
]−max
tEθ [NBt(θ)]
• That’s the difficult part!
– Can do nested Monte Carlo, but takes forever to get accurate results– Recent methods based on Gaussian Process regression very efficient
Strong et al (2014)Heath et al (2016)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 27 / 39
4. Uncertainty analysis Expected Value of Partial Perfect Information
• θ = all the model parameters; can be split into two subsets– The “parameters of interest” φ, e.g. prevalence of a disease, HRQL measures, length
of stay in hospital, ...– The “remaining parameters” ψ, e.g. cost of treatment with other established
medications,
• We are interested in quantifying the value of gaining more information on φ, whileleaving the current level of uncertainty on ψ unchanged
• In formulæ:– First, consider the expected utility (EU) if we were able to learn φ but not ψ– If we knew φ perfectly, best decision = the maximum of this EU– Of course we cannot learn φ perfectly, so take the expected value– And compare this with the maximum expected utility overall
– This is the EVPPI!
EVPPI = Eφ
[maxt
Eψ|φ [NBt(θ)]
]−max
tEθ [NBt(θ)]
• That’s the difficult part!
– Can do nested Monte Carlo, but takes forever to get accurate results– Recent methods based on Gaussian Process regression very efficient
Strong et al (2014)Heath et al (2016)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 27 / 39
4. Uncertainty analysis Expected Value of Partial Perfect Information
• θ = all the model parameters; can be split into two subsets– The “parameters of interest” φ, e.g. prevalence of a disease, HRQL measures, length
of stay in hospital, ...– The “remaining parameters” ψ, e.g. cost of treatment with other established
medications,
• We are interested in quantifying the value of gaining more information on φ, whileleaving the current level of uncertainty on ψ unchanged
• In formulæ:– First, consider the expected utility (EU) if we were able to learn φ but not ψ– If we knew φ perfectly, best decision = the maximum of this EU– Of course we cannot learn φ perfectly, so take the expected value– And compare this with the maximum expected utility overall– This is the EVPPI!
EVPPI = Eφ
[maxt
Eψ|φ [NBt(θ)]
]−max
tEθ [NBt(θ)]
• That’s the difficult part!– Can do nested Monte Carlo, but takes forever to get accurate results– Recent methods based on Gaussian Process regression very efficient
Strong et al (2014)Heath et al (2016)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 27 / 39
4. Uncertainty analysis Expected Value of Sample Information
EVSI = Eθ,d|θ
maxt
Eθ|d [NBt(θ)]︸ ︷︷ ︸Value of decision based on
sample information(for a given study design)
− max
tEθ [NBt∗(θ)]︸ ︷︷ ︸
Value of decision based oncurrent information
Prior predictivedistribution
(pre-posterior)
Posterior given data d
• Computationally complex– Requires specific knowledge of the model for (future/hypothetical) data collection– Again, recent methods have improved efficiency
• Can be used to drive design of new study (eg sample size calculations)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 28 / 39
4. Uncertainty analysis Expected Value of Sample Information
●
0 500 1000 1500
0.0
0.5
1.0
1.5
Sample Size
Per
Per
son
EV
SI
0.0250.250.50.750.975EVPPI
5 10 15 20 250
2000
4000
6000
8000
1000
0
Probability of Cost−Effective Trial
Time Horizon
Inci
denc
e P
opul
atio
n
Prob=0
Prob=.5
Prob=1
https://github.com/giabaio/EVSI
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 29 / 39
4. Uncertainty analysis Expected Value of Sample Information
20 40 60 80 100 120 140
−60
0−
400
−20
00
200
400
Economic Value of Study
Sample Size of XN
Eco
nom
ic v
alue
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 29 / 39
General (Bayesian) process of HTA
NStandardtreatment
N − SEt
No side effects(1− πt)
SEt
Blood-relatedside effects
(πt)
At
Ambulatory care(γ)
SEt −At
Hospital admission(1− γ)
et = 0, ct = cdrugt + camb
et = 0, ct = cdrugt + chosp
et = 1, ct = cdrugt
Economic outcomes
⇒
# JAGS model (saved to ‘modelChemo.txt’)model {
pi[1] ∼ dbeta(a.pi,b.pi)pi[2] <- pi[1]*rhorho ∼ dnorm(m.rho,tau.rho)gamma ∼ dbeta(a.gamma,b.gamma)c.amb ∼ dlnorm(m.amb,tau.amb)c.hosp ∼ dlnorm(m.hosp,tau.hosp)for (t in 1:2) {
SE[t] ∼ dbin(pi[t],N)A[t] ∼ dbin(gamma,SE[t])H[t] <- SE[t] - A[t]
}}
⇓
# Creates the variables of cost & effectivenesse <- c <- matrix(NA,1000,2)e <- N - SEfor (t in 1:2) {
c[,t] <- c.drug[t]*(N-SE[,t]) +(c.amb+c.drug[t])*A[,t] +(c.hosp+c.drug[t])*H[,t]
}
⇐
# Calls JAGS in background to run the modellibrary(R2jags)data <- list("a.pi","b.pi","a.gamma","b.gamma",
"m.amb","tau.amb","m.hosp","tau.hosp","m.rho","tau.rho","N")
filein <- "modelChemo.txt"params <- c("pi","gamma","c.amb","c.hosp",
"rho","SE","A","H")inits <- function()
list(pi=c(runif(1),NA),gamma=runif(1),c.amb=rlnorm(1),c.hosp=rlnorm(1),rho=runif(1))
chemo <- jags(data,inits,params,n.iter=20000,model.file=filein,n.chains=2,n.burnin=9500,n.thin=42,DIC=FALSE)
print(chemo,digits=3,intervals=c(0.025, 0.975))attach.jags(chemo)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 30 / 39
General (Bayesian) process of HTA
NStandardtreatment
N − SEt
No side effects(1− πt)
SEt
Blood-relatedside effects
(πt)
At
Ambulatory care(γ)
SEt −At
Hospital admission(1− γ)
et = 0, ct = cdrugt + camb
et = 0, ct = cdrugt + chosp
et = 1, ct = cdrugt
Economic outcomes
⇒
# JAGS model (saved to ‘modelChemo.txt’)model {
pi[1] ∼ dbeta(a.pi,b.pi)pi[2] <- pi[1]*rhorho ∼ dnorm(m.rho,tau.rho)gamma ∼ dbeta(a.gamma,b.gamma)c.amb ∼ dlnorm(m.amb,tau.amb)c.hosp ∼ dlnorm(m.hosp,tau.hosp)for (t in 1:2) {
SE[t] ∼ dbin(pi[t],N)A[t] ∼ dbin(gamma,SE[t])H[t] <- SE[t] - A[t]
}}
⇓
# Creates the variables of cost & effectivenesse <- c <- matrix(NA,1000,2)e <- N - SEfor (t in 1:2) {
c[,t] <- c.drug[t]*(N-SE[,t]) +(c.amb+c.drug[t])*A[,t] +(c.hosp+c.drug[t])*H[,t]
}
⇐
# Calls JAGS in background to run the modellibrary(R2jags)data <- list("a.pi","b.pi","a.gamma","b.gamma",
"m.amb","tau.amb","m.hosp","tau.hosp","m.rho","tau.rho","N")
filein <- "modelChemo.txt"params <- c("pi","gamma","c.amb","c.hosp",
"rho","SE","A","H")inits <- function()
list(pi=c(runif(1),NA),gamma=runif(1),c.amb=rlnorm(1),c.hosp=rlnorm(1),rho=runif(1))
chemo <- jags(data,inits,params,n.iter=20000,model.file=filein,n.chains=2,n.burnin=9500,n.thin=42,DIC=FALSE)
print(chemo,digits=3,intervals=c(0.025, 0.975))attach.jags(chemo)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 30 / 39
General (Bayesian) process of HTA
NStandardtreatment
N − SEt
No side effects(1− πt)
SEt
Blood-relatedside effects
(πt)
At
Ambulatory care(γ)
SEt −At
Hospital admission(1− γ)
et = 0, ct = cdrugt + camb
et = 0, ct = cdrugt + chosp
et = 1, ct = cdrugt
Economic outcomes
⇒
# JAGS model (saved to ‘modelChemo.txt’)model {
pi[1] ∼ dbeta(a.pi,b.pi)pi[2] <- pi[1]*rhorho ∼ dnorm(m.rho,tau.rho)gamma ∼ dbeta(a.gamma,b.gamma)c.amb ∼ dlnorm(m.amb,tau.amb)c.hosp ∼ dlnorm(m.hosp,tau.hosp)for (t in 1:2) {
SE[t] ∼ dbin(pi[t],N)A[t] ∼ dbin(gamma,SE[t])H[t] <- SE[t] - A[t]
}}
⇓
# Creates the variables of cost & effectivenesse <- c <- matrix(NA,1000,2)e <- N - SEfor (t in 1:2) {
c[,t] <- c.drug[t]*(N-SE[,t]) +(c.amb+c.drug[t])*A[,t] +(c.hosp+c.drug[t])*H[,t]
}
⇐
# Calls JAGS in background to run the modellibrary(R2jags)data <- list("a.pi","b.pi","a.gamma","b.gamma",
"m.amb","tau.amb","m.hosp","tau.hosp","m.rho","tau.rho","N")
filein <- "modelChemo.txt"params <- c("pi","gamma","c.amb","c.hosp",
"rho","SE","A","H")inits <- function()
list(pi=c(runif(1),NA),gamma=runif(1),c.amb=rlnorm(1),c.hosp=rlnorm(1),rho=runif(1))
chemo <- jags(data,inits,params,n.iter=20000,model.file=filein,n.chains=2,n.burnin=9500,n.thin=42,DIC=FALSE)
print(chemo,digits=3,intervals=c(0.025, 0.975))attach.jags(chemo)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 30 / 39
General (Bayesian) process of HTA
NStandardtreatment
N − SEt
No side effects(1− πt)
SEt
Blood-relatedside effects
(πt)
At
Ambulatory care(γ)
SEt −At
Hospital admission(1− γ)
et = 0, ct = cdrugt + camb
et = 0, ct = cdrugt + chosp
et = 1, ct = cdrugt
Economic outcomes
⇒
# JAGS model (saved to ‘modelChemo.txt’)model {
pi[1] ∼ dbeta(a.pi,b.pi)pi[2] <- pi[1]*rhorho ∼ dnorm(m.rho,tau.rho)gamma ∼ dbeta(a.gamma,b.gamma)c.amb ∼ dlnorm(m.amb,tau.amb)c.hosp ∼ dlnorm(m.hosp,tau.hosp)for (t in 1:2) {
SE[t] ∼ dbin(pi[t],N)A[t] ∼ dbin(gamma,SE[t])H[t] <- SE[t] - A[t]
}}
⇓
# Creates the variables of cost & effectivenesse <- c <- matrix(NA,1000,2)e <- N - SEfor (t in 1:2) {
c[,t] <- c.drug[t]*(N-SE[,t]) +(c.amb+c.drug[t])*A[,t] +(c.hosp+c.drug[t])*H[,t]
}
⇐
# Calls JAGS in background to run the modellibrary(R2jags)data <- list("a.pi","b.pi","a.gamma","b.gamma",
"m.amb","tau.amb","m.hosp","tau.hosp","m.rho","tau.rho","N")
filein <- "modelChemo.txt"params <- c("pi","gamma","c.amb","c.hosp",
"rho","SE","A","H")inits <- function()
list(pi=c(runif(1),NA),gamma=runif(1),c.amb=rlnorm(1),c.hosp=rlnorm(1),rho=runif(1))
chemo <- jags(data,inits,params,n.iter=20000,model.file=filein,n.chains=2,n.burnin=9500,n.thin=42,DIC=FALSE)
print(chemo,digits=3,intervals=c(0.025, 0.975))attach.jags(chemo)
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 30 / 39
BCEA: a package for Bayesian cost-effectiveness analysis
What is BCEA not?
• BCEA is not a package to automatically run a Bayesian analysis– It cannot build the health economic model for you– It does not prepare the data to be used in the model– It does not automatically run the MCMC simulations– It does not choose the prior distributions for you
So what is it, then?
• BCEA provides a set of specific functions to systematically post-process the outputof a (Bayesian) health economic model
• Uses R (http://cran.r-project.org/)– Very good at interacting with standard MCMC software• BUGS (www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml)• JAGS (www.mcmc-jags.sourceforge.net/)• Stan (http://mc-stan.org/users/interfaces/rstan)
– Free and there is a very large community of contributors– Specifically designed for statistical analysis and has very good graphical capabilities
http://www.statistica.it/gianluca/BCEA
https://github.com/giabaio/BCEA
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 31 / 39
BCEA: a package for Bayesian cost-effectiveness analysis
What is BCEA not?
• BCEA is not a package to automatically run a Bayesian analysis– It cannot build the health economic model for you– It does not prepare the data to be used in the model– It does not automatically run the MCMC simulations– It does not choose the prior distributions for you
So what is it, then?
• BCEA provides a set of specific functions to systematically post-process the outputof a (Bayesian) health economic model
• Uses R (http://cran.r-project.org/)– Very good at interacting with standard MCMC software• BUGS (www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml)• JAGS (www.mcmc-jags.sourceforge.net/)• Stan (http://mc-stan.org/users/interfaces/rstan)
– Free and there is a very large community of contributors– Specifically designed for statistical analysis and has very good graphical capabilities
http://www.statistica.it/gianluca/BCEA
https://github.com/giabaio/BCEA
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 31 / 39
The R package BCEA — Baio et al (2017)
bcea
plot
• ceplane.plot• contour• contour2• ceac.plot• evi.plot• eib.plot
• ib.plot
summary
evppiCreateInputsstruct.psa
plot
diag.evppi
multi.ce
mce.plot
ceaf.plot
ceef.plot
CEriskav plot
mixedAn
plot
summary
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 32 / 39
SAVI — http://savi.shef.ac.uk/SAVI/
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 33 / 39
BCEAweb — https://egon.stats.ucl.ac.uk/projects/BCEAweb/
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 34 / 39
Let’s go all the way?...
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 35 / 39
Let’s go all the way?...
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 35 / 39
Conclusions
• Bayesian modelling particularly effective in health economic evaluations
• Allows the incorporation of external, additional information to the current analysis– Previous studies– Elicitation of expert opinions
• In general, Bayesian models are more flexible and allow the inclusion of complexrelationships between variables and parameters
– This is particularly effective in decision-models, where information from differentsources may be combined into a single framework
– Useful in the case of individual-level data (eg from Phase III RCT)
• Using MCMC methods, it is possible to produce the results in terms of simulationsfrom the posterior distributions
– These can be used to build suitable variables of cost and benefit– Particularly effective for running “probabilistic sensitivity analysis”
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 36 / 39
Conclusions
• Bayesian modelling particularly effective in health economic evaluations
• Allows the incorporation of external, additional information to the current analysis– Previous studies– Elicitation of expert opinions
• In general, Bayesian models are more flexible and allow the inclusion of complexrelationships between variables and parameters
– This is particularly effective in decision-models, where information from differentsources may be combined into a single framework
– Useful in the case of individual-level data (eg from Phase III RCT)
• Using MCMC methods, it is possible to produce the results in terms of simulationsfrom the posterior distributions
– These can be used to build suitable variables of cost and benefit– Particularly effective for running “probabilistic sensitivity analysis”
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 36 / 39
Conclusions
• Bayesian modelling particularly effective in health economic evaluations
• Allows the incorporation of external, additional information to the current analysis– Previous studies– Elicitation of expert opinions
• In general, Bayesian models are more flexible and allow the inclusion of complexrelationships between variables and parameters
– This is particularly effective in decision-models, where information from differentsources may be combined into a single framework
– Useful in the case of individual-level data (eg from Phase III RCT)
• Using MCMC methods, it is possible to produce the results in terms of simulationsfrom the posterior distributions
– These can be used to build suitable variables of cost and benefit– Particularly effective for running “probabilistic sensitivity analysis”
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 36 / 39
Shameless self marketing
Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 37 / 39
Some references
Baio, G. (2012).
Bayesian Methods in Health Economics.Chapman Hall, CRC Press, Boca Raton, FL.(https://www.crcpress.com/Bayesian-Methods-in-Health-Economics/Baio/p/book/9781439895559)
Baio, G., A. Berardi, and A. Heath (2017).
Bayesian Cost-Effectiveness Analysis with the R package BCEA.Springer, New York, NY. (http://www.springer.com/gp/book/9783319557168)
Briggs, A., M. Sculpher, and K. Claxton (2006).
Decision modelling for health economic evaluation.Oxford University Press, Oxford, UK.
Heath, A., I. Manolopoulou, and G. Baio (2016).
Estimating the expected value of partial perfect information in health economic evaluations using Integrated NestedLaplace Approximation.Statistics in Medicine 35(23), 4264-4280.
Spiegelhalter, D., K. Abrams, and J. Myles (2004).
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Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 38 / 39
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Gianluca Baio (UCL) Modelli decisionali in HTA – Part I Congresso BIAS, 29 Sep 2017 39 / 39