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Estimating the cost-effectiveness of an
intervention in a clinical trial when partial cost
information is available: A Bayesian approach
Nicola Cooper Centre for Biostatics and Genetic Epidemiology, Department of Health
Science,University of Leicester, UK
Co-authors:
Paul Lambert, Alex Sutton, Keith Abrams (Centre for Biostatics and Genetic Epidemiology, Department of Health Science,University of Leicester, UK),
Cindy Billingham (Cancer Research UK Trials Unit, University of Birmingham, UK)
Econometric Methods for Correcting for Missing Cost & Utilization Data 5th World iHEA Congress, Barcelona, July 2005
OBJECTIVE
• Assess cost-effectiveness when partial or no cost data is available for some individuals randomised into a trial
• Develop a Bayesian model to address:– Complexities of missing cost component
data– Interrelationships between cost and
survival – Semi-continuous distribution of cost data
(proportion have zero cost)
BACKGROUND TO THE MIC2 TRIAL
Cullen MH, Billingham LJ et al (1999) J ClinOncol ; 17: 3188-3194
Extensive stage non-small cell lung cancer
Randomise 11/88 - 03/96: 351 eligible patients
CT+PALChemotherapy + palliative care
PALStandard palliative care
Primary endpoint: survival,Secondary endpoints: response, toxicity, QoL
Results: CT+PAL gave a median additional 2 months extra survival time (p=0.03)
MIC2 COSTINGS STUDYBillingham LJ, et al. Patterns, costs and cost-effectiveness of care in a trial of
chemotherapy for advanced non-small cell lung cancer. Lung Cancer 2002; 37: 219-225.
• Retrospective study initiated in 1995• Subgroup of 116 West Midlands patients• Aim: examine patterns of care and costs on
both treatment arms• Timeframe: trial entry to death• Perspective: health service• Details of care obtained from hospital, GP
and hospice notes • Full details obtained for 82 patients
Note: Treatment cost component available for most trial patients
MISSING DATA PROBLEM
TOTAL Treatment Hospital GP Hospice N
82 (71%) 5 (4%) 6 (5%) 2 (2%) 13 (11%) 7 (6%) 1 (1%)
• Retrospective design missing patient notes 34 patients have at least one cost component missing and hence total cost missing
Survival time data available for all 351 patients in trial
All patients, except 7, dead at time of analysis
COST DATA DESCRIPTION
Treatment Hospital GP Hospice N 115 89 93 103
N with zero cost 12 (10%) 0 2 (2%) 65 (63%) Minimum (£) 115 63 18 64 Maximum (£) 4002 15444 1206 10250
Median (£) 1035 2028 216 0 (all data) 1625 (non-zero data)
Mean (£) 1208 2976 303 915 (all data) 2479 (non-zero data)
SD (£) 870 3050 273 2043 (all data) 2742 (non-zero data)
MODELLING DETAILS
• All models estimated using Markov chain Monte Carlo methods using WinBUGS
• All prior distributions intended to be vague
MODEL 1: Complete case• Re-parameterisation of O’Hagan et al.(2001): Assumes survival and cost have a bivariate Normal distribution
2CCS
CS2S
C
S
gi
gi
gg
gg
g
g ,N~C
S
• Applied to only patients with complete cost & effectiveness data
where Sgi denotes the survival time for the ith individual in the gth treatment group & Cgi the corresponding total cost.
MODEL 1 (cont.)
• Difference in mean survival time & cost between treatment groups calculated & incremental net monetary benefit statistic calculated for different values of
1212
INMB CCSS
•A plot of the sampled values of the survival & cost difference produces the cost-effectiveness plane
•An acceptability curve can also be constructed
Model 1
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 2
Difference in Mean Survival (months)D
iffe
ren
ce in
Me
an
Co
st (
tho
usa
nd
s o
f £
)
-5 0 5
02
46
SE
NENW
SW
Model 3
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 4
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 5
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
NE - CT more effective, but more costlySE - CT more effective and less costlySW - PAL more effective, but more costlyNW - PAL more effective and less costly
Cost: n = 82, Clinical: n = 82
NE - CT more effective, but more costly
SE - CT more effective and less costly
SW - PAL more effective, but more costly
NW - PAL more effective and less costly
Model N for Costs
N for Survival
Difference in Cost
(000’s of £) (95% CrI)
Difference in Survival (months) (95% CrI)
Prob CE at £2000 per additional month of
life 1 Complete Case
82 82 2.79
(1.21 to 4.35) -0.35
(-3.64 to 3.03) 0.16
MODEL 2: Modelling missing cost components assuming multivariate normality
• Total cost split into 4 component costs: Treatment (TRT), GP, Hospital (HL), Hospice (HL).
• Models the joint distribution of the 4 cost components and survival
• Expressed as 5 interrelated conditional univariate distributions
• Applied to all patients in the economic sub-study
)()|(
),|(),,|(
),,,|(),,,,(
SPSCP
SCCPSCCCP
SCCCCPSCCCCP
TRT
TRTGP
TRTGPHL
TRTGPHLHCTRTGPHLHC
PAL GroupCT Group
Cost Components
GP Hospital HospiceTreatment
TotalCost
TotalCost
SurvivalTime
SurvivalTime
Net MonetaryBenefit
SurvivalDifference
CostDifference
MODEL 2 (cont.)
• The interrelationship between each cost component & survival is allowed to vary between the two treatment groups, as is the variance of the cost components
• The interrelationship between the cost components is the same in both treatment groups
• All variables centred at their mean; thus 11, 11,
11, & 11 are the mean costs for treatment, GP,
hospital and hospice respectively
MODEL 2 (cont.)
•The mean total cost for an individual in each treatment group is then calculated
21212121
11111111
2
1
δβαφμ
δβαφμ
C
C
+++=
+++=
• As before, the difference between groups for survival time and cost is then calculated and a cost-effectiveness plane, etc. constructed
Model 1
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 2
Difference in Mean Survival (months)D
iffe
ren
ce in
Me
an
Co
st (
tho
usa
nd
s o
f £
)-5 0 5
02
46
SE
NENW
SW
Model 3
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 4
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 5
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
NE - CT more effective, but more costlySE - CT more effective and less costlySW - PAL more effective, but more costlyNW - PAL more effective and less costly
Cost: n = 82, Clinical: n = 82 Cost: n = 115, Clinical: n = 115
Model N for Costs
N for Survival
Difference in Cost
(000’s of £) (95% CrI)
Difference in Survival (months) (95% CrI)
Prob CE at £2000 per additional month of
life 1 Complete Case
82 82 2.79
(1.21 to 4.35) -0.35
(-3.64 to 3.03) 0.16
2 Normal for all cost components
115 115 2.79
(1.34 to 4.31) 1.57
(-2.06 to 5.09) 0.54
MODEL 3: Incorporation of semi-continuous distribution for one of the
cost components• As Model 2 but a hurdle (delta or two-part) model is applied to the Hospice cost component (Cooper et al. MDM 2003)
Considerable proportion (63%) of patients had zero cost for hospice (i.e. they did not go to one)
Models the probability the hospice cost is zero using logistic regression
Then fits a linear regression model to the positive values
Predicted cost for an individual is given by the expected cost (obtained from linear model) multiplied by probability of incurring a cost (obtained from logistic model)
MODEL 3: DISTRIBUTION OF HOSPICE
COST
0 2 4 6 8 10
02
04
06
08
0
Hospice Cost
MODEL 3: DATASETS
• Model 3a: all patients in the economic sub-study (n=115)
• Model 3b: all patients in the economic sub-study for costs (n=115) and all trial patients for effectiveness (n=351)
• Model 3c: All trial participants to estimate both cost (n=351) and effect (n=351)
Model 1
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 2
Difference in Mean Survival (months)D
iffe
ren
ce in
Me
an
Co
st (
tho
usa
nd
s o
f £
)-5 0 5
02
46
SE
NENW
SW
Model 3
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 4
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 5
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
NE - CT more effective, but more costlySE - CT more effective and less costlySW - PAL more effective, but more costlyNW - PAL more effective and less costly
Model 3a
Model 3b Model 3c
Cost: n = 82, Clinical: n = 82 Cost: n = 115, Clinical: n = 115 Cost: n = 115, Clinical: n = 115
Model 1
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 2
Difference in Mean Survival (months)D
iffe
ren
ce in
Me
an
Co
st (
tho
usa
nd
s o
f £
)-5 0 5
02
46
SE
NENW
SW
Model 3
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 4
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 5
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
NE - CT more effective, but more costlySE - CT more effective and less costlySW - PAL more effective, but more costlyNW - PAL more effective and less costly
Model 3a
Model 3c
Cost: n = 82, Clinical: n = 82 Cost: n = 115, Clinical: n = 115 Cost: n = 115, Clinical: n = 115
Model 3bCost: n = 115, Clinical: n = 351
Model 1
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 2
Difference in Mean Survival (months)D
iffe
ren
ce in
Me
an
Co
st (
tho
usa
nd
s o
f £
)-5 0 5
02
46
SE
NENW
SW
Model 3
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 4
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
Model 5
Difference in Mean Survival (months)
Diff
ere
nce
in M
ea
n C
ost
(th
ou
san
ds
of
£)
-5 0 5
02
46
SE
NENW
SW
NE - CT more effective, but more costlySE - CT more effective and less costlySW - PAL more effective, but more costlyNW - PAL more effective and less costly
Model 3a
Model 3b Model 3c
Cost: n = 82, Clinical: n = 82 Cost: n = 115, Clinical: n = 115 Cost: n = 115, Clinical: n = 115
Cost: n = 115, Clinical: n = 351 Cost: n = 351, Clinical: n = 351
Model N for Costs
N for Survival
Difference in Cost
(000’s of £) (95% CrI)
Difference in Survival (months) (95% CrI)
Prob CE at £2000 per additional month of
life 1 Complete Case
82 82 2.79
(1.21 to 4.35) -0.35
(-3.64 to 3.03) 0.16
2 Normal for all cost components
115 115 2.79
(1.34 to 4.31) 1.57
(-2.06 to 5.09) 0.54
3a Hurdle model for hospice cost
115 115 2.79
(1.30 to 4.26) 1.61
(-1.97 to 5.23) 0.56
3b Including all survival data.
115 351 2.76
(1.28 to 4.25) 2.07
(0.35 to 3.87) 0.76
3c Including all Patient Data
351 351 2.59
(1.51 to 3.71) 2.07
(0.31 to 3.86) 0.79
ACCEPTABILITY CURVES FOR MODELS
Cost per Additional Month of Life
P(C
ost
Effe
ctiv
e)
0 5000 10000 15000 20000 25000 30000
0.0
0.2
0.4
0.6
0.8
1.0
Model 1Model 2Model 3Model 4Model 5
Model 1Model 2Model 3aModel 3bModel 3c
£2000
CONCLUSIONS
• Design & analysis of cost studies is important
• Maximise information use taking into account parameter uncertainty
• MCMC very flexible for these complex models
• Much simpler if no missing data! (But often unrealistic)
FURTHER ISSUES• Other distributions/transformations for cost
data• Breaking down cost components to item
use?– Too many parameters?
• Take account of censoring
• Adding other covariates
• Incorporate Quality of Life (in this example measured on a different sub-sample)
Copy of slides available at: http://www.hs.le.ac.uk/personal/njc21/