Estimating the cost-effectiveness of an intervention in a clinical trial when partial cost...

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)

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Model 2

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Model 3


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Model 4


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Model 5


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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


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Model 2


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Model 3


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Model 4


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Model 5


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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)




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


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Model 2


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Model 3


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Model 4


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Model 5


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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


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Model 2


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Model 3


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Model 4


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Model 5


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Model 3a

Model 3c


Model 3bCost: n = 115, Clinical: n = 351

Model 1


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Model 2


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Model 3


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Model 4


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Model 5


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Model 3a

Model 3b Model 3c


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)




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/

Estimating the cost-effectiveness of an intervention in a clinical trial when partial cost...

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