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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 5 th World iHEA Congress, Barcelona, July 2005

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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)

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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+PAL Chemotherapy + palliative care PAL Standard 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)

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MIC2 COSTINGS STUDY Billingham 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

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MISSING DATA PROBLEM 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

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COST DATA DESCRIPTION

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MODELLING DETAILS All models estimated using Markov chain Monte Carlo methods using WinBUGS All prior distributions intended to be vague

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MODEL 1: Complete case Re-parameterisation of O’Hagan et al.(2001): Assumes survival and cost have a bivariate Normal distribution Applied to only patients with complete cost & effectiveness data where S gi denotes the survival time for the i th individual in the g th treatment group & C gi the corresponding total cost.

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MODEL 1 (cont.) Difference in mean survival time & cost between treatment groups calculated & incremental net monetary benefit statistic calculated for different values of A plot of the sampled values of the survival & cost difference produces the cost-effectiveness plane An acceptability curve can also be constructed

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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

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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

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PAL GroupCT Group Cost Components GP HospitalHospiceTreatment Total Cost Total Cost Survival Time Survival Time Net Monetary Benefit Survival Difference Cost Difference

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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

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MODEL 2 (cont.) The mean total cost for an individual in each treatment group is then calculated As before, the difference between groups for survival time and cost is then calculated and a cost-effectiveness plane, etc. constructed

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Cost: n = 82, Clinical: n = 82 Cost: n = 115, Clinical: n = 115

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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)

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MODEL 3: DISTRIBUTION OF HOSPICE COST

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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)

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Model 3a Model 3bModel 3c Cost: n = 82, Clinical: n = 82 Cost: n = 115, Clinical: n = 115

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Model 3a Model 3c Cost: n = 82, Clinical: n = 82 Cost: n = 115, Clinical: n = 115 Model 3b Cost: n = 115, Clinical: n = 351

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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 = 351Cost: n = 351, Clinical: n = 351

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ACCEPTABILITY CURVES FOR MODELS Model 1 Model 2 Model 3a Model 3b Model 3c £2000

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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)

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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/

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