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Generalisable regression methods for costeffectiveness using copulas

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  • Casey Quinn
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    Abstract

    Objectives: Covariate explanation of clinical trial cost and outcome is critical to allow reliable estimates of cost-effectiveness. The ordinary simultaneous equations approach however must specify a bivariate distribution for both cost and health outcome that is not typically a product of the best-fitting marginal distribution of each. This paper advocates estimating costs and outcomes simultaneously using copulas to model conditional dependence. The copula is a function that maps univariate marginal distributions of any to some joint distribution. Methods- Copulas are used to fit the bivariate distribution of the simultaneous model for individual cost and outcome in a clinical trial for hysterectomy. These are used to generate counter-factual outcomes and individual-level incremental net benefits due to each procedure, as well as replicating non-parametric techniques for comparison with standard methods. Results- Parametric results from the use of copulas compared to an ordinary Seemingly Unrelated Regression model show better fit with consistent estimates, allowing for the fact that the data is drawn from an underpowered clinical trial. Results also show that estimated coefficients vary in size, sign and statistical significance in different arms of the clinical trial. Non-parametric results compared with standard cost-effectiveness techniques also show more precise estimates of incremental net benefit. Conclusions- Regression-based approaches to cost-effectiveness have the potential to overcome a lot of the limiting assumptions made using non-parametric approaches. By using known information on covariates we can get more precise estimates of the parameters used in standard cost-effectiveness analysis, more precise posterior information and more precise posterior probabilities. Using copulas generates more precise estimation of conditionally-dependent marginal effects.

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    Bibliographic Info

    Paper provided by HEDG, c/o Department of Economics, University of York in its series Health, Econometrics and Data Group (HEDG) Working Papers with number 05/13.

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    Date of creation: Nov 2005
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    Handle: RePEc:yor:hectdg:05/13

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    Postal: HEDG/HERC, Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
    Phone: (0)1904 323776
    Fax: (0)1904 323759
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    Web page: http://www.york.ac.uk/economics/postgrad/herc/hedg/
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    Related research

    Keywords: Cost-effectiveness analysis; incremental net benefit; simultaneous equations; copula;

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    References

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    1. Drummond, Michael F. & Sculpher, Mark J. & Torrance, George W. & O'Brien, Bernie J. & Stoddart, Greg L., 2005. "Methods for the Economic Evaluation of Health Care Programmes," OUP Catalogue, Oxford University Press, edition 3, number 9780198529453.
    2. Jean-David Fermanian, 2003. "Goodness of Fit Tests for Copulas," Working Papers 2003-34, Centre de Recherche en Economie et Statistique.
    3. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
    4. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, 06.
    5. Aaron A. Stinnett & John Mullahy, 1998. "Net Health Benefits: A New Framework for the Analysis of Uncertainty in Cost-Effectiveness Analysis," NBER Technical Working Papers 0227, National Bureau of Economic Research, Inc.
    6. Valentino Dardanoni & Peter Lambert, 2001. "Horizontal inequity comparisons," Social Choice and Welfare, Springer, vol. 18(4), pages 799-816.
    7. Claxton, Karl, 1999. "The irrelevance of inference: a decision-making approach to the stochastic evaluation of health care technologies," Journal of Health Economics, Elsevier, vol. 18(3), pages 341-364, June.
    8. Jun Shao, 1990. "Bootstrap estimation of the asymptotic variances of statistical functionals," Annals of the Institute of Statistical Mathematics, Springer, vol. 42(4), pages 737-752, December.
    9. Andrew R. Willan & Andrew H. Briggs & Jeffrey S. Hoch, 2004. "Regression methods for covariate adjustment and subgroup analysis for non-censored cost-effectiveness data," Health Economics, John Wiley & Sons, Ltd., vol. 13(5), pages 461-475.
    10. Anthony O'Hagan & John W. Stevens, 2003. "Assessing and comparing costs: how robust are the bootstrap and methods based on asymptotic normality?," Health Economics, John Wiley & Sons, Ltd., vol. 12(1), pages 33-49.
    11. Elisabetta Strazzera & Margarita Genius, 2004. "The Copula Approach to Sample Selection Modelling: An Application to the Recreational Value of Forests," Working Papers 2004.73, Fondazione Eni Enrico Mattei.
    12. Elisabeth Fenwick & Karl Claxton & Mark Sculpher, 2001. "Representing uncertainty: the role of cost-effectiveness acceptability curves," Health Economics, John Wiley & Sons, Ltd., vol. 10(8), pages 779-787.
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