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Non-parametric methods for cost-effectiveness analysis: the central limit theorem and the bootstrap compared


  • Richard M. Nixon

    (MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK)

  • David Wonderling

    (National Collaborating Centre for Acute Care, Royal College of Surgeons of England, London, UK)

  • Richard D. Grieve

    (Department of Public Health and Policy, London School of Hygiene and Tropical Medicine, London, UK)


Cost-effectiveness analyses (CEA) alongside randomised controlled trials commonly estimate incremental net benefits (INB), with 95% confidence intervals, and compute cost-effectiveness acceptability curves and confidence ellipses. Two alternative non-parametric methods for estimating INB are to apply the central limit theorem (CLT) or to use the non-parametric bootstrap method, although it is unclear which method is preferable. This paper describes the statistical rationale underlying each of these methods and illustrates their application with a trial-based CEA. It compares the sampling uncertainty from using either technique in a Monte Carlo simulation. The experiments are repeated varying the sample size and the skewness of costs in the population. The results showed that, even when data were highly skewed, both methods accurately estimated the true standard errors (SEs) when sample sizes were moderate to large (n>50), and also gave good estimates for small data sets with low skewness. However, when sample sizes were relatively small and the data highly skewed, using the CLT rather than the bootstrap led to slightly more accurate SEs. We conclude that while in general using either method is appropriate, the CLT is easier to implement, and provides SEs that are at least as accurate as the bootstrap. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • Richard M. Nixon & David Wonderling & Richard D. Grieve, 2010. "Non-parametric methods for cost-effectiveness analysis: the central limit theorem and the bootstrap compared," Health Economics, John Wiley & Sons, Ltd., vol. 19(3), pages 316-333.
  • Handle: RePEc:wly:hlthec:v:19:y:2010:i:3:p:316-333
    DOI: 10.1002/hec.1477

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    References listed on IDEAS

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    Cited by:

    1. Janet MacNeil Vroomen & Iris Eekhout & Marcel G. Dijkgraaf & Hein van Hout & Sophia E. de Rooij & Martijn W. Heymans & Judith E. Bosmans, 2016. "Multiple imputation strategies for zero-inflated cost data in economic evaluations: which method works best?," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 17(8), pages 939-950, November.
    2. Edmond S.-W. Ng & Richard Grieve & James R. Carpenter, 2013. "Two-stage nonparametric bootstrap sampling with shrinkage correction for clustered data," Stata Journal, StataCorp LP, vol. 13(1), pages 141-164, March.
    3. Theodoros Mantopoulos & Paul M. Mitchell & Nicky J. Welton & Richard McManus & Lazaros Andronis, 2016. "Choice of statistical model for cost-effectiveness analysis and covariate adjustment: empirical application of prominent models and assessment of their results," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 17(8), pages 927-938, November.
    4. Bebu, Ionut & Luta, George & Mathew, Thomas & Kennedy, Paul A. & Agan, Brian K., 2016. "Parametric cost-effectiveness inference with skewed data," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 210-220.

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