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Comparing alternative models: log vs Cox proportional hazard?

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  • Anirban Basu

    (Harris School of Public Policy, The University of Chicago, Chicago, USA)

  • Willard G. Manning
  • John Mullahy

Abstract

Health economists often use log models (based on OLS or generalized linear models) to deal with skewed outcomes such as those found in health expenditures and inpatient length of stay. Some recent studies have employed Cox proportional hazard regression as a less parametric alternative to OLS and GLM models, even when there was no need to correct for censoring. This study examines how well the alternative estimators behave econometrically in terms of bias when the data are skewed to the right. Specifically we provide evidence on the performance of the Cox model under a variety of data generating mechanisms and compare it to the estimators studied recently in Manning and Mullahy (2001). No single alternative is best under all of the conditions examined here. However, the gamma regression model with a log link seems to be more robust to alternative data generating mechanisms than either OLS on ln(y) or Cox proportional hazards regression. We find that the proportional hazard assumption is an essential requirement to obtain consistent estimate of the E(y∣x) using the Cox model. Copyright © 2004 John Wiley & Sons, Ltd.

Suggested Citation

  • Anirban Basu & Willard G. Manning & John Mullahy, 2004. "Comparing alternative models: log vs Cox proportional hazard?," Health Economics, John Wiley & Sons, Ltd., vol. 13(8), pages 749-765.
  • Handle: RePEc:wly:hlthec:v:13:y:2004:i:8:p:749-765
    DOI: 10.1002/hec.852
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    File URL: http://hdl.handle.net/10.1002/hec.852
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    References listed on IDEAS

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    1. Etzioni, Ruth D. & Feuer, Eric J. & Sullivan, Sean D. & Lin, Danyu & Hu, Chengcheng & Ramsey, Scott D., 1999. "On the use of survival analysis techniques to estimate medical care costs," Journal of Health Economics, Elsevier, vol. 18(3), pages 365-380, June.
    2. Mullahy, John, 1998. "Much ado about two: reconsidering retransformation and the two-part model in health econometrics," Journal of Health Economics, Elsevier, vol. 17(3), pages 247-281, June.
    3. Blough, David K. & Madden, Carolyn W. & Hornbrook, Mark C., 1999. "Modeling risk using generalized linear models," Journal of Health Economics, Elsevier, vol. 18(2), pages 153-171, April.
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    Cited by:

    1. Anirban Basu & James J. Heckman & Salvador Navarro-Lozano & Sergio Urzua, 2007. "Use of instrumental variables in the presence of heterogeneity and self-selection: An application in breast cancer patients," Health, Econometrics and Data Group (HEDG) Working Papers 07/07, HEDG, c/o Department of Economics, University of York.
    2. Jones, A. & Lomas, J. & Rice, N., 2014. "Going Beyond the Mean in Healthcare Cost Regressions: a Comparison of Methods for Estimating the Full Conditional Distribution," Health, Econometrics and Data Group (HEDG) Working Papers 14/26, HEDG, c/o Department of Economics, University of York.
    3. Andrew M. Jones & James Lomas & Nigel Rice, 2014. "Applying Beta‐Type Size Distributions To Healthcare Cost Regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(4), pages 649-670, June.
    4. Manning, Willard G. & Basu, Anirban & Mullahy, John, 2005. "Generalized modeling approaches to risk adjustment of skewed outcomes data," Journal of Health Economics, Elsevier, vol. 24(3), pages 465-488, May.
    5. Thompson, Simon G. & Nixon, Richard M. & Grieve, Richard, 2006. "Addressing the issues that arise in analysing multicentre cost data, with application to a multinational study," Journal of Health Economics, Elsevier, vol. 25(6), pages 1015-1028, November.
    6. Barbos, Andrei & Deng, Yi, 2012. "The Impact of a Public Option in the Health Insurance Market," MPRA Paper 40849, University Library of Munich, Germany.
    7. Stargardt, Tom & Schreyögg, Jonas, 2012. "A framework to evaluate the effects of small area variations in healthcare infrastructure on diagnostics and patient outcomes of rare diseases based on administrative data," Health Policy, Elsevier, vol. 105(2), pages 110-118.
    8. Anirban Basu & Bhakti V. Arondekar & Paul J. Rathouz, 2006. "Scale of interest versus scale of estimation: comparing alternative estimators for the incremental costs of a comorbidity," Health Economics, John Wiley & Sons, Ltd., vol. 15(10), pages 1091-1107.
    9. Manos Matsaganis & Theodore Mitrakos & Panos Tsakloglou, 2009. "Modelling health expenditure at the household level in Greece," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 10(3), pages 329-336, July.
    10. Andrew M. Jones & James Lomas & Peter T. Moore & Nigel Rice, 2016. "A quasi-Monte-Carlo comparison of parametric and semiparametric regression methods for heavy-tailed and non-normal data: an application to healthcare costs," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(4), pages 951-974, October.
    11. Smith, William C. & Anderson, Emily & Salinas, Daniel & Horvatek, Renata & Baker, David P., 2015. "A meta-analysis of education effects on chronic disease: The causal dynamics of the Population Education Transition Curve," Social Science & Medicine, Elsevier, vol. 127(C), pages 29-40.
    12. Basu A & Manning WG, 2009. "Estimating Lifetime or Episode-of-illness Costs," Health, Econometrics and Data Group (HEDG) Working Papers 09/12, HEDG, c/o Department of Economics, University of York.
    13. Jones, A.M, 2010. "Models For Health Care," Health, Econometrics and Data Group (HEDG) Working Papers 10/01, HEDG, c/o Department of Economics, University of York.
    14. Law, Michael R. & Grépin, Karen A., 2010. "Is newer always better? Re-evaluating the benefits of newer pharmaceuticals," Journal of Health Economics, Elsevier, vol. 29(5), pages 743-750, September.
    15. Amal Malehi & Fatemeh Pourmotahari & Kambiz Angali, 2015. "Statistical models for the analysis of skewed healthcare cost data: a simulation study," Health Economics Review, Springer, vol. 5(1), pages 1-16, December.
    16. Anirban Basu & James J. Heckman & Salvador Navarro-Lozano & Sergio Urzua, 2007. "Use of instrumental variables in the presence of heterogeneity and self-selection: an application to treatments of breast cancer patients," Health Economics, John Wiley & Sons, Ltd., vol. 16(11), pages 1133-1157.
    17. Manos Matsaganis & Theodore Mitrakos & Panos Tsakloglou, 2008. "Modelling Household Expenditure on Health Care in Greece," Working Papers 68, Bank of Greece.

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