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Scale of interest versus scale of estimation: comparing alternative estimators for the incremental costs of a comorbidity

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  • Anirban Basu
  • Bhakti V. Arondekar
  • Paul J. Rathouz

Abstract

We investigate how the scale of estimation in risk‐adjustment models for health‐care costs affects the covariate effect, where the scale of interest for the covariate effect may be different from the scale of estimation. As an illustrative example, we use claims data to estimate the incremental costs associated with heart failure within one year subsequent to myocardial infarction. Here, the scale of interest for the effect of heart failure on costs is additive. However, traditional methods for modeling costs use predetermined scale of estimation – for example, ordinary least squares (OLS) regression assumes an additive scale while log‐transformed OLS and generalized linear models with log‐link assume a multiplicative scale of estimation. We compare these models with a new flexible model that lets the data determine the appropriate scale of estimation. We use a variety of goodness‐of‐fit measures along with a modified Copas test to assess robustness, lack of fit, and over‐fitting properties of the alternative estimators. Biases up to 19% in the scale of interest are observed due to the misrepresentation of the scale of estimation. The new flexible model is found to appropriately represent the scale of estimation and less susceptible to over‐fitting despite estimating additional parameters in the link and the variance functions. Copyright © 2006 John Wiley & Sons, Ltd.

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  • 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, October.
  • Handle: RePEc:wly:hlthec:v:15:y:2006:i:10:p:1091-1107
    DOI: 10.1002/hec.1099
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    1. Andrew M. Jones & James Lomas & Nigel Rice, 2015. "Healthcare Cost Regressions: Going Beyond the Mean to Estimate the Full Distribution," Health Economics, John Wiley & Sons, Ltd., vol. 24(9), pages 1192-1212, September.
    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. Qun Wang & Alex Z Fu & Stephan Brenner & Olivier Kalmus & Hastings Thomas Banda & Manuela De Allegri, 2015. "Out-of-Pocket Expenditure on Chronic Non-Communicable Diseases in Sub-Saharan Africa: The Case of Rural Malawi," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-15, January.
    5. Jeffrey Hoch & Carolyn Dewa, 2007. "Lessons from Trial-Based Cost-Effectiveness Analyses of Mental Health Interventions," PharmacoEconomics, Springer, vol. 25(10), pages 807-816, October.
    6. Kai Yeung & Anirban Basu & Ryan N. Hansen & Sean D. Sullivan, 2018. "Price elasticities of pharmaceuticals in a value based‐formulary setting," Health Economics, John Wiley & Sons, Ltd., vol. 27(11), pages 1788-1804, November.
    7. Marcel Bilger & Willard G. Manning, 2015. "Measuring Overfitting In Nonlinear Models: A New Method And An Application To Health Expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 24(1), pages 75-85, January.
    8. 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.
    9. 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.
    10. Karine Moschetti & Katia Iglesias & Stéphanie Baggio & Venetia Velonaki & Olivier Hugli & Bernard Burnand & Jean-Bernard Daeppen & Jean-Blaise Wasserfallen & Patrick Bodenmann, 2018. "Health care costs of case management for frequent users of the emergency department: Hospital and insurance perspectives," PLOS ONE, Public Library of Science, vol. 13(9), pages 1-15, September.
    11. Bilger M. & Manning W.G, 2011. "Measuring overfitting and mispecification in nonlinear models," Health, Econometrics and Data Group (HEDG) Working Papers 11/25, HEDG, c/o Department of Economics, University of York.
    12. Sungchul Park & Anirban Basu, 2018. "Alternative evaluation metrics for risk adjustment methods," Health Economics, John Wiley & Sons, Ltd., vol. 27(6), pages 984-1010, June.
    13. Steven C. Hill & G. Edward Miller, 2010. "Health expenditure estimation and functional form: applications of the generalized gamma and extended estimating equations models," Health Economics, John Wiley & Sons, Ltd., vol. 19(5), pages 608-627, May.
    14. Borislava Mihaylova & Andrew Briggs & Anthony O'Hagan & Simon G. Thompson, 2011. "Review of statistical methods for analysing healthcare resources and costs," Health Economics, John Wiley & Sons, Ltd., vol. 20(8), pages 897-916, August.

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