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Use of Propensity Scores in Non-Linear Response Models: The Case for Health Care Expenditures

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  • Anirban Basu
  • Daniel Polsky
  • Willard G. Manning

Abstract

Under the assumption of no unmeasured confounders, a large literature exists on methods that can be used to estimating average treatment effects (ATE) from observational data and that spans regression models, propensity score adjustments using stratification, weighting or regression and even the combination of both as in doubly-robust estimators. However, comparison of these alternative methods is sparse in the context of data generated via non-linear models where treatment effects are heterogeneous, such as is in the case of healthcare cost data. In this paper, we compare the performance of alternative regression and propensity score-based estimators in estimating average treatment effects on outcomes that are generated via non-linear models. Using simulations, we find that in moderate size samples (n= 5000), balancing on estimated propensity scores balances the covariate means across treatment arms but fails to balance higher-order moments and covariances amongst covariates, raising concern about its use in non-linear outcomes generating mechanisms. We also find that besides inverse-probability weighting (IPW) with propensity scores, no one estimator is consistent under all data generating mechanisms. The IPW estimator is itself prone to inconsistency due to misspecification of the model for estimating propensity scores. Even when it is consistent, the IPW estimator is usually extremely inefficient. Thus care should be taken before naively applying any one estimator to estimate ATE in these data. We develop a recommendation for an algorithm which may help applied researchers to arrive at the optimal estimator. We illustrate the application of this algorithm and also the performance of alternative methods in a cost dataset on breast cancer treatment.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14086.

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Date of creation: Jun 2008
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Handle: RePEc:nbr:nberwo:14086

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  1. Michael LECHNER, 2008. "A Note on the Common Support Problem in Applied Evaluation Studies," Annales d'Economie et de Statistique, ENSAE, issue 91-92, pages 217-235.
  2. Joshua Angrist & Jinyong Hahn, 2004. "When to Control for Covariates? Panel Asymptotics for Estimates of Treatment Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 58-72, February.
  3. Jack Hadley & Daniel Polsky & Jeanne S. Mandelblatt & Jean M. Mitchell & Jane C. Weeks & Qin Wang & Yi-Ting Hwang, 2003. "An exploratory instrumental variable analysis of the outcomes of localized breast cancer treatments in a medicare population," Health Economics, John Wiley & Sons, Ltd., vol. 12(3), pages 171-186.
  4. Manning, Willard G. & Mullahy, John, 2001. "Estimating log models: to transform or not to transform?," Journal of Health Economics, Elsevier, vol. 20(4), pages 461-494, July.
  5. James J. Heckman & Salvador Navarro-Lozano, 2003. "Using Matching, Instrumental Variables and Control Functions to Estimate Economic Choice Models," NBER Working Papers 9497, National Bureau of Economic Research, Inc.
  6. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173.
  7. Coyte, Peter C. & Young, Wendy & Croxford, Ruth, 2000. "Costs and outcomes associated with alternative discharge strategies following joint replacement surgery: analysis of an observational study using a propensity score," Journal of Health Economics, Elsevier, vol. 19(6), pages 907-929, November.
  8. James J. Heckman & Jeffrey A. Smith, 1998. "Evaluating the Welfare State," NBER Working Papers 6542, National Bureau of Economic Research, Inc.
  9. 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.
  10. Manning, Willard G., 1998. "The logged dependent variable, heteroscedasticity, and the retransformation problem," Journal of Health Economics, Elsevier, vol. 17(3), pages 283-295, June.
  11. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, 07.
  12. Nandita Mitra & Alka Indurkhya, 2005. "A propensity score approach to estimating the cost-effectiveness of medical therapies from observational data," Health Economics, John Wiley & Sons, Ltd., vol. 14(8), pages 805-815.
  13. Manning, Willard G, et al, 1987. "Health Insurance and the Demand for Medical Care: Evidence from a Randomized Experiment," American Economic Review, American Economic Association, vol. 77(3), pages 251-77, June.
  14. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
  15. 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.
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Cited by:
  1. Albert Okunade & Andrew Hussey & Mustafa Karakus, 2009. "Overweight Adolescents and On-time High School Graduation: Racial and Gender Disparities," Atlantic Economic Journal, International Atlantic Economic Society, vol. 37(3), pages 225-242, September.

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