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Consistent estimation of polychotomous treatment effects with selection-bias and unobserved heterogeneity using panel data correlated random coefficients model

  • Aniket A. KawatkarEmail author
  • Joel W. Hay
  • William Stohl
  • Michael B. Nichol
Article

Abstract

We estimate multiple treatment effects in presence of selection-bias and response heterogeneity, using panel data. A control function was added to a fixed-effects based correlated random coefficients model. Selection model to create the control function was contrasted between multinomial logit and multinomial probit. For the multinomial logit model, parametric and semi-parametric bias correction techniques, as proposed in Lee (Econometrica 51(2):507–512, 1983), Dubin and McFadden (Econometrica 52(2):345–362, 1984) and Dahl (Econometrica 70(6):2367–2420, 2002) respectively, were implemented. We find that controlling time-varying endogeneity, allowing response heterogeneity, the type of bias correction method and the choice of the selection model, each had significant impact on the estimated treatment effects. Using the case of biologic DMARDs, we show that in the presence of heterogeneity and multiple treatments, the specification of the latent index model should be carefully chosen along with selection bias correction techniques appropriate to the choice of the latent index model. These issues have an important impact on policy. Under one set of assumptions, we may accept a formulary expansion policy on biologic DMARDs to be cost-neutral, while rejecting the same policy as not cost-saving under another set of assumptions.

Keywords

Control functions Heterogeneous treatment effects Instrumental variables Multiple endogeneity Comparative effectiveness Correlated random coefficients 

JEL

C31 C33 C36 I10 

References

  1. Arellano, M., Bond, S.: Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Rev. Econ. Stud. 58(2), 277–297 (1991)CrossRefGoogle Scholar
  2. Arellano, M., Bover, O.: Another look at the instrumental variable estimation of error-components models. J. Econ. 68(1), 29–51 (1995)CrossRefGoogle Scholar
  3. Barrios, J.: Generalized sample selection bias correction under RUM. Econ. Lett. 85(1), 129–132 (2004)CrossRefGoogle Scholar
  4. Belsley, D.A., Kuh, E., Welsch, R.E.: Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley, New York (1980)CrossRefGoogle Scholar
  5. Blundell, R., Bond, S.: Initial conditions and moment restrictions in dynamic panel data models. J. Econ. 87(1), 115–143 (1998)CrossRefGoogle Scholar
  6. Bourguignon, F., Fournier, M., Gurgand, M.: Selection bias corrections based on the multinomial logit model: Monte Carlo comparisons. J. Econ. Surv. 21(1), 174–205 (2007)CrossRefGoogle Scholar
  7. Bullano, M.F., McNeeley, B.J., Yu, Y.F., Quimbo, R., Burawski, L.P., Yu, E.B., Woolley, J.M.: Comparison of costs associated with the use of etanercept, infliximab, and adalimumab for the treatment of rheumatoid arthritis. Manag. Care Interface 19(9), 47–53 (2006)PubMedGoogle Scholar
  8. Cush, J.J.: Biological drug use: US perspectives on indications and monitoring. Ann. Rheum. Dis. 64(Suppl 4), 18–23 (2005)Google Scholar
  9. Dahl, G.B.: Mobility and the return to education: testing a Roy model with multiple markets. Econometrica 70(6), 2367–2420 (2002)CrossRefGoogle Scholar
  10. Deb, P., Trivedi, P.K.: Specification and simulated likelihood estimation of a non-normal treatment-outcome model with selection: application to health care utilization. Econ. J. 9, 307–331 (2006)Google Scholar
  11. Deb, P., Li, C., Trivedi, P.K., Zimmer, D.M.: The effect of managed care on use of health care services: results from two contemporaneous household surveys. Health Econ. 15(7), 743–760 (2006a)CrossRefPubMedGoogle Scholar
  12. Deb, P., Munkin, M.K., Trivedi, P.K.: Bayesian analysis of the two-part model with endogeneity: application to health care expenditure. J. Appl. Econ. 21, 1081–1099 (2006b)CrossRefGoogle Scholar
  13. Duan, N.: A non-parametric retransformation method. J. Am. Stat. Assoc. 78(383), 605–610 (1983)CrossRefGoogle Scholar
  14. Dubin, J.A., McFadden, D.L.: An econometric analysis of residential electric appliance holdings and consumption. Econometrica 52(2), 345–362 (1984)CrossRefGoogle Scholar
  15. Elixhauser, A., Steiner, C., Harris, D.R., Coffey, R.M.: Comorbidity measures for use with administrative data. Med. Care 36(1), 8–27 (1998)CrossRefPubMedGoogle Scholar
  16. Fernández-Val, I., Vella, F.: Bias corrections for two-step fixed effects panel data estimators. J. Econ. 163(2), 144–162 (2011)CrossRefGoogle Scholar
  17. Greene, W.: Econometric Analysis, 5th edn. Prentice Hall, Upper Saddle River (2002)Google Scholar
  18. Grijalva, C.G., Chung, C.P., Arbogast, P.G., Stein, C.M., Mitchel Jr., E.F., Griffin, M.R.: Assessment of adherence to and persistence on disease-modifying antirheumatic drugs (DMARDs) in patients with rheumatoid arthritis. Medical Care 45(10 Supl 2), s66–S76 (2007)CrossRefPubMedGoogle Scholar
  19. Hay, J.W.: Occupational choice and occupational earnings: a method for dealing with selection bias among economic activities. In: Schultz, T.P., Wolpin, K.I. (eds.) Research in Population Economics. JAI Press, Greenwich (1984)Google Scholar
  20. Hay, J.W.: Occupational choice and occupational earnings: selectivity bias in a simultaneous logit-OLS model. Ph.D. Dissertation, Economics, Yale University, New Haven (1980)Google Scholar
  21. Heckman, J.J.: The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models. Ann. Econ. Soc. Meas. 5(4), 475–492 (1976)Google Scholar
  22. Heckman, J.J., Navarro-Lozano, S.: Using matching, instrumental variables, and control functions to estimate economic choice models. Rev. Econ. Stat. 86(1), 30–57 (2004)CrossRefGoogle Scholar
  23. Heckman, J.J., Robb, R.: Alternative methods for evaluating the impact of interventions: an overview. J. Econ. 30(1–2), 239–267 (1985)CrossRefGoogle Scholar
  24. Heckman, J.J., Urzua, S.: Comparing IV with structural models: what simple IV can and cannot identify. J. Econ. 156(1), 27–37 (2010)CrossRefGoogle Scholar
  25. Heckman, J.J., Urzua, S., Vytlacil, E.: Understanding instrumental variables in models with essential heterogeneity. Rev. Econ. Stat. 88(3), 389–432 (2006)CrossRefGoogle Scholar
  26. Heckman, J.J., Urzua, S., Vytlacil, E.: Instrumental Variables in Models with Multiple Outcomes: The General Unordered Case. University College Dublin, Dublin (2008)Google Scholar
  27. Heckman, J.J., Vytlacil, E.: Instrumental variables methods for the correlated random coefficient model: estimating the average rate of return to schooling when the return is correlated with schooling. J. Hum. Resour. 33(4), 974–987 (1998)CrossRefGoogle Scholar
  28. Heckman, J.J., Vytlacil, E.J.: Econometric evaluation of social programs, part II: using the marginal treatment effect to organize alternative economic estimators to evaluate social programs and to forecast their effects in new environments. In: Arrow, K., Intriligator, M. (eds.) Handbook of Econometrics, vol. 6B. Elsevier, Amsterdam (2007)Google Scholar
  29. Imbens, G.W., Angrist, J.D.: Identification and estimation of local average treatment effects. Econometrica 62(2), 467–475 (1994)CrossRefGoogle Scholar
  30. Kawatkar, A.A., Hay, J.W., Stohl, W., Nichol, M.B.: Incremental expenditure of biologic disease modifying antirheumatic treatment using instrumental variables in panel data. Health Econ. 22, 807–823 (2012a)CrossRefPubMedGoogle Scholar
  31. Kawatkar, A.A., Jacobsen, S.J., Levy, G.D., Medhekar, S.S., Venkatasubramaniam, K.V., Herrinton, L.J.: Direct medical expenditure associated with rheumatoid arthritis in a nationally representative sample from the medical expenditure panel survey. Arthr. Care Res. (Hoboken) 64, 1649–1656 (2012b)CrossRefGoogle Scholar
  32. Kravitz, R.L., Duan, N., Braslow, J.: Evidence-based medicine, heterogeneity of treatment effects, and the trouble with averages. Milbank Q. 82(4), 661–687 (2004)CrossRefPubMedPubMedCentralGoogle Scholar
  33. Kvien, T.K.: Epidemiology and burden of illness of rheumatoid arthritis. Pharmacoeconomics 22(2 Suppl 1), 1–12 (2004)CrossRefPubMedGoogle Scholar
  34. Lee, L.F.: Some approaches to the correction of selectivity bias. Rev. Econ. Stud. 49(3), 355–372 (1982)CrossRefGoogle Scholar
  35. Lee, L.F.: Generalized econometric models with selectivity. Econometrica 51(2), 507–512 (1983)CrossRefGoogle Scholar
  36. Manning, W.: Dealing with skewed data on costs and expenditures. In: Jones, A. (ed.) The Elgar Companion to Health Economics. Edward Elgar Publishing Ltd, Northampton (2006)Google Scholar
  37. McFadden, D.L.: Econometric models of probabilistic choice. In: Manski, C.F. (ed.) Structural Analysis of Discrete Data with Econometric Applications. MIT Press, Cambridge (1981)Google Scholar
  38. Michaud, K., Messer, J., Choi, H.K., Wolfe, F.: Direct medical costs and their predictors in patients with rheumatoid arthritis: a three-year study of 7,527 patients. Arthr. Rheum. 48(10), 2750–2762 (2003)CrossRefGoogle Scholar
  39. Michaud, K., Wolfe, F.: Comorbidities in rheumatoid arthritis. Best Pract. Res. Clin. Rheumatol. 21(5), 885–906 (2007)CrossRefPubMedGoogle Scholar
  40. Ollendorf, D.A., Klingman, D., Hazard, E., Ray, S.: Differences in annual medication costs and rates of dosage increase between tumor necrosis factor-antagonist therapies for rheumatoid arthritis in a managed care population. Clin. Ther. 31(4), 825–835 (2009)CrossRefPubMedGoogle Scholar
  41. Saag, K.G., Teng, G.G., Patkar, N.M., Anuntiyo, J., Finney, C., Curtis, J.R., Paulus, H.E., Mudano, A., Pisu, M., Elkins-Melton, M., Outman, R., Allison, J.J., Suarez Almazor, M., Bridges Jr., S.L., Chatham, W.W., Hochberg, M., MacLean, C., Mikuls, T., Moreland, L.W., O’Dell, J., Turkiewicz, A.M., Furst, D.E.: American College of Rheumatology 2008 recommendations for the use of nonbiologic and biologic disease-modifying antirheumatic drugs in rheumatoid arthritis. Arthr. Rheum. 59(6), 762–784 (2008)CrossRefGoogle Scholar
  42. Smedstad, L.M., Moum, T., Guillemin, F., Kvien, T.K., Finch, M.B., Suurmeijer, T.P., van den Heuvel, W.J.: Correlates of functional disability in early rheumatoid arthritis: a cross-sectional study of 706 patients in four European countries. Br. J. Rheumatol. 35(8), 746–751 (1996a)CrossRefPubMedGoogle Scholar
  43. Smedstad, L.M., Moum, T., Vaglum, P., Kvien, T.K.: The impact of early rheumatoid arthritis on psychological distress. A comparison between 238 patients with RA and 116 matched controls. Scand. J. Rheumatol. 25(6), 377–382 (1996b)CrossRefPubMedGoogle Scholar
  44. Terza, J.V.: Econometric models with normal polychotomous selectivity. Econ. Lett. 19(2), 165–170 (1985)CrossRefGoogle Scholar
  45. Wooldridge, J.M.: Econometric Analysis of Cross Section and Panel Data, 2nd edn. The MIT Press, Cambridge (2010)Google Scholar
  46. Wu, E., Chen, L., Birnbaum, H., Yang, E., Cifaldi, M.: Cost of care for patients with rheumatoid arthritis receiving TNF-antagonist therapy using claims data. Curr. Med. Res. Opin. 23(8), 1749–1759 (2007)CrossRefPubMedGoogle Scholar
  47. Zimmer, D.M., Trivedi, P.K.: Using trivariate copulas to model sample selection and treatment effects: application to family health care demand. J. Bus. Econ. Stat. 24, 63–76 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Aniket A. Kawatkar
    • 1
    Email author
  • Joel W. Hay
    • 2
  • William Stohl
    • 3
  • Michael B. Nichol
    • 2
  1. 1.Department of Research and EvaluationKaiser Permanente Southern CaliforniaPasadenaUSA
  2. 2.Schaeffer Center for Health Policy and Economics, School of PharmacyUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Division of Rheumatology, Department of Medicine, Keck School of MedicineUniversity of Southern CaliforniaLos AngelesUSA

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