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

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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.

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References

  • 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)

    Article  Google Scholar 

  • Arellano, M., Bover, O.: Another look at the instrumental variable estimation of error-components models. J. Econ. 68(1), 29–51 (1995)

    Article  Google Scholar 

  • Barrios, J.: Generalized sample selection bias correction under RUM. Econ. Lett. 85(1), 129–132 (2004)

    Article  Google Scholar 

  • Belsley, D.A., Kuh, E., Welsch, R.E.: Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley, New York (1980)

    Book  Google Scholar 

  • Blundell, R., Bond, S.: Initial conditions and moment restrictions in dynamic panel data models. J. Econ. 87(1), 115–143 (1998)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    PubMed  Google Scholar 

  • Cush, J.J.: Biological drug use: US perspectives on indications and monitoring. Ann. Rheum. Dis. 64(Suppl 4), 18–23 (2005)

    Google Scholar 

  • Dahl, G.B.: Mobility and the return to education: testing a Roy model with multiple markets. Econometrica 70(6), 2367–2420 (2002)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  PubMed  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Duan, N.: A non-parametric retransformation method. J. Am. Stat. Assoc. 78(383), 605–610 (1983)

    Article  Google Scholar 

  • Dubin, J.A., McFadden, D.L.: An econometric analysis of residential electric appliance holdings and consumption. Econometrica 52(2), 345–362 (1984)

    Article  Google Scholar 

  • Elixhauser, A., Steiner, C., Harris, D.R., Coffey, R.M.: Comorbidity measures for use with administrative data. Med. Care 36(1), 8–27 (1998)

    Article  CAS  PubMed  Google Scholar 

  • Fernández-Val, I., Vella, F.: Bias corrections for two-step fixed effects panel data estimators. J. Econ. 163(2), 144–162 (2011)

    Article  Google Scholar 

  • Greene, W.: Econometric Analysis, 5th edn. Prentice Hall, Upper Saddle River (2002)

    Google Scholar 

  • 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)

    Article  PubMed  Google Scholar 

  • 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 

  • 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)

  • 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 

  • 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)

    Article  Google Scholar 

  • Heckman, J.J., Robb, R.: Alternative methods for evaluating the impact of interventions: an overview. J. Econ. 30(1–2), 239–267 (1985)

    Article  Google Scholar 

  • Heckman, J.J., Urzua, S.: Comparing IV with structural models: what simple IV can and cannot identify. J. Econ. 156(1), 27–37 (2010)

    Article  Google Scholar 

  • Heckman, J.J., Urzua, S., Vytlacil, E.: Understanding instrumental variables in models with essential heterogeneity. Rev. Econ. Stat. 88(3), 389–432 (2006)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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 

  • Imbens, G.W., Angrist, J.D.: Identification and estimation of local average treatment effects. Econometrica 62(2), 467–475 (1994)

    Article  Google Scholar 

  • 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)

    Article  PubMed  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  PubMed  PubMed Central  Google Scholar 

  • Kvien, T.K.: Epidemiology and burden of illness of rheumatoid arthritis. Pharmacoeconomics 22(2 Suppl 1), 1–12 (2004)

    Article  PubMed  Google Scholar 

  • Lee, L.F.: Some approaches to the correction of selectivity bias. Rev. Econ. Stud. 49(3), 355–372 (1982)

    Article  Google Scholar 

  • Lee, L.F.: Generalized econometric models with selectivity. Econometrica 51(2), 507–512 (1983)

    Article  Google Scholar 

  • 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 

  • 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 

  • 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)

    Article  Google Scholar 

  • Michaud, K., Wolfe, F.: Comorbidities in rheumatoid arthritis. Best Pract. Res. Clin. Rheumatol. 21(5), 885–906 (2007)

    Article  PubMed  Google Scholar 

  • 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)

    Article  CAS  PubMed  Google Scholar 

  • 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)

    Article  CAS  Google Scholar 

  • 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)

    Article  CAS  PubMed  Google Scholar 

  • 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)

    Article  CAS  PubMed  Google Scholar 

  • Terza, J.V.: Econometric models with normal polychotomous selectivity. Econ. Lett. 19(2), 165–170 (1985)

    Article  Google Scholar 

  • Wooldridge, J.M.: Econometric Analysis of Cross Section and Panel Data, 2nd edn. The MIT Press, Cambridge (2010)

    Google Scholar 

  • 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)

    Article  PubMed  Google Scholar 

  • 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)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Research and Evaluation, Kaiser Permanente Southern California, Pasadena, CA, USA

    Aniket A. Kawatkar

  2. Schaeffer Center for Health Policy and Economics, School of Pharmacy, University of Southern California, Los Angeles, CA, USA

    Joel W. Hay & Michael B. Nichol

  3. Division of Rheumatology, Department of Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA

    William Stohl

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  1. Aniket A. Kawatkar
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  2. Joel W. Hay
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  3. William Stohl
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  4. Michael B. Nichol
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Correspondence to Aniket A. Kawatkar.

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Kawatkar, A.A., Hay, J.W., Stohl, W. et al. Consistent estimation of polychotomous treatment effects with selection-bias and unobserved heterogeneity using panel data correlated random coefficients model. Health Serv Outcomes Res Method 18, 75–95 (2018). https://doi.org/10.1007/s10742-018-0177-4

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  • DOI: https://doi.org/10.1007/s10742-018-0177-4

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