Causal difference-in-differences estimation for evaluating the impact of semi-continuous medical home scores on health care for children

Abstract

Difference-in-differences (DID) is a popular approach in observational and quasi-experimental studies to estimate the effects of a treatment with discrete statuses. In many studies, however, the treatment can have a range of dosages or exposure levels. In our paper, “medical homeness” is a semi-continuous score ranging from 0 to 100 to indicate the extent to which a patient-centered medical home model is achieved. We developed a causal DID approach to estimating the effects of a treatment with semi-continuous dosages. The proposed approach allows for mixed-type designs as well as different propensity models. We applied the proposed approach to evaluate the dosage effect of medical homeness scores on the utilization and quality of children’s health care. We found that there was a roughly linear effect of medical homeness scores on the annual number of visits to doctor offices when medical homeness scores were below 60 points. The number of office visits did not further increase when medical homeness scores were above 60. A similar relationship was found between medical homeness scores and ratings for health care quality.

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References

  1. Abadie, A.: Semiparametric difference-in-differences estimators. Rev. Econ. Stud. 72(1), 1–19 (2005)

    Article  Google Scholar 

  2. American Academy of Pediatrics Medical Home Initiatives for Children With Special Needs Project Advisory Committee and others. Policy statement: organizational principles to guide and define the child health care system and/or improve the health of all children. Pediatrics 113(5 Suppl), 1545 (2004)

  3. Andersen, R.M.: Revisiting the behavioral model and access to medical care: does it matter? J. Health Soc. Behav. 36, 1–10 (1995)

    CAS  Article  Google Scholar 

  4. Beal, A., Hernandez, S., Doty, M.: Latino access to the patient-centered medical home. J. Gen. Internal Med. 24(3), 514 (2009)

    Article  Google Scholar 

  5. Bethell, C.D., Read, D., Brockwood, K.: Using existing population-based data sets to measure the american academy of pediatrics definition of medical home for all children and children with special health care needs. Pediatrics 113(Supplement 4), 1529–1537 (2004)

    PubMed  Google Scholar 

  6. Cohen, J.W., Monheit, A.C., Beauregard, K.M., Cohen, S.B., Lefkowitz, D.C., Potter, D., Sommers, J.P., Taylor, A.K., Arnett III, R.H.: The medical expenditure panel survey: a national health information resource. Inquiry 33, 373–389 (1996)

    PubMed  Google Scholar 

  7. Conley, T.G., Taber, C.R.: Inference with difference in differences with a small number of policy changes. Rev. Econ. Stat. 93(1), 113–125 (2011)

    Article  Google Scholar 

  8. Damiano, P.C., Momany, E.T., Tyler, M.C., Penziner, A.J., Lobas, J.G.: Cost of outpatient medical care for children and youth with special health care needs: investigating the impact of the medical home. Pediatrics 118(4), e1187–e1194 (2006)

    Article  Google Scholar 

  9. Dickens, M.D., Green, J.L., Kohrt, A.E., Pearson, H.A.: The medical home. Pediatrics 90(5), 774–774 (1992)

    Google Scholar 

  10. Domino, M.E., Humble, C., Lawrence Jr., W.W., Wegner, S.: Enhancing the medical homes model for children with asthma. Med. Care 47(11), 1113–1120 (2009)

    Article  Google Scholar 

  11. Ferrari, S., Cribari-Neto, F.: Beta regression for modelling rates and proportions. J. Appl. Stat. 31(7), 799–815 (2004)

    Article  Google Scholar 

  12. Fisher, E.S.: Building a medical neighborhood for the medical home. N. Engl. J. Med. 359(12), 1202–1205 (2008)

    CAS  Article  Google Scholar 

  13. Fu, A.Z., Dow, W.H., Liu, G.G.: Propensity score and difference-in-difference methods: a study of second-generation antidepressant use in patients with bipolar disorder. Health Serv. Outcomes Res. Methodol. 7(1–2), 23–38 (2007)

    Article  Google Scholar 

  14. Han, B., Yu, H., Friedberg, M.W.: Evaluating the impact of parent-reported medical home status on children’s health care utilization, expenditures, and quality: a difference-in-differences analysis with causal inference methods. Health Serv. Res. 52(2), 786–806 (2017)

    Article  Google Scholar 

  15. Hastie, T.J. (ed.): Generalized additive models. In: Statistical Models in S. Routledge, New York (2017)

  16. Hirano, K., Imbens, G.W.: The propensity score with continuous treatments. In: Shewhart, W.A., Wilks, S.S., Gelman, A., Meng, X. (eds.) Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives (2005)

  17. Homer, C.J., Klatka, K., Romm, D., Kuhlthau, K., Bloom, S., Newacheck, P., Van Cleave, J., Perrin, J.M.: A review of the evidence for the medical home for children with special health care needs. Pediatrics 122(4), e922–e937 (2008)

    Article  Google Scholar 

  18. Imai, K., Van Dyk, D.A.: Causal inference with general treatment regimes: generalizing the propensity score. J. Am. Stat. Assoc. 99(467), 854–866 (2004)

    Article  Google Scholar 

  19. Lechner, M.: The estimation of causal effects by difference-in-difference methods. Found. Trends Econom. 4(3), 165–224 (2011)

    Article  Google Scholar 

  20. Li, Q., Racine, J.S.: Nonparametric Econometrics: Theory and Practice. Princeton University Press, Princeton (2007)

    Google Scholar 

  21. MacCallum, R.C., Zhang, S., Preacher, K.J., Rucker, D.D.: On the practice of dichotomization of quantitative variables. Psychol. Methods 7(1), 19 (2002)

    Article  Google Scholar 

  22. Rittenhouse, D.R., Shortell, S.M.: The patient-centered medical home: will it stand the test of health reform? JAMA 301(19), 2038–2040 (2009)

    CAS  Article  Google Scholar 

  23. Rittenhouse, D.R., Thom, D.H., Schmittdiel, J.A.: Developing a policy-relevant research agenda for the patient-centered medical home: a focus on outcomes. J. Gen. Internal Med. 25(6), 593–600 (2010)

    Article  Google Scholar 

  24. Romaire, M.A., Bell, J.F.: The medical home, preventive care screenings, and counseling for children: evidence from the medical expenditure panel survey. Acad. Pediatrics 10(5), 338–345 (2010)

    Article  Google Scholar 

  25. Romaire, M.A., Bell, J.F., Grossman, D.C.: Health care use and expenditures associated with access to the medical home for children and youth. Med. Care 50, 262–269 (2012)

    Article  Google Scholar 

  26. Rosenbaum, P.R.: The consquences of adjustment for a concomitant variable that has been affected by the treatment. J. R. Stat. Soc. Ser. A (General) 147, 656–666 (1984)

    Article  Google Scholar 

  27. Rosenbaum, P.R., Rubin, D.B.: The central role of the propensity score in observational studies for causal effects. Biometrika 70(1), 41–55 (1983)

    Article  Google Scholar 

  28. Sia, C., Tonniges, T.F., Osterhus, E., Taba, S.: History of the medical home concept. Pediatrics 113(Supplement 4), 1473–1478 (2004)

    PubMed  Google Scholar 

  29. Slusky, D.J.: Significant placebo results in difference-in-differences analysis: the case of the acas parental mandate. East. Econ. J. 43(4), 580–603 (2017)

    Article  Google Scholar 

  30. Stange, K.C., Nutting, P.A., Miller, W.L., Jaén, C.R., Crabtree, B.F., Flocke, S.A., Gill, J.M.: Defining and measuring the patient-centered medical home. J. Gen. Internal Med. 25(6), 601–612 (2010)

    Article  Google Scholar 

  31. Stevens, G.D., Seid, M., Pickering, T.A., Tsai, K.-Y.: National disparities in the quality of a medical home for children. Maternal Child Health J. 14(4), 580–589 (2010)

    Article  Google Scholar 

  32. Strickland, B., McPherson, M., Weissman, G., Van Dyck, P., Huang, Z.J., Newacheck, P.: Access to the medical home: results of the national survey of children with special health care needs. Pediatrics 113(Supplement 4), 1485–1492 (2004)

    PubMed  Google Scholar 

  33. Strickland, B.B., Jones, J.R., Ghandour, R.M., Kogan, M.D., Newacheck, P.W.: The medical home: health care access and impact for children and youth in the United States. Pediatrics 127, 604–611 (2011)

    Article  Google Scholar 

  34. Stuart, E.A., Huskamp, H.A., Duckworth, K., Simmons, J., Song, Z., Chernew, M.E., Barry, C.L.: Using propensity scores in difference-in-differences models to estimate the effects of a policy change. Health Serv. Outcomes Res. Methodol. 14(4), 166–182 (2014)

    Article  Google Scholar 

  35. Yang, L., Tsiatis, A.A.: Efficiency study of estimators for a treatment effect in a pretest-posttest trial. Am. Stat. 55(4), 314–321 (2001)

    Article  Google Scholar 

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Funding

This study was funded by the Grant R21HD078881 from Eunice Kennedy Shriver National Institute of Child Health & Human Development and by the Grant R01HS023336 from the Agency for Healthcare Research and Quality.

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Correspondence to Bing Han.

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Appendix

Appendix

Properties 1 to 3 are simply by the definition of \({\mathcal {G}}\), \(r^\delta \), and R.

Proof of Property 4

For any \(\zeta \ge 0\) and by iterative expectations,

$$\begin{aligned} \begin{aligned}&P(d \le \zeta |Y_1(\delta ) -Y_0, {\mathcal {G}}) = E\Big \{ E \big [ I\{ d \le \zeta \}|Y_1(\delta ) -Y_0, {\mathbf {X}} \big ] \Big | Y_1(\delta ) -Y_0, {\mathcal {G}} \Big \}. \\ \end{aligned} \end{aligned}$$

By the ignorability assumption, the last expression is equal to

$$\begin{aligned} \begin{aligned} E\Big \{ E\big [ I\{ d \le \zeta \}|{\mathbf {X}} \big ] | Y_1(\delta ) -Y_0, {\mathcal {G}} \Big \} = E \Big \{ \int _0^\zeta r^a \text {d}a \big | Y_1(\delta ) -Y_0, {\mathcal {G}} \Big \} , \text { by Property 1.} \end{aligned} \end{aligned}$$

Since \(r^a\) is fully determined by \({\mathcal {G}}\), the last expression is equal to \(\int _0^\zeta r^a \text {d}a= P(d \le \zeta | {\mathbf {X}}).\)

Proof of Property 5

By Property 2,

$$\begin{aligned} E[ Y_1(d) - Y_0 | d=\delta , R=s] = E[ Y_1(\delta ) - Y_0 | d=\delta , R=s]= E[ Y_1(\delta ) - Y_0 | d=\delta , r^\delta =s]. \end{aligned}$$
(17)

Then following essentially the same technique in Theorem 2 in Hirano and Imbens (2002), we first show \(f(Y_1(\delta ) - Y_0 | d=\delta , r^\delta =s) = f(Y_1(\delta ) - Y_0 | r^\delta =s).\)

Given \(s \ne 0\),

$$\begin{aligned} \begin{aligned} f(Y_1(\delta ) - Y_0 | d=\delta , r^\delta =s)&=\frac{f(d=\delta | Y_1(\delta ) - Y_0, r^\delta =s)f(Y_1(\delta ) - Y_0| r^\delta =s)}{f(d=\delta |r^\delta =s)}\\&=s^{-1}f(d=\delta | Y_1(\delta ) - Y_0, r^\delta =s)f(Y_1(\delta ) - Y_0| r^\delta =s). \end{aligned} \end{aligned}$$

In addition,

$$\begin{aligned} \begin{aligned}&f(d=\delta | Y_1(\delta ) - Y_0, r^\delta =s) \\&\quad = \int f(d=\delta , {\mathbf {X}} | Y_1(\delta ) - Y_0, r^\delta =s) \text {d}{\mathbf {X}} \\&\quad =\int f(d=\delta | {\mathbf {X}} , Y_1(\delta ) - Y_0, r^\delta =s) f ({\mathbf {X}} | Y_1(\delta ) - Y_0, r^\delta =s) \text {d} {\mathbf {X}} \\&\quad =\int f(d=\delta | {\mathbf {X}} , r^\delta =s) f ({\mathbf {X}} | Y_1(\delta ) - Y_0, r^\delta =s) \text {d} {\mathbf {X}},\quad \text {by ignorability,}\\&\quad = \int s f ({\mathbf {X}} | Y_1(\delta ) - Y_0, r^\delta =s) \text {d} {\mathbf {X}}= s. \end{aligned} \end{aligned}$$

Therefore, \(f(Y_1(\delta ) - Y_0 | d=\delta , r^\delta =s) = f(Y_1(\delta ) - Y_0| r^\delta =s)\).

Revisit the last expression in (17),

$$\begin{aligned} \begin{aligned}&E[ Y_1(\delta ) - Y_0 | d=\delta , r^\delta =s]\\&\quad = \int (Y_1(\delta ) - Y_0 ) f(Y_1(\delta ) - Y_0 | d=\delta , r^\delta =s) \text {d}(Y_1(\delta ) - Y_0)\\&\quad =\int (Y_1(\delta ) - Y_0 ) f(Y_1(\delta ) - Y_0| r^\delta =s) \text {d}(Y_1(\delta ) - Y_0)\\&\quad = E[ Y_1(\delta ) - Y_0 | r^\delta =s]. \end{aligned} \end{aligned}$$

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Han, B., Yu, H. Causal difference-in-differences estimation for evaluating the impact of semi-continuous medical home scores on health care for children. Health Serv Outcomes Res Method 19, 61–78 (2019). https://doi.org/10.1007/s10742-018-00195-9

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Keywords

  • Medical home
  • Difference-in-differences
  • Causal inference