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Regression Trees Identify Relevant Interactions: Can This Improve the Predictive Performance of Risk Adjustment?

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  • Florian Buchner
  • Jürgen Wasem
  • Sonja Schillo

Abstract

Risk equalization formulas have been refined since their introduction about two decades ago. Because of the complexity and the abundance of possible interactions between the variables used, hardly any interactions are considered. A regression tree is used to systematically search for interactions, a methodologically new approach in risk equalization. Analyses are based on a data set of nearly 2.9 million individuals from a major German social health insurer. A two‐step approach is applied: In the first step a regression tree is built on the basis of the learning data set. Terminal nodes characterized by more than one morbidity‐group‐split represent interaction effects of different morbidity groups. In the second step the ‘traditional’ weighted least squares regression equation is expanded by adding interaction terms for all interactions detected by the tree, and regression coefficients are recalculated. The resulting risk adjustment formula shows an improvement in the adjusted R2 from 25.43% to 25.81% on the evaluation data set. Predictive ratios are calculated for subgroups affected by the interactions. The R2 improvement detected is only marginal. According to the sample level performance measures used, not involving a considerable number of morbidity interactions forms no relevant loss in accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

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  • Florian Buchner & Jürgen Wasem & Sonja Schillo, 2017. "Regression Trees Identify Relevant Interactions: Can This Improve the Predictive Performance of Risk Adjustment?," Health Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 74-85, January.
    • Handle: RePEc:wly:hlthec:v:26:y:2017:i:1:p:74-85
    DOI: 10.1002/hec.3277
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    1. Buchner, Florian & Goepffarth, Dirk & Wasem, Juergen, 2013. "The new risk adjustment formula in Germany: Implementation and first experiences," Health Policy, Elsevier, vol. 109(3), pages 253-262.
    2. Van de ven, Wynand P.M.M. & Ellis, Randall P., 2000. "Risk adjustment in competitive health plan markets," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 14, pages 755-845, Elsevier.
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    4. van de Ven, Wynand P.M.M. & Beck, Konstantin & Buchner, Florian & Schokkaert, Erik & Schut, F.T. (Erik) & Shmueli, Amir & Wasem, Juergen, 2013. "Preconditions for efficiency and affordability in competitive healthcare markets: Are they fulfilled in Belgium, Germany, Israel, the Netherlands and Switzerland?," Health Policy, Elsevier, vol. 109(3), pages 226-245.
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    1. Pilny, Adam & Wübker, Ansgar & Ziebarth, Nicolas R., 2017. "Introducing risk adjustment and free health plan choice in employer-based health insurance: Evidence from Germany," Journal of Health Economics, Elsevier, vol. 56(C), pages 330-351.
    2. Mohnen Sigrid M. & Rotteveel Adriënne H. & Doornbos Gerda & Polder Johan J., 2020. "Healthcare Expenditure Prediction with Neighbourhood Variables – A Random Forest Model," Statistics, Politics and Policy, De Gruyter, vol. 11(2), pages 111-138, December.
    3. Alexandre Vimont & Henri Leleu & Isabelle Durand-Zaleski, 2022. "Machine learning versus regression modelling in predicting individual healthcare costs from a representative sample of the nationwide claims database in France," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 23(2), pages 211-223, March.
    4. A. A. Withagen-Koster & R. C. Kleef & F. Eijkenaar, 2018. "Examining unpriced risk heterogeneity in the Dutch health insurance market," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 19(9), pages 1351-1363, December.
    5. Tuukka Holster & Shaoxiong Ji & Pekka Marttinen, 2024. "Risk adjustment for regional healthcare funding allocations with ensemble methods: an empirical study and interpretation," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 25(7), pages 1117-1131, September.
    6. Marica Iommi & Savannah Bergquist & Gianluca Fiorentini & Francesco Paolucci, 2022. "Comparing risk adjustment estimation methods under data availability constraints," Health Economics, John Wiley & Sons, Ltd., vol. 31(7), pages 1368-1380, July.

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