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Left-truncated health insurance claims data: theoretical review and empirical application

Author

Listed:
  • Rafael Weißbach

    (University of Rostock)

  • Achim Dörre

    (University of Rostock)

  • Dominik Wied

    (University of Cologne)

  • Gabriele Doblhammer

    (University of Rostock
    DZNE)

  • Anne Fink

    (DZNE)

Abstract

From the inventory of the health insurer AOK in 2004, we draw a sample of a quarter million people and follow each person’s health claims continuously until 2013. Our aim is to estimate the effect of a stroke on the dementia onset probability for Germans born in the first half of the 20th century. People deceased before 2004 are randomly left-truncated, and especially their number is unknown. Filtrations, modelling the missing data, enable circumventing the unknown number of truncated persons by using a conditional likelihood. Dementia onset after 2013 is a fixed right-censoring event. For each observed health history, Jacod’s formula yields its conditional likelihood contribution. Asymptotic normality of the estimated intensities is derived, related to a sample size definition including the number of truncated people. The standard error results from the asymptotic normality and is easily computable, despite the unknown sample size. The claims data reveal that after a stroke, with time measured in years, the intensity of dementia onset increases from 0.02 to 0.07. Using the independence of the two estimated intensities, a 95% confidence interval for their difference is [0.053, 0.057]. The effect halves when we extend the analysis to an age-inhomogeneous model, but does not change further when we additionally adjust for multi-morbidity.

Suggested Citation

  • Rafael Weißbach & Achim Dörre & Dominik Wied & Gabriele Doblhammer & Anne Fink, 2024. "Left-truncated health insurance claims data: theoretical review and empirical application," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(1), pages 31-68, March.
    • Handle: RePEc:spr:alstar:v:108:y:2024:i:1:d:10.1007_s10182-023-00471-1
    DOI: 10.1007/s10182-023-00471-1
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    References listed on IDEAS

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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. Weißbach, Rafael & Mollenhauer, Thomas, 2011. "Modelling Rating Transitions," VfS Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48698, Verein für Socialpolitik / German Economic Association.
    3. Rafael Weißbach & Yongdai Kim & Achim Dörre & Anne Fink & Gabriele Doblhammer, 2021. "Left-censored dementia incidences in estimating cohort effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 38-63, January.
    4. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521405515, December.
    5. Weißbach, Rafael & Walter, Ronja, 2010. "A likelihood ratio test for stationarity of rating transitions," Journal of Econometrics, Elsevier, vol. 155(2), pages 188-194, April.
    6. Weißbach, Rafael & Schmal, Friederike, 2019. "Estimating the probability of a non-Markovian rating transition from partially unobserved histories," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 12(3), pages 256-267, June.
    7. Rafael Weißbach & Dominik Wied, 2022. "Truncating the exponential with a uniform distribution," Statistical Papers, Springer, vol. 63(4), pages 1247-1270, August.
    8. Rafael Weißbach & Patrick Tschiersch & Claudia Lawrenz, 2009. "Testing time-homogeneity of rating transitions after origination of debt," Empirical Economics, Springer, vol. 36(3), pages 575-596, June.
    9. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models 2 volume set," Cambridge Books, Cambridge University Press, number 9780521478373, July.
    10. Yongdai Kim & Lancelot James & Rafael Weissbach, 2012. "Bayesian analysis of multistate event history data: beta-Dirichlet process prior," Biometrika, Biometrika Trust, vol. 99(1), pages 127-140.
    11. Yaniv Tenzer & Micha Mandel & Or Zuk, 2022. "Testing Independence Under Biased Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 2194-2206, October.
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