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Inference for Shared-Frailty Survival Models with Left-Truncated Data

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  • Gerard J. van den Berg
  • Bettina Drepper
Abstract
Shared-frailty survival models specify that systematic unobserved determinants of duration outcomes are identical within groups of individuals. We consider random-effects likelihood-based statistical inference if the duration data are subject to left-truncation. Such inference with left-truncated data can be performed in previous versions of the Stata software package for parametric and semi-parametric shared frailty models. We show that with left-truncated data, the commands ignore the weeding-out process before the left-truncation points, affecting the distribution of unobserved determinants among group members in the data, namely among the group members who survive until their truncation points. We critically examine studies in the statistical literature on this issue as well as published empirical studies that use the commands. Simulations illustrate the size of the (asymptotic) bias and its dependence on the degree of truncation.

Suggested Citation

  • Gerard J. van den Berg & Bettina Drepper, 2016. "Inference for Shared-Frailty Survival Models with Left-Truncated Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 1075-1098, June.
    • Handle: RePEc:taf:emetrv:v:35:y:2016:i:6:p:1075-1098
    DOI: 10.1080/07474938.2014.975640
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    References listed on IDEAS

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    1. Ridder, Geert & Tunali, Insan, 1999. "Stratified partial likelihood estimation," Journal of Econometrics, Elsevier, vol. 92(2), pages 193-232, October.
    2. Lancaster,Tony, 1992. "The Econometric Analysis of Transition Data," Cambridge Books, Cambridge University Press, number 9780521437899, September.
    3. Mario Cleves & William W. Gould & Roberto G. Gutierrez & Yulia Marchenko, 2010. "An Introduction to Survival Analysis Using Stata," Stata Press books, StataCorp LP, edition 3, number saus3, March.
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    1. Jose Garcia-Louzao & Linas Tarasonis, 2023. "Productivity-enhancing reallocation during the Great Recession: evidence from Lithuania," Oxford Economic Papers, Oxford University Press, vol. 75(3), pages 729-749.
    2. Marie Böhnstedt & Jutta Gampe & Monique A. A. Caljouw & Hein Putter, 2023. "Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 585-607, July.
    3. Hellwig, Michael & Hüschelrath, Kai, 2018. "When Do Firms Leave Cartels? Determinants And The Impact On Cartel Survival," International Review of Law and Economics, Elsevier, vol. 54(C), pages 68-84.
    4. Haywood, Luke, 2016. "Wealth effects on job preferences," Labour Economics, Elsevier, vol. 38(C), pages 1-11.
    5. Jain, Apoorva & Peter, Klara Sabirianova, 2017. "A Joint Hazard-Longitudinal Model of the Timing of Migration, Immigrant Quality, and Labor Market Assimilation," IZA Discussion Papers 10887, Institute of Labor Economics (IZA).
    6. Frank Eriksson & Torben Martinussen & Thomas H. Scheike, 2015. "Clustered Survival Data with Left-truncation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1149-1166, December.
    7. repec:ajn:jobafd:2017:p:36-41 is not listed on IDEAS
    8. Volha Lazuka, 2019. "Early-Life Assets in Oldest-Old Age: Evidence From Primary Care Reform in Early Twentieth Century Sweden," Demography, Springer;Population Association of America (PAA), vol. 56(2), pages 679-706, April.

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    More about this item

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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