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

Author

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  • van den Berg, Gerard J.

    () (University of Bristol)

  • Drepper, Bettina

    () (Tilburg University)

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 the Stata software package. 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, that is, 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. We provide a Stata command file that maximizes the likelihood function that properly takes account of the interplay between truncation and dynamic selection.

Suggested Citation

  • van den Berg, Gerard J. & Drepper, Bettina, 2011. "Inference for Shared-Frailty Survival Models with Left-Truncated Data," IZA Discussion Papers 6031, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp6031
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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.
    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, April.
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    Cited by:

    1. repec:eee:irlaec:v:54:y:2018:i:c:p:68-84 is not listed on IDEAS
    2. 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 for the Study of Labor (IZA).
    3. 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.
    4. Hellwig, Michael & Hüschelrath, Kai, 2017. "When do firms leave cartels? Determinants and the impact on cartel survival," ZEW Discussion Papers 17-002, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.

    More about this item

    Keywords

    left-truncation; likelihood function; dynamic selection; hazard rate; unobserved heterogeneity; duration analysis; stata; twin data;

    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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