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

Gerard J. van den Berg*, Bettina Drepper

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)1075-1098
Number of pages24
JournalEconometric Reviews
Issue number6
Publication statusPublished - 2 Jul 2016


  • Duration analysis
  • Dynamic selection
  • Hazard rate
  • Left-truncation
  • Likelihood function
  • Stata
  • Twin data
  • Unobserved heterogeneity


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