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

25 Pages Posted: 23 Oct 2011

See all articles by Gerard J. van den Berg

Gerard J. van den Berg

VU University Amsterdam - Department of Economics; Centre for Economic Policy Research (CEPR); IZA Institute of Labor Economics; Tinbergen Institute

Bettina Drepper

Tilburg University


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 studiesthat 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.

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

JEL Classification: C41, C34

Suggested Citation

van den Berg, Gerard J. and Drepper, Bettina, Inference for Shared-Frailty Survival Models with Left-Truncated Data. IZA Discussion Paper No. 6031. Available at SSRN:

Gerard J. Van den Berg (Contact Author)

VU University Amsterdam - Department of Economics ( email )

De Boelelaan 1105
1081 HV Amsterdam
+31 20 444 6132 (Phone)
+32 20 444 6020 (Fax)

Centre for Economic Policy Research (CEPR)

United Kingdom

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072

Tinbergen Institute

Burg. Oudlaan 50
Rotterdam, 3062 PA

Bettina Drepper

Tilburg University

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