Re: st: Left truncation in survival analysis

[Steven Samuels <sjsamuels@gmail.com>]

Well, re-reading Wooldridge's 2002 book, p. 700, I see that he refers to "left censoring" as an observation problem ("if some or all of the starting times a_i are not observed" whereas "left truncation" is the sample selection problem.  That's consistent, but I think that "left-truncation" would cover both cases.

Steve

Ref: Wooldridge, Jeffrey M. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, Mass.: MIT Press
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It would be interesting to know how these variant usages arise.

The earliest references I have about truncation is Sampford (1954). He  uses the word "truncated" if some event times fall outside the interval of observation, but he states that Hald (1952) used the word "censoring" to refer to cases when the numbers of "truncated" observations are known.  In Turnbull (1976) the distinction is clear, as it is in the text by Klein et al. (2003) The original meaning of truncation is that the analyst is aware of observations only if they are observed in certain intervals.   Thus if data are left-truncated, only those that survive past the truncation point are observed.  The failure times for these can then be interval-censored, left-censored, right-censored, or not censored at all.  I wonder how D'Addio and Ronsholm cope with the distinction.   

References: 
Hald, A. (1952) Statistical Theory with Engineering Applications. John Wiley and Sons, Inc.

Klein, John P., and Melvin L. Moeschberger. 2003. Survival Analysis : Techniques for Censored and Truncated Data. 2nd ed. ed. New York: Springer

Sampford MR.(1954). The estimation of response-time distribution, 111: Truncation and survival. Biometrics, 10, 531-561.

Turnbull, B.W. (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J. R. Statist. Soc. B, 38, 290-295.

Steve

On Apr 29, 2011, at 9:00 AM, Yigit Aydede wrote:

Hi Steve,
I saw your two recent posting on Statalist. Thanks again. As you suggested, I guess the best way is to remove subjects with unknown t0 from my analysis.  By the way, I've found a paper ("Left-Censoring in Duration data: Theory and Applications" by Anna Christina D'Addio and Michael Rosholm. Working Paper No: 2002-5 Department of Economics, University of Aarhus Denmark) that describes my case as "left-censoring" and offers some solutions.  It has a good summary for all possible cases.

Thanks again
--Yigit

Yigit Aydede
Department of Economics
Sobey School of Business
Saint Mary's University
Yigit.aydede@smu.ca


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