st: survival analysis with unknown censoring

["Wagner, Stefan" <swagner@bwl.lmu.de>]

I am analyzing survival times with no time-varying co-variates. At the moment, I am using a Cox proportional hazards model based on STATA's stcox.

The data is characterized as follows: 

For all observations in the sample it is known when an individual joined the risk pool, i.e., starting dates are known for all observations. Basically, spells can be terminated by two different outcomes A and B. Unfortunately, I only observe one of those two outcomes, A. For those cases, I also know when A happened and I can compute the duration of spells ending in A as (date of A minus entry date). 

For the remaining observations it is impossible to determine whether the spell already was terminated by event B or whether the observation is still at risk.

Due to this data structure it seems unreasonable to treat observations that didn't end in A as censored observations as I cannot know whether they are still in the risk pool (here duration would be date today minus entry date) or whether they left the risk pool to destination B (then duration would be date of B minus entry date). 

Currently, I am estimating the Cox model only for observations that ended in A excluding all other observations from the estimation. As a robustness check, I also estimate a Heckman selection model where the selection is defined over (spell ended in A yes/no) and duration is the dependent variable in stage 2. Results of both exercises are comparable.

Is anyone aware of how to deal with this problem in a better way? Or some literature looking at potential biases from excluding observations with unknown spell-endings? Thanks for your support!

Stefan


**************************************************************************************
Stefan Wagner
 
INNO-tec
Institut für Innovationsforschung, Technologiemanagement und Entrepreneurship
Ludwig-Maximilians-Universität München
Kaulbachstr. 45/III
80539 München
Tel.: ++49/89/2180-2877
Fax: ++49/89/2180-6284
swagner@bwl.lmu.de
http://www.inno-tec.de/personen/mitarbeiter/wagner/index.html
 



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