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st: Re: streg

From (Roberto G. Gutierrez, StataCorp.)
Subject   st: Re: streg
Date   Thu, 19 Sep 2002 14:56:10 -0500

Carolina Meier-Hirmer <> asks:

> how is the adjustment for delayed entry (left-truncation) done within the
> parametric models of streg?

If you mean "how is it done in terms of what the user needs to do", then 
the answer is:

-stset- is used to establish four new variables for each observation:  _t0,
_t, _d, and _st.  _t0 is the entry time, _t the exit time, _d is the
failure/censor indicator, and _st is an indicator dictating whether the
observation is valid for use with Stata's -st- estimation/data manipulation
commands.  In the simplest of data with no left-truncation the entry time
corresponds to analysis time zero for all observations.  To specify a nonzero
entry time use the enter() option to -stset-.  For instance,

  . stset studytime, fail(died) enter(first_interview)

Once _t0 is -stset-, any left-truncation _t0 may exhibit is automatically
handled by all -st- commands.


If you mean "how is it done mathematically", then the answer is:

Left-truncation in parametric models is handled by conditioning on the fact
that had the respondent failed prior to entry, he/she would have never been
around to enroll in your study.  Thus, any failure/censor time that you do
observe is "given" that the subject survived to the point of entry.

Thus the likelihood term is

           L_j = S(t_j)^{1-d_j} f(t_j)^{d_j}

where the conditioning term is the denominator -- the probability of surviving
past the entry point.  Naturally, when t_0 is zero, S(t_0j) = 1 and the term
has no effect.

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