Carolina Meier-Hirmer <meierhi@paracelsus.fdm.uni-freiburg.de> 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}
---------------------------
S(t_0j)
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.
--Bobby
rgutierrez@stata.com
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