st: -stset- with stock-sampling, frailty and TVC

[Antoine Terracol <Antoine.Terracol@univ-paris1.fr>]

Dear _all,

Suppose I have a stock-sample of duration data where I happen to know 
the values of the covariates before the first observation of the 
individuals (because of a retrospective questionnaire, for example).

A typical individual might look like:

id   x    time  fail  tstock
1    1    1.5    0     2
1    2    2.5    0     2
1    3    4      1     2

I am interested in estimating a parametric model with frailty.

What would be the correct way to -stset- my data so that Stata uses the 
path of the covariates before the sampling date?

if I specify

. stset time, id(id) fail(fail) enter(tstock)

Stata will discard the first row of the individual in the above example 
(_st will be 0).

In a model without frailty, this would not matter since the sub-survival 
functions between 0 and enter() disappear from the likelihood.

With frailty, however, this is not true since we deal with the ratio of 
unconditional survival functions (integrated w.r.t the distribution of 
the frailty). Using the above -stset- command, we in fact assume that 
the covariate is constant from time 0 to the first observed value with 
date>=enter()

Does anyone know how to correctly -stset- my data?

Best,
Antoine


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