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Re: st: Just what are -tvc- and -texp- doing in -stcox-?

From (Roberto G. Gutierrez, StataCorp)
Subject   Re: st: Just what are -tvc- and -texp- doing in -stcox-?
Date   Fri, 31 Jul 2009 10:34:01 -0500

Jocelyn Andrel <> asks:

> I'm having trouble with -stcox-. I need to produce predicted survival
> curves, but my model has a time-dependent covariate, so I can't use -tvc-
> and -texp-, I have to use -stspilt-, then -stcox-. Which would be fine,
> except my unsplit and split model simply don't match. Here's the background:
> the data is time to death from a cancer, the time-dependent covariate is
> radiation after surgery. Some people had it, some didn't, so the radiation
> variable is dichotomous (0/1) for radiation, then the time of radiation is
> there for those who had it, and missing for those who didn't.

> I really have two questions:
> 1. How do -tvc- and -texp- work?
> 2. What's wrong with this code?

> My code looks like:

> stset timetoevent, failures(censor) id(id)
> stcox age, tvc(rad) texp(timeofrad)

> or

> stsplit at(failures)
> gen radtvc = rad*(_t > timeofrad)
> stcox age radtvc

-tvc()- and -texp()- work by interacting the variables in -tvc()- with the 
time expression specified in -texp()-.  For example

   . stcox age, tvc(rad) texp(_t > 10)

would be equivalent to

   . stsplit, at(failures)
   . gen radtvc = rad * (_t > 10)
   . stcox age radtvc

However, what Jocelyn is encountering is that the equivalence vanishes when 
the constant 10, say, is replace by the variable -timeofrad-.  The reason 
is that, given the time-varying nature of -texp()-, the values of -timeofrad- 
correspond to observations whose analysis times coincide with observed 
failures times, not with the observations as given in the original data.

As such, -texp()- should only be used with functions of analysis time that do
not include variables.  This is also mentioned in the Technical Note on page
134 of the Stata 11 [ST] manual.  

That stated, an error message would be more appropriate here.  We'll make that
change as part of a future ado update.

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