Stata The Stata listserver
[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

Re: st: Questions regarding -tvc- and proportional hazards


From   rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Questions regarding -tvc- and proportional hazards
Date   Fri, 20 Aug 2004 17:05:57 -0500

Joseph Wagner <WagnerJ@edc.pitt.edu> asks about time-varying covariates 
in -stcox- and the test of proportional hazards.

He writes:

> My survival analysis uses date of infection with hep c as the origin and the
> endpoint as date of esld, or last date of follow up.  I have dates of HIV
> and ART as well.  I set up my data with four observations per person, one
> for hep c date, one for hiv date, one for art date, and one for esld or last
> follow up date.  I also have age at hep c infection, (agebase).

...

> When I analyze that data using -tvc- I have hiv and art do NOT increase the
> risk of esld (I realize I have a power issue):

> stcox agebase, tvc(hiv art) mgale(mg) schoenfeld(sc*) scaledsch(ssc*)

First of all, the -tvc()- option to -stcox- is for use when you want a
covariate to vary with time, but vary in such a way that can be expressed as

    (variable in your data) * (some function of time, _t)

By default, "some function" is just the identity function _t, but you can
override that with the -texp()- option.  When Joseph specifies

   . stcox agebase, tvc(hiv art) mgale(mg) schoenfeld(sc*) scaledsch(ssc*)

he is saying that the log relative hazard (LRH) is 

    LRH = b_1 * agebase + b_2*hiv*_t + b_3*arg*_t        (1)

However, since Joseph already captured the time-varying nature of -hiv- and
-arg- by having split records, specifying them as -tvc()- is not necessary to
tell Stata that these variables are time-varying.  In fact, if you simply
specify

   . stcox agebase hiv art                               (2)

then, because you have split records, the time-varying nature of -hiv- and
-arg- is captured.  This is a perfectly valid model.   

If you examine (1), you can see that it can be used for two purposes:  (i) I
have covariates -hiv*_t- and -arg*_t- and I think LRH is time-constant and the
PH assumption is true or (ii) I have covariates -hiv- and -arg- that are
either time-constant or time-varying in a way already captured by split
records, and I think that LRH itself is time-varying and the PH assumption is
violated.  (ii) is more in line with Joseph's data, since I can't think of 
a good interpretation for a covariate like -hiv*_t-.

Joseph is also interested in testing the proportional hazards assumption.
He proceeds by fitting (1) and the using -stphtest- and finds the test to 
be insignificant.  However, because he fit (1) he has already stipulated that
the LRH is time-varying in -hiv- and -arg-, and so I am not surprised by this
result.

In order to test proportional hazards, what Joseph should do is either 

     a.  Fit (2), then use -stphtest-.  When he does so, he is testing to 
         see if the LRH is time-varying (not time-constant as PH contends) 
         in either one, some, or all of -agebase-, -hiv-, and -art-.

     b.  Fit 

         . stcox agebase hiv art, tvc(hiv art) ...

         and then test the significance of the coefficients in -tvc(hiv art)-
         by typing at post-estimation

         . test [t]

         which tests the coefficients in the time-varying part of the model.
         This checks to see if the LRH is time-varying in either of -hiv- or
         -art-, or both.

The difference between a. and b. is slight -- a. allows for time variance with
respect to -agebase-, b. doesn't.

--Bobby
rgutierrez@stata.com
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



© Copyright 1996–2014 StataCorp LP   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index