# st: Questions regarding -tvc- and proportional hazards

 From "Wagner, Joseph" <[email protected]> To "'STATAList'" <[email protected]> Subject st: Questions regarding -tvc- and proportional hazards Date Fri, 20 Aug 2004 10:33:35 -0400

```I apologize for the length of this post but I have a problem that has many
of us at work stumped.

I have the STATA press book "An Introduction to Survival Analysis Using
Stata" and I am trying to perform a survival analysis using -tvc-.  I have
persons who all have hepatitis C (a risk factor for End Stage Liver Disease
- ESLD) and then eventually get become HIV+ and then eventually start taking
drugs for HIV (ART).  HIV and ART are both risk factors for ESLD.  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).

+-----------------------------------------------------------+
|  id   visit     examdat    exitdate   hiv      art   esld |
|-----------------------------------------------------------|
|   1       1   15jun1970   15jun1983    no    No Rx     no |
|   1       2   15jun1983   15jun1988   yes    No Rx     no |
|   1       3   15jun1988   14dec1988   yes      ART     no |
|   1       4   15jun1989   15jun1989   yes      ART    yes |
|-----------------------------------------------------------|
|   2       1   15jun1970   14jun1981    no    No Rx     no |
|   2       2   14jun1981   15jun1987   yes    No Rx     no |
|   2       3   15jun1987   14jun1988   yes      ART     no |
|   2       4   14jun1989   14jun1989   yes      ART    yes |
|-----------------------------------------------------------|

The example in the book though uses values of a continuous variable that
change relative to time.  My data however, uses a categorical variable that
changes with respect to time.  I assumed this did not matter - what was
important is that the variable varies with respect to time.

I'm having trouble trusting my results though.  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*)

No. of subjects =          157                     Number of obs   =
628
No. of failures =           24
Time at risk    =         3913
LR chi2(3)      =
31.56
Log likelihood  =    -93.64632                     Prob > chi2     =
0.0000

----------------------------------------------------------------------------
--
_t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
rh           |
agebase |   1.776424   .2582205     3.95   0.000      1.33603
2.361985
-------------+--------------------------------------------------------------
--
t            |
hiv |   1.041784   .0412923     1.03   0.302     .9639167
1.125943
art |   1.062477   .0416937     1.54   0.123     .9838228
1.14742
----------------------------------------------------------------------------
--

stphtest, rank detail

Test of proportional hazards assumption

Time:  Rank(t)
----------------------------------------------------------------
|       rho            chi2       df       Prob>chi2
------------+---------------------------------------------------
agebase     |     -0.38675         1.72        1         0.1902
hiv         |     -0.23011         0.70        1         0.4015
art         |      0.36422         1.04        1         0.3079
------------+---------------------------------------------------
global test |                      2.88        3         0.4108
----------------------------------------------------------------

So there doesn't appear to be any evidence that my model violates the
proportional hazards assumption.

If I don't use -tvc- I get very different hazards:

stcox agebase hiv art

----------------------------------------------------------------------------
--
_t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
agebase |   1.786311   .2587296     4.01   0.000     1.344835
2.372714
hiv |   3.392652   2.445086     1.70   0.090      .826186
13.93159
art |   3.892577   3.060481     1.73   0.084     .8336669
18.17531
----------------------------------------------------------------------------
--

Did I assume correctly that I should use the -tvc- option and therefore
trust those results?  If so what about proportional hazards?  I read the
chapter on time dependent variables in Collet's book "Modelling Survival
Data in Medical Research" and I understood him to say that when a variable X
depends on time t, the relative hazard is also time dependent.  Therefore
the hazard of death at time t is no longer proportional to the baseline
hazard, and the model is no longer a proportional hazards model.  So I
interpret this to mean that whenever one uses -tvc- the assumption of
proportional hazards is always violated.  Is this correct?  If so, why would
-stphtest- indicate that there was no violation?

-------------------------------------------
Joseph Wagner, MPH
130 Desoto Street
Parran Hall Room 134
Epidemiology Data Center
University of Pittsburgh
Pittsburgh, PA  15261
PHONE:(412) 624-5295
FAX: (412) 624-3775
Email: [email protected]
http://www.edc.gsph.pitt.edu
-------------------------------------------

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```