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st: RE: interaction term between categorical and continuous variable in survival analysis


From   "Kieran McCaul" <Kieran.McCaul@uwa.edu.au>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: interaction term between categorical and continuous variable in survival analysis
Date   Wed, 9 Sep 2009 07:08:35 +0800

...


With the interaction, the treatment effect, 0.767, is the effect at age=0.
Assuming that you have entered age as age in years, this isn't very informative.

You should centre the age.

qui sum age, meanonly
gen age2=age-`r(mean)'

Now run the regressions using age2.

You should get the same result in the model without the interaction.  In the model with the interaction, the treatment effect will be the effect at the average age.

The interaction term is not significant, which suggests that you should drop the interaction term, but you could use -lrtest- to check that there is no improvement in fit.

Also, fitting age as a continuous variable assumes that the hazard ratio is log-linear with age.  For common cancers in human populations, this is probably OK, but there are exceptions.  Cancers in children, for example, or testicular cancer.

______________________________________________
Kieran McCaul MPH PhD
WA Centre for Health & Ageing (M573)
University of Western Australia
Level 6, Ainslie House
48 Murray St
Perth 6000
Phone: (08) 9224-2701
Fax: (08) 9224 8009
email: Kieran.McCaul@uwa.edu.au
http://myprofile.cos.com/mccaul 
http://www.researcherid.com/rid/B-8751-2008
______________________________________________
If you live to be one hundred, you've got it made.
Very few people die past that age - George Burns


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of moleps islon
Sent: Wednesday, 9 September 2009 6:49 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: interaction term between categorical and continuous variable in survival analysis

Modeling time to death in  cancer both age and treatment (binary) have
a clearly significant effect;

stcox age tx

        _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      age |   1.023254   .0040953     5.74   0.000     1.015259    1.031312
      tx |   .4005361   .0407233    -9.00   0.000     .3281696    .4888605


However I´d like to check for the interaction between the two:
gen age_tx=age*tx
stcox age tx age_tx

          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      age  |   1.026575   .0049524     5.44   0.000     1.016915    1.036328
      tx |   .7671728   .3931694    -0.52   0.605       .28097    2.094723
       age_tx|   .9886413   .0087311    -1.29   0.196     .9716759    1.005903


So my model can now be simplified to B1(age)+tx(B2+B3*age). However as
long as both B2 and B3 are p>0.05 how do I interpret this? Should I
use lincom tx+age_tx?

. lincom tx+age_tx,hr


------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   .7584587   .3821458    -0.55   0.583     .2825258    2.036131
------------------------------------------------------------------------------

Intuitively I´d say that this new beta is rather similar to the
original tx beta and that age doesnt matter for treatment here, but I
really dont understand exactly what this linear combination of tx and
age_tx parameter is telling me?



Anyone care for an explanation?

Regards,
M

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