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st: Interpreting Cox interaction-revisited


From   moleps islon <moleps2@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Interpreting Cox interaction-revisited
Date   Sat, 31 Oct 2009 18:44:56 +0100

Dear listers,
In fitting a multivariable model for survival after treatment for
cancer I get that radiotherapy is beneficial and that multiple lesions
are detrimental (surprise..) Also the proportional hazard assumption
is not fulfilled for radiotherapy. However, after defining an
interaction between the two I get that the interaction is siginificant
and that the PH assumption on the model is fulfilled. In trying to
interpret this I would greatly appreciate it if someone could comment:

gen interact=rt*multiple
local g rt multiple
local u `g' interact
stcox `g'
eststo a
stcox `u' - all factors significant
------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        rt |   .5674932     .10614    -3.03   0.002     .3933306    .8187732
multiple |    7.46303   2.458919     6.10   0.000     3.912564    14.23538
 interact |   .1807812   .0658104    -4.70   0.000     .0885702    .3689937


lrtest a -->significant.

Analyzing the interaction further::

lincom rt+interact,eform

         _t |     exp(b)   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   .1025921   .0324932    -7.19   0.000     .0551466    .1908572

lincom multiple+interact,eform

          _t |     exp(b)   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   1.349175   .2142533     1.89   0.059     .9883139    1.841797


I interpret this to mean that rt decreases the hazard of death within
one unit of time by 90% if there are multiple metastases, whilst only
decreasing the hazard of death by 45% when there isnt multiplicity.

Conversely, that the HR is 7.46 for patients with multiplicity without
rt, but that multiplicity is only border-zone sigificant if the
patient receives rt.

Am I right in my interpretation?

regards,
M
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