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# Re: st: Interaction between continious and categorical variable in Cox model

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: Interaction between continious and categorical variable in Cox model Date Wed, 26 May 2010 07:46:06 +0000 (GMT)

```--- On Wed, 26/5/10, Sanam P wrote:
> I have included interaction between a categorical variable
> with 4 levels with a continuous variable in a Cox regression
> model using :
>
> xi:stcox ... i.categorical*continuous
>
> The model now include below variables involved in the
> interaction, with their Hazards ratios and p-values.
>
>
> Categorical-2
> Categorical-3
> Categorical-4
> Continuous
> Categorical X continious~2
> Categorical X continious~3
> Categorical X continious~4
>
> I think that  HR of "categorical-2"  means the risk in
> second category of the categorical variable compared with
> first category when the continious variable is equal to
> zero. and the hazards related to the "continiuos' means the
> slope of the continious variable at first level of the
> categorical variable.
>
> I was wondering whether you could kindly guide me how to
> calculate and interpret hazards for the last 3 terms
> involved in the interaction term.

Consider the example below:

*----------- begin example ------------
sysuse cancer, clear
stset studytime, failure(died)
replace age = age - 50
xi: stcox i.drug*age
*------------ end example --------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

The hazard ratios for _Idrug_2 says that the hazard of death
for someone taking drug 2 is (.1308-1)*100% = -87% smaller
than that hazard of someone taking drug 1 (the placebo) given
that they are 50 years old. The effect of age says that for
someone who receives the placebo, the hazard increases by
11% for every year (s)he gets older. The effect of _IdruXage_2
says that the effect of receiving drug 2 increases by 4% for
every year that the patient gets older. Alternatively, you
can also say that the effect of age increases by 4% if the
patient gets drug 2 rather than the placebo.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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```