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# Re: st: parametric survival analysis - choosing the probability distribution

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: parametric survival analysis - choosing the probability distribution Date Wed, 8 Jun 2011 11:58:11 +0200

```On Tue, Jun 7, 2011 at 10:56 PM, Magdalena Kapelko wrote:
> Can you suggest me a way to solve the problem that the proportionality
> assumption for cox model does not hold? Is there any other model I can
> choose from?

The proportional hazard function means that at every point in time the
hazard in one group is always the same factor bigger or smaller than
the hazard in the comparison group. These ratios are the hazard ratios
you get in the output of -stcox-. When this assumption fails it means
that these ratios aren't constant over time. You can include such
interactions with time in your -stcox- model using the -tvc()- and
-texp()- options. Often it is enough to split time into two groups and
get an "early hazard ratio" and a "late hazard ratio" for only a few
variables.

Consider the example below. The -tvc()- option says which variable is
allowed to change over time, and the -texp()- specifies the functional
form of time for this interaction. In this case I used -_t>12-, which
is a logical statement so if this statement is true it gets a 1
otherwise a 0. So this is an indicator/dummy variable indicating
whether or not one year has passed (in this example time is measured
in months). In the -tvc()- option you can see that I let the variable
age  change by time and I also add the main effect of age to the
model. So, the main effect of age is the effect of age before 1 year
passed and the interaction effect indicates the factor change in the
main effect after one year. So getting a year older increases the
hazard of death by a factor of 1.11 (i.e. 11%) in the first year after
getting ill, while this effect of age increases by a factor of 1.04
(i.e. 4%) after the first year of getting ill. So the effect of age
after one year is 1.04*1.11= 1.15.

Notice that these hazard ratios (and ratio of hazard ratios for the
interaction effect) are the exponentiated coefficients. So we can get
the hazard after one year by summing the coefficients and
exponentiating the result, this is what the -lincom- command with the
-hr- option does.

*----------------- begin example ------------------
sysuse cancer, clear
stset studytime, failure(died)
stcox i.drug age, tvc(age) texp(_t>12)

// hazard ratio after 1 year
lincom _b[main:age] + _b[tvc:age], hr
*---------------- end example --------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

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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