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Re: st: stcox question

From   Maarten Buis <>
Subject   Re: st: stcox question
Date   Wed, 28 Mar 2012 10:05:18 +0200

On Tue, Mar 27, 2012 at 4:46 PM, Robert Davidson wrote:
> I am estimating several hazard models, using stcox, using the by
> command to separate by whether or not the the observations (people)
> have criminal records.
> I am estimating a standard model: by crime, sort: stcox (varlist) and
> clustering the standard errors.
> I would like to test whether some of my coefficients/hazard rates (of
> variables in varlist) for one type (say those with criminal records)
> are significantly larger than for the other type.  Is there a way I
> can do this that does not involve running the model on the full sample
> and creating an interaction term (criminal record * var x)?  I would
> like to avoid all of the issues that arise with interaction
> coefficients in binary models as people in my area are quite skeptical
> of the interpretation of such interactions.  I know I can estimate a
> logit model and use the Norton et al. correction for the interaction,
> but I would like to find a more convincing way to test this difference
> across models.

However you are going to estimate this, there is just no getting
around the fact that what you want to estimate is an interaction
effect. But things are not as bad as you think. The Norton et al.
correction only applies to marginal effects, if you interpret your
model in the natural metric of the model than there is no need for a
correction. This is particularly relevant for -stcox- as there is no
meaningful marginal effect for that model.

The logic behind Cox regression is that it estimates hazard rate
ratios (note: this is _not_  the same as hazard rate) without
estimating the baseline hazard function. This is a strength in the
sense that you cannot make mistakes in things you don't estimate, but
it is also a weakness in the sense that you can only interpret those
hazard ratios; all other statistics you might be interested in but
require the baseline hazard in order to compute it (including marginal
effects) cannot be computed from the results of a Cox model. Moreover,
I don't think marginal effects make any sense within the context of
survival analysis: you have the usual problem that there can be
substantial variation in marginal effects between observation and on
top of that there can be substantial variation in marginal effects
within an observation over time.

So with a Cox regression you are going to interpret your coefficients
within the natural metric of that model (hazard rate ratios)  because
marginal effects cannot be computed and even if they could they would
make no sense. Since you are using the natural metric there is no need
for any corrections, so it is easy. In other words: I would just do
the interaction model and interpret the exponentiated interaction
terms as ratios of hazard rate ratios. A link to various examples
including Cox regression is given here:

Hope this helps,

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

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