Re: st: stcox question

[Robert Davidson <rhd773@gmail.com>]

Maarten,

Thank you for your detailed reponse; it is quite helpful.

Best Regards,
Rob,

On Wed, Mar 28, 2012 at 4:05 AM, Maarten Buis <maartenlbuis@gmail.com> wrote:
> 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:
> <http://www.maartenbuis.nl/publications/interactions.html>
>
> 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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