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# Re: st: Why do the stcox CI differ when using margins?

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: Why do the stcox CI differ when using margins? Date Mon, 25 Feb 2013 13:16:56 +0000

```This is not my field, but my impression is that you are expecting
-margins- to give a sensible answer to what is here a dubious
question.

-margins- is doing what you asked for, which implies _symmetric_
confidence intervals for the hazard ratios following a delta-method
calculation. Manifestly, that is not what -stcox- does. But -margins-
starts with the -stcox- estimates as basis and does what it can to
summarize the evidence in its own terms.

In general, different criteria for confidence intervals will lead to
different results, especially with any inbuilt asymmetry or
nonlinearity or small sample sizes.

It's the sheerest of flukes that none of the intervals displayed in
your example go negative. Increase the confidence level, and that will
happen.

Nick

On Mon, Feb 25, 2013 at 12:50 PM, Radoslaw Panczak <r.panczak@gmail.com> wrote:

> I'm trying to understand how the margins and marginsplot work after
> stcox command in Stata.
>
> Starting with a dumb example:
>
> webuse stan3
> stset
> stcox i.posttran i.surg
>
> We can obtain following results:
>
> ------------------------------------------------------------------------------
>           _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>   1.posttran |   1.173034   .3444712     0.54   0.587     .6597023    2.085801
>    1.surgery |   .3449043   .1482592    -2.48   0.013     .1485267    .8009264
> ------------------------------------------------------------------------------
>
> Now, when I use
>
> margins, over( posttran surgery )
>
> The output is
>
> Predictive margins                                Number of obs   =        172
> Model VCE    : OIM
>
> Expression   : Relative hazard, predict()
> over         : posttran surgery
>
> ----------------------------------------------------------------------------------
>                  |            Delta-method
>                  |     Margin   Std. Err.      z    P>|z|     [95%
> Conf. Interval]
> -----------------+----------------------------------------------------------------
> posttran#surgery |
>             0 0  |          1          .        .       .            .
>           .
>             0 1  |   .3449043   .1482592     2.33   0.020     .0543217
>    .6354869
>             1 0  |   1.173034   .3444712     3.41   0.001     .4978826
>    1.848185
>             1 1  |   .4045843   .2057569     1.97   0.049     .0013083
>    .8078604
> ----------------------------------------------------------------------------------
>
> What is puzzling me here is the fact that estimates and their Std.
> errors are the same as when using stcox. However - the CI, z and p are
> now different.
>
> What is causing such behaviour?
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```