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Re: st: stcox output: p-value and CI don't agree


From   Philip Ryan <philip.ryan@adelaide.edu.au>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: stcox output: p-value and CI don't agree
Date   Wed, 08 Aug 2007 11:49:38 +0930

sacrificial line


well... it's your data and code but it sure looks suspiciously like that coefficient is not the hazard ratio.

Stata seems to have formed the confidence limits in the usual (asymptotic) way from the reported coefficient and its standard error, for example, the upper limit is:


. di 0.7626117 +(invnormal(.975) * 0.2860169)
1.3231945

as reported, and the CI is symmetrical around the estimate, which isn't likely for the CI of a hazard ratio.

Also the two-tailed P value arises in the usual way:

. di 2*(1-normal(.7626117/.2860169))
.00766874

... reported to 3dps as 0.008.

Finally, if you estimated the hazard ratio in -stcox- the header would be "Observed Haz. Ratio", not "Observed coefficient".

So, everything seems to check out and is internally consistent _if_ the "coefficient" is just that, the coefficient. Unless something else happened upstream, I can't explain it.


Phil


At 11:26 AM 8/08/2007, you wrote:

Thank you Phil. In this case, it's the hazard ratio that was obtained, and the 95% CI includes one. The column header is displayed that way because I bootstrapped the standard errors.

I appreciate your reply, and apologize for not specifying that point.
Michael


I don't see the contradiction.

Presumably you estimated the coefficient using the -nohr- option? So you get the log hazard ratio reported rather than the hazard ratio.
The P value is less than 0.05, the 95% CI does not cross zero. Reject the null either way.

Phil





At 11:09 AM 8/08/2007, you wrote:

Hello,
I've obtained contradictory p-value and 95% confidence interval from -stcox-.
I'm puzzled as I've not seen this before in my studies, and not sure about how to further explore these perplexing results. I'd appreciate any pointers.

------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
tcm | .7626117 .2860169 2.67 0.008 .2020288 1.323195
------------------------------------------------------------------------------

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Professor,
Discipline of Public Health

Director, Data Management & Analysis Centre

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Faculty of Health Sciences

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South Australia

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