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


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: stcox output: p-value and CI don't agree
Date   Wed, 08 Aug 2007 00:46:58 -0500

At 10:26 PM 8/7/2007, Michael McCulloch wrote:
Finally, if you estimated the hazard ratio in -stcox- the header would be "Observed Haz. Ratio", not "Observed coefficient".
Thank you Philip, but with all due respect I promise it's the hazard ratio that is returned. The following is the code I used, but for the purpose of this question, applied to the Stata system data file <cancer.dta>. Note that the plain -stcox- and bootstrapped -Cox- have the same effect size, but a different header.
OK, here are the bootstrapped results using your code:

. bootstrap drug=r(drug), reps(100): boot_hr
(running boot_hr on estimation sample)

Bootstrap replications (100)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
.................................................. 100

Bootstrap results Number of obs = 48
Replications = 100

command: boot_hr
drug: r(drug)

------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
drug | .2580584 .0692074 3.73 0.000 .1224144 .3937025
------------------------------------------------------------------------------

The z value = the incorrectly labeled hazard ratio (.2580584) divided by the bootstrap standard error.

Now contrast that with the following:

. set seed 12358

. bootstrap, reps(100): stcox drug
(running stcox on estimation sample)

Bootstrap replications (100)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
.................................................. 100

Cox regression -- Breslow method for ties

No. of subjects = 48 Number of obs = 48
No. of failures = 31
Time at risk = 744
Wald chi2(1) = 19.56
Log likelihood = -86.389289 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
_t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
drug | .2580584 .0790376 -4.42 0.000 .1415839 .4703513
------------------------------------------------------------------------------

Note that (a) the hazard ratio is now labeled correctly, and (b) z does NOT equal the hazard ratio divided by the bootstrap std. error. Finally, consider

. set seed 12358

. bootstrap, reps(100): stcox drug, nohr
(running stcox on estimation sample)

Bootstrap replications (100)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
.................................................. 100

Cox regression -- Breslow method for ties

No. of subjects = 48 Number of obs = 48
No. of failures = 31
Time at risk = 744
Wald chi2(1) = 19.56
Log likelihood = -86.389289 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
drug | -1.354569 .306278 -4.42 0.000 -1.954863 -.7542754
------------------------------------------------------------------------------

Here, z does equal observed coefficient/bootstrap std. error.

So again, I think the source of the earlier confusion stems from the fact that Stata was doing things wrong. But, if you use the bootstrap prefix command (which seems a lot simpler anyway) then you get the right results. If you need to do it your way, I strongly suspect StataCorp has to fix some bugs first; unless there is some bug in your program I am overlooking.

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME: (574)289-5227
EMAIL: Richard.A.Williams.5@ND.Edu
WWW: http://www.nd.edu/~rwilliam

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