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

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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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