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

[Michael McCulloch <mm@pinest.org>]

Thank you Richard. Yes, I do need to run the analysis within my 
bootstrap program, and not using the bootstrap prefix or 
-vce(bootstrap)- option after -stcox-. The reason for that is that 
the data are -stset- using -iweights-.

Jeff Pitbaldo responded to a previous posting of mine (st: stcox: 
weighted regression changes the # of observations) that: "-bootstrap- 
is not meant for weighted data.   Currently -stcox- with the 
-vce(bootstrap)- option does not complain when weights have been 
-stset, but it should (we will fix this soon)."

The reason I posted my question using <cancer.dta> is so I could 
demonstrate my code so it would be reproducible. I do appreciate the 
thoughtful and incisive attention of the Statalist users.

I'm still stymied!
Michael




> 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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