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

[Philip Ryan <philip.ryan@adelaide.edu.au>]

OK.  I was wrong and I was (perhaps) right.

I was wrong is assuming you were merely doing:

.stcox drug, vce(bootstrap)

in which case the header of the "coefficient" column is, as it should 
be, "Observed Haz Ratio".

But in fact you were using a separate bootstrapping program, and, as 
you rightly say, the "coefficient" IS the bootstrap estimate of the 
hazard ratio (since you are bootstrapping exp_b[drug]).

But you are not bootstrapping estimates of the upper and lower 
confidence intervals on the exponential scale.   Stata just sees the 
100 instances of the "coefficients" as numbers, not hazard ratios, it 
gets their mean which it reports as the final estimate of 
"coefficient" (OK) and it gets their standard deviation and it just 
does the usual normal large sample approximation to a confidence 
interval.  But the coverage of this confidence interval may not be 
very good, because the hazard ratio is not usually well approximated 
by a normal distribution.  One usually deals with this by operating 
on the log scale - more closely approximating the normal distribution 
- and exponentiating afterwards.

So, what happens to your paradoxical example if you bootstrap 
_b[drug] rather than exp(_b[drug]) and exponentiate the reported 
coefficient, the lower limit and the upper limit as the final step? 
Does this resolve the inconsistency?

Phil


At 12:56 PM 8/08/2007, you 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.
>
> My question is this: in the case where Cox proportional hazards 
> regression results in apparently contradictory p-value and 95% CI, 
> what steps would one follow to investigate this observed result?
>
> I'd appreciate any strategy pointers that anybody might have.
> Thank you!
> Michael
>
> *--------------- begin code in question -----------------------
>
> *************
> * plain cox
> *************
> * load data and define as survival data
> sysuse cancer, clear
> stset studytim, failure(died)
> * run cox
> stcox drug
>
> *************
> * bootstrap cox
> *************
> * load data and define as survival data
> sysuse cancer, clear
> stset studytim, failure(died)
>
> * define program
> capture program drop boot_hr
>         program define boot_hr, rclass
>
>         * cox
>         stcox drug
>         indeplist, local
>         foreach var of varlist `X' {
>                 return scalar `var' = exp(_b[`var'])
>         }
>
> end
> * set seed for reproducibility, since bootstrap is a random sampling
> set seed 12358
>
> * run program
> bootstrap drug=r(drug), reps(100): boot_hr
> *--------------- end code in question -----------------------
>
>
>
>
>
>
> *
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Philip Ryan
Professor,
Discipline of Public Health

Director, Data Management & Analysis Centre

Associate Dean (IT)
Faculty of Health Sciences

postal address:
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