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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 14:02:09 +0930


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
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