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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 Professor, Discipline of Public Health Director, Data Management & Analysis Centre Associate Dean (IT) Faculty of Health Sciences postal address: Discipline of Public Health Mail Drop 511 University of Adelaide 5005 South Australia location: Level 6, Room 6-18 Bice Building Royal Adelaide Hospital North Terrace Adelaide tel +61 8 8303 3570 fax +61 8 8223 4075 http://www.public-health.adelaide.edu.au/ CRICOS Provider Number 00123M ----------------------------------------------------------- This email message is intended only for the addressee(s) and contains information that may be confidential and/or copyright. If you are not the intended recipient please notify the sender by reply email and immediately delete this email. Use, disclosure or reproduction of this email by anyone other than the intended recipient(s) is strictly prohibited. No representation is made that this email or any attachments are free of viruses. Virus scanning is recommended and is the responsibility of the recipient. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: stcox output: p-value and CI don't agree***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

**References**:**st: stcox output: p-value and CI don't agree***From:*Michael McCulloch <mm@pinest.org>

**Re: st: stcox output: p-value and CI don't agree***From:*Philip Ryan <philip.ryan@adelaide.edu.au>

**Re: st: stcox output: p-value and CI don't agree***From:*Michael McCulloch <mm@pinest.org>

**Re: st: stcox output: p-value and CI don't agree***From:*Philip Ryan <philip.ryan@adelaide.edu.au>

**Re: st: stcox output: p-value and CI don't agree***From:*Michael McCulloch <mm@pinest.org>

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