# [R] Cox proportional hazards confidence intervals

peter dalgaard pdalgd at gmail.com
Mon Nov 21 09:25:32 CET 2011

```On Nov 21, 2011, at 05:50 , David Winsemius wrote:

>
> On Nov 20, 2011, at 6:34 PM, Paul Johnston wrote:
>> ...
>> I had intended to report logrank P values with the hazard ratio and CI
>> obtained from this function.  In one case the P was 0.04 yet the CI
>> crossed one, which confused me, and certainly will raise questions by
>> reviewers.  In retrospect I can see that the CI calculated by coxph is
>> intimately related to the Wald p-value (which in this specific case
>> was 0.06), so this would appear to me not a good strategy for
>> reporting my results (mixing the logrank test with the HR and CIs from
>> coxph).
>>
>> I can report the Wald p-values instead, but I have read that the Wald
>> test is inferior to the score test or LR test.  My questions for
>> survival analysis jockeys out there / TT:
>>
>> 1. Should I just stop here and use the wald.p.value?  This appears to
>> be what Stata does with the stcox function (albeit Breslow method).
>
> I don't understand two things: Why would your report the inferior result, and I suppose  I also wonder why does it make that much difference? The estimate is what it is and a p-value of .04 is not that different from one of .06. Or are we dealing with religious beliefs here?
>

Well, it is an annoying inconsistency, but one that happens all over the place.

Consider the single binomial sample: Most applied statistics textbooks teach the students to calculate the error margin for a CI as 1.96*sqrt(phat*(1-phat)/n), but the cutoff for testing p=p0 uses 1.96*sqrt(p0*(1-p0)/n). This will (and does) give rise to situations where the test and the CI disagrees.

It is fixable by using the error margins at the upper and lower confidence limits, but it leads to nonlinear equations that you'd rather not inflict on students. (For the binomial sample it's a quadratic equation and prop.test actually uses it.)

I'd just leave it, and, if anyone complains, put in a note to the effect that "the slight inconsistency between p-value and CI is due to different large-sample approximations".
--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

```