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

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject Re: st: stcox output: p-value and CI don't agree Date Wed, 08 Aug 2007 01:00:27 -0500

```At 11:32 PM 8/7/2007, Philip Ryan wrote:

```
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.
Interesting! So I guess I am wrong in saying there is a bug in Stata, even though it is clearly not producing the intended results here.

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?
```I think so.  Here are the results:

. 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 |  -1.354569    .306278    -4.42   0.000    -1.954863   -.7542754
------------------------------------------------------------------------------

I still don't see why you need the program though; what is wrong with

bootstrap, reps(100): stcox drug

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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