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Re: st: stcox output: p-value and CI don't agree
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
OFFICE: (574)631-6668, (574)631-6463
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