The article gives 68/855 events (restenosis, or re-clogging of the newly opened heart arteries)
with the Liberte stent & 67/956 with the standard stent.
It is possible to analyse these data using -csi- (follows Rothman, according to
the manual), or -binreg, rd (uses many methods, depending on options). Both permit
more than one method of estimation for the confidence interval.
According to the FDA's requirements, the device passes if the upper limit of the 90% CI is less than 3%; or if the (twosided) test gives p<0.1.
In addition, I found a good add-on that does several of the tests mentioned in the article:
-rdcii- by Joseph Coveney ([email protected]). Code below for those who want to try it out.
I found several tests gave CI that excluded a 3% disadvantage in restenosis rates for the new stents (The FDA's requirement for non-inferiority) : Rothman: 2.985%, Test-based: 2.979%, most of the methods derived from -binreg-, which differ on how the SE is calculated, and could be said to be variations of the Wald test, and from -rdci- the Wallenstein: 2.996% , but not Agresti-Caffo: 3.002%, Newcombe Method 10: 3.015%, or Miettinen-Nurminen: 3.019%.
Of the other points raised in the article, the lack of blinding is inevitable for the surgeons. The restenosis should ideally have been assessed by experts blind to the allocation. More worrying is that given the lack of randomisation, no attempt was made to correct for possible imbalances in the analysis. Although there was an attempt at matching, there were substantial and significant differences in a number of important predictors of outcome. In Stata, this could be done using -binreg, rd-, but not all packages would permit it.
It also appears there was no prespecified sample size calculation. If so, the study might have stopped as soon as they got a significant result on their primary endpoint by the pre-specified method of analysis (p=0.0487 is remarkably close to p=0.05), and the researchers are now paying the penalty for this.
set level 90
csi 68 67 787 889
di "Rothman: " %5.3f 100*r(ub_rd) "%"
csi 68 67 787 889, tb
di "Test-based: " %5.3f 100*r(ub_rd) "%"
clear
tabi 68 67 \ 787 889
gen reclog = row == 1
gen liberte = col == 1
binreg reclog liberte [fw=pop], rd
lincom liberte-.03, level(90)
expand pop
set more off
foreach vce in oim robust opg bootstrap jackknife eim jackknife1 unbiased {
di "binreg reclog liberte , rd vce(`vce')
binreg reclog liberte , rd vce(`vce')
test liberte =0.03
}
rdcii 68 67 787 889
di "Agresti-Caffo: " %5.3f 100*r(ub_ac) "%"
di "Newcombe Method 10: " %5.3f 100*r(ub_ne) "%"
di "Wallenstein: " %5.3f 100*r(ub_wa) "%"
di "Miettinen-Nurminen: " %5.3f 100*r(ub_mn) "%"
Date: Thu, 14 Aug 2008 16:08:56 +0100 (BST)
From: Maarten buis <[email protected]>
Subject: Re: st: Wald interval and the WSJ
- --- David Airey <[email protected]> wrote:
> And also the article doesn't emphasize effect size, which might make
> the quibbling over p values moot too.
Actually, the point estimate seems to suggest that the new stent does
better then the old one, if I read the original article
(http://content.onlinejacc.org/cgi/content/full/49/16/1676) correctly,
and I know absolutely nothing about cardiology other than that a
working hart is sorta crucial in staying alive.
I read this article as follows: The thing under study is how well two
types of stents prevent a thing called TVR (target vessel
revascularization) which is apperently a bad thing. In the group with
old stents this occured 68 times out of 855 (7.95%), while in the group
with new stents this occured 67 out of 956 times (7.01%). The purpose
of this study is to test the hypothesis that the proportion new -
porportion old > .03 .
I have been looking around if I could reproduce the tests reported in
the Wall Street Journal using Stata, but remained unsuccesful. This
probably says more about me than about Stata, because statistically
this is also unfamiliar terain for me, as I almost always do some sort
of regression, moreover if I where to look at tests like these I would
probably prefer odds ratios rather than risk differences.
- -- Maarten
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