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Re: st: Wald interval and the WSJ


From   Steven Samuels <sjhsamuels@earthlink.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Wald interval and the WSJ
Date   Thu, 14 Aug 2008 12:35:39 -0400

The 1-sided .95 confidence interval for the treatment difference given in the article excludes the null value of .03; the problem is that the proper non-inferiority test statistic would have p>.05. Fleiss, Levin, Paik (Statistical Methods for Rates and Propotions, 2nd Ed, Wiley, pp 168-174) show one proper non-inferiority statistic (I'm not sure which of the listed alternatives it corresponds to). In an ordinary Wald Z Statistic, the denominator contains terms in p1(1-p1)/n1 and p0(1-p0)/n0. In the non-inferiority setting, the probabilities are changed to: P1 and P0, where P1 - P0 =.03 (the null hypothesis. These are the maximum likelihood estimates under the null hypothesis.

With the article data. P1 = .062 and P2 = .092. The denominator term in the test statistic for the Wald test is 0.012401. The denominator term with P1 and P2 is .012591. The ratio is .984876. Therefore the proper Z statistic would be equal to the Wald statistic reduced by this ratio.

Now, the p-value for the Wald statistic in the paper was .0487, equivalent to Z = 1.6575912. The "proper z" would have been 1.6325, with a p-value of 0.0512, close to what the WSJ article reported for the alternatives.

-Steve

On Aug 14, 2008, at 11:08 AM, Maarten buis wrote:


--- David Airey <david.airey@Vanderbilt.Edu> 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

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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