# Re: st: Wald interval and the WSJ

 From Steven Samuels <[email protected]> To [email protected] 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 <[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.

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
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

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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