Re: st: Wald interval and the WSJ

[Steven Samuels <sjhsamuels@earthlink.net>]

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
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> 1081 HV Amsterdam
> The Netherlands
>
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