I misnumbered the probabilities in the 2nd paragraph and probably
confused everyone. The paragraph should have been:
With the article data. P0 = .062 and P1 = .092. The denominator
term in the test statistic for the Wald test is 0.012401. The
denominator term with P0 and P1 is .012591. The ratio is .984876.
Therefore the proper Z statistic would be equal to the Wald statistic
reduced by this ratio.
-Steve
On Aug 14, 2008, at 12:35 PM, Steven Samuels wrote:
> 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.
>>
>> 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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>
Steven Samuels
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