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Re: st: Wald interval and the WSJ


From   Steven Samuels <samplerx@earthlink.net>
To   Steven Samuels <sjhsamuels@earthlink.net>
Subject   Re: st: Wald interval and the WSJ
Date   Thu, 14 Aug 2008 13:39:23 -0400

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 <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/
>> -----------------------------------------
>>
>> Send instant messages to your online friends http:// 
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>

Steven Samuels
845-246-0774
18 Cantine's Island
Saugerties, NY 12477
EFax: 208-498-7441





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