Sample Size using mcnemar test for two dependent binomial populations

[Ashish Bandhu]

Hi Statalist users


I need your help in estimating the sample size for an interventional study where the baseline employment rate is 43%. An intervention is to plan and anticipate that 30% improvement in the employment rate so expected employment rate would be around 56% (43*30%). I have used the following command in Stata




power pairedproportions 0.43 0.56, corr(0.8)




but getting error
the resulting discordant proportions p12 and p21 must be between 0 and 1

Any help will be highly appreciated.


Thanks
Ashish

[Rich Goldstein]

why are you using a correlation of .8? it will work with a smaller corr:

. power pairedproportions 0.43 0.56, corr(0.5)

Performing iteration ...

Estimated sample size for a two-sample paired-proportions test
Large-sample McNemar's test
H0: p+1 = p1+  versus  Ha: p+1 != p1+

Study parameters:

        alpha =    0.0500
        power =    0.8000
        delta =    0.1300  (difference)
          p1+ =    0.4300
          p+1 =    0.5600
         corr =    0.5000

Estimated sample size:

            N =       120

added: just to be clear: I did not believe that a corr of .8 and the proportions you present are possible - and neither does Stata; the .5 is arbitrary for the example

[Ashish Bandhu]

why are you using a correlation of .8? it will work with a smaller corr:

. power pairedproportions 0.43 0.56, corr(0.5)

Performing iteration ...

Estimated sample size for a two-sample paired-proportions test
Large-sample McNemar's test
H0: p+1 = p1+ versus Ha: p+1 != p1+

Study parameters:

alpha = 0.0500
power = 0.8000
delta = 0.1300 (difference)
p1+ = 0.4300
p+1 = 0.5600
corr = 0.5000

Estimated sample size:

N = 120

added: just to be clear: I did not believe that a corr of .8 and the proportions you present are possible - and neither does Stata; the .5 is arbitrary for the example

Can you make me understand why correlation 0.8 is not possible?by the way it is arbitrary

Some online calculator for sample size is working with this

[Rich Goldstein]

just on reading your post, I could not see an easy way to have that much difference in proportions with that high a correlation; for a mathematical explanation; see equation 1 in the methods and formulas section of the write-up in the manual for power paired proportions

I can't comment on "some online calculator" without, at least, a url

[Ashish Bandhu]

just on reading your post, I could not see an easy way to have that much difference in proportions with that high a correlation; for a mathematical explanation; see equation 1 in the methods and formulas section of the write-up in the manual for power paired proportions

I can't comment on "some online calculator" without, at least, a url

For your reference
https://statulator.com/SampleSize/ss2PP.html

[Leonardo Guizzetti]

For your reference
https://statulator.com/SampleSize/ss2PP.html

As an aside, I could not reproduce the calculations made by that tool, nor find reference to the specific method being used. I would not trust any such statistical tool that did not openly and clearly tell you the underlying method being used and/or point to a credible reference.

[Rich Goldstein]

as with Leonardo Guizzetti , the only cites I could find at this site were to the site itself - I would not trust such a site