Jérôme Martin
☆    

France,
2013-03-22 18:32
(4836 d 16:13 ago)

(edited on 2013-03-23 11:48)
Posting: # 10264
Views: 7,128
 

 Sample size for a pilot study to estimate the CVintra [Power / Sample Size]

Dear All (especially Helmut who has posted this),

I'm back to an old subject of this forum, but I haven't find an answer in a new topic. So, this is my question:
In this table you have computed one-sided 80% CI of different CVintra and presented the Upper Limit:

   n  10%   15%   20%   30%   40%    50%

   4  21.4  32.4  43.8  68.7  97.2  131

   6  15.6  23.6  31.6  48.2  65.8   84.8

  12  12.7  19.1  25.6  38.7  52.1   66.0

  16  12.2  18.3  24.4  36.9  49.5   62.5

  24  11.6  17.5  23.3  35.1  47.1   59.8

  32  11.3  17.0  22.7  34.2  45.8   57.6


The value of 80% CI is discussed and challenged in the thread (75%?...). I agree with your rationale. Furthermore, in a more recent post there is discussions and examples with two-sided 95% CI, both with R code (alpha/2) or CVCL() function in PowerTOST.
So, did you have rules (personnal SOP or references) for the % of CI (75, 80, 95...) and if it is more relevant with one-sided or two-sided CI?

All the best,
Jérôme
ElMaestro
★★★

Denmark,
2013-03-22 21:32
(4836 d 13:14 ago)

@ Jérôme Martin
Posting: # 10265
Views: 5,942
 

 Sample size for a pilot study to estimate the CVintra

Hi Jérôme,

I do not intend to answer on behalf of Helmut but I'd nevertheless like to offer my unqualified and unnecessary opinion on this matter.

❝ ... if it is more relevant with one-sided or two-sided CI?


We have a Flemish saying here in Gent. It goes like this:
" Dans un bol ou saladier, râper les pommes de terre et saler. Ajouter un peu de farine, les oeufs et le persil. Faire chauffer une bonne quantité d'huile dans une poêle et verser la pâte par petites cuillerées. Bien faire dorer les beignets de chaque côté. Servir avec une bonne salade.
Toute décharge doit être située et conçue de manière à remplir les conditions requises pour prévenir la pollution du sol, des eaux souterraines ou des eaux de surface, et pour assurer que les lixiviats sont recueillis de manière efficace, en temps opportun et dans les conditions requises, conformément au point 2. La protection du sol, des eaux souterraines et des eaux de surface doit être assurée, pendant la phase d'exploitation/activité, par une barrière géologique assortie d'un revêtement de base étanche et, pendant les phases d'inactivité ou après la désaffectation, par une barrière géologique assortie d'un revêtement de surface étanche."

-which means in direct English translation: "It is better to be on the safe side when conducting bioequivalence studies."

We plan a study on basis of an expected variability which we may have from a pilot trial etc. but the variability itself is -just like the point estimate- estimated. So if we calculate an upper confidence for the variability limit then we can use that for a worst-case-within-reasonable-limits estimate and plug that limit of the variability into the sample size estimation machinery in order to have more confidence that out trial is adequately powered. That's why as I see it it is only relevant with an upper limit for the confidence limit of the variability. I don't think regulators would care since power is the applicant's problem so I would imagine you have free hands to implement your own way to be on the safe side re. power.

Pass or fail!
ElMaestro
Jérôme Martin
☆    

France,
2013-03-26 18:52
(4832 d 15:54 ago)

(edited on 2013-03-27 09:34)
@ ElMaestro
Posting: # 10288
Views: 5,533
 

 Sample size for a pilot study to estimate the CVintra

Hi ElMaestro,

Thanks to share your opinion ;-)

❝ We have a Flemish saying here in Gent. It goes like this:

❝ " Dans un bol ou saladier, râper les pommes de terre et saler. Ajouter un peu de farine, les oeufs et le persil. Faire chauffer une bonne quantité d'huile dans une poêle et verser la pâte par petites cuillerées. Bien faire dorer les beignets de chaque côté. Servir avec une bonne salade."

This part corresponds to a french receipe known as crique. I'm not sue it is intentional (I'm a native french speaker), but as far as I know, this taste good ;-)

❝ -which means in direct English translation: "It is better to be on the safe side when conducting bioequivalence studies."

I totally agree with your conclusion and since it appears that I have probably hands free I give you different options I computed based on Helmut ideas (One-sided, alpha=20%) :

One-sided, alpha=20%:
     10   15   20   30   40    50
4  21.4 32.4 43.8 68.7 97.2 131.1
6  15.6 23.6 31.6 48.2 65.8  84.8
12 12.7 19.1 25.6 38.7 52.1  66.0
16 12.2 18.3 24.4 36.9 49.5  62.5
24 11.6 17.5 23.3 35.1 47.1  59.3
32 11.3 17.0 22.7 34.2 45.8  57.6


Two-sided, alpha=20%:
     10   15   20    30    40    50
4  31.5 48.5 67.2 112.5 175.8 270.4
6  19.5 29.5 39.9  61.9  86.5 114.7
12 14.4 21.6 29.0  44.0  59.7  76.3
16 13.4 20.2 27.0  40.9  55.3  70.2
24 12.5 18.8 25.2  38.0  51.2  64.7
32 12.1 18.1 24.2  36.6  49.1  62.0


One-sided, alpha=5%:
     10   15    20    30    40    50
4  46.3 73.7 107.2 209.0 413.0 874.7
6  24.0 36.5  49.7  79.0 114.3 158.5
12 16.0 24.1  32.4  49.4  67.6  87.3
16 14.6 22.0  29.5  44.9  61.0  78.0
24 13.4 20.1  26.9  40.8  55.0  69.9
32 12.8 19.2  25.6  38.7  52.2  66.0


Two-sided, alpha=5%:
     10    15    20    30     40     50
4  69.4 118.7 192.5 539.3 1872.2 8200.5
6  29.3  44.9  61.8 101.8  155.1  230.5
12 17.6  26.6  35.8  55.1   76.1   99.4
16 15.8  23.9  32.0  48.9   66.8   86.1
24 14.2  21.3  28.6  43.4   58.8   75.1
32 13.4  20.1  26.9  40.8   55.1   70.0


If we assume that alpha=5% is too stringent, with alpha=20%, 16 people for a pilot study seems a good tradeof either one or two-sided.
Any opinions?
ElMaestro
★★★

Denmark,
2013-03-26 23:24
(4832 d 11:21 ago)

@ Jérôme Martin
Posting: # 10292
Views: 5,504
 

 Sample size for a pilot study to estimate the CVintra

Hello Jérôme,

❝ If we assume that alpha=5% is too stringent, with alpha=20%, 16 people for a pilot study seems a good tradeof either one or two-sided.

❝ Any opinions?


I would plainly and simply say that the higher the sample size the larger the chance that you get a good estimate of the variability and of many other things.

As for the tables, I am not entirely convinced they are a definitive source of truth. They are created on basis of assumptions re. variance distributions, I think. But we have also seen that in earlier threads that there are general potential violations of the underlying assumptions for the normal linear model as crossovers are concerned. Does that influence the variances estimates and/or their confidence intervals? I think it might but I cannot tell how.

I worhsip NLYWs and am a fan of simulations so believe it might be a good idea to use a distribution-free approach for variance CIs. Bootstrap/resampling (with sample replacement) of trial data and derive a variance CI form that, wouldn't that be an ok alternative?

Pass or fail!
ElMaestro
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