Bioequivalence and Bioavailability Forum

Compliance ★ India, 2013-07-23 16:09 (3927 d 12:47 ago) Posting: # 11038 Views: 10,069	Sample size calculation by power-tost software [Software] Post reply
	Dear All, can any one tell us how to calculate sample size by using power-tost software. we had tried a lot but unable to understand how to use this software. Regards, Compliance Edit: Category changed. [Helmut]

d_labes
★★★

Berlin, Germany,
2013-07-23 18:23
(3927 d 10:32 ago)

@ Compliance
Posting: # 11039
Views: 9,155

Sample size estimation with PowerTOST

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Dear Compliance,

❝ can any one tell us how to calculate sample size by using power-tost software. we had tried a lot but unable to understand how to use this software.

That's a very broad and unspecific question. Could you please be more elaborate?

Did you read the manual?
Had you had a look at the examples in it?

As a little primer:
Need to estimate the (classical) sample size for a 2x2 crossover. Assumed CV (from previous studies, from pilot study or from literature) is 30% (0.3 as ratio). Assumed distribution is log-normal.
Just type in the R-console:
sampleN.TOST(CV=0.3)
Hit the ENTER key.
That is it, because most of the arguments of the function have reasonable default values. Again, RTFM!

Response after hitting ENTER (printing all the default settings):

+++++++++++ Equivalence test - TOST +++++++++++

            Sample size estimation

-----------------------------------------------

Study design:  2x2 crossover 

log-transformed data (multiplicative model)



alpha = 0.05, target power = 0.8

BE margins        = 0.8 ... 1.25 

Null (true) ratio = 0.95,  CV = 0.3



Sample size (total)

 n     power

40   0.815845

BTW: I strongly recommend you Helmut's lectures, especially those dealing with sample size estimation. They have at many places hints how it could be done with PowerTOST.

Hope this helps.

—
Regards,

Detlew

Ben
★

2013-07-28 15:08
(3922 d 13:47 ago)

(edited by Ben on 2013-07-28 16:06)
@ d_labes
Posting: # 11085
Views: 9,040

PowerTOST Usage

Post reply

Dear Detlew,

I tried to send a direct messag via Helmuts forum form, but I suspect that it has not worked properly. So, I will give it another try in here as I have two specific questions related to the usage of the R package PowerTOST (which somehow fits to this post I guess) and it would be great if you could shed some light on that.
First, every time I want to use the helper functions CV2se and se2CV I am confused why it is called that way, and not „CV2sd“ and „sd2CV“, respectively. Standard error always reminds me of sd/sqrt(n) or sd*sqrt(2/n) which is not what we want to plug in here...?!
My second question refers to the option „logscale=FALSE“. When logscale=FALSE then I wonder how the argument CV looks like. CV is actually sd/mean, but then one also requires to know something about the mean. A better argument would be the standard deviation and a look into your code reveals that in fact you directly put CV <- se. But when looking into the manual, there is no reference that it will be handled this way and moreover, in the example from sampleN.TOST you write „total CV=20%“ when putting CV=0.2 as an argument. Shouldn‘t it then be „total SD = 0.2“ (not in percent)?

Thank you,
Ben

d_labes
★★★

Berlin, Germany,
2013-07-28 20:00
(3922 d 08:55 ago)

@ Ben
Posting: # 11086
Views: 9,070

PowerTOST naming issues

Post reply

Dear Ben,

❝ First, every time I want to use the helper functions CV2se and se2CV I am confused why it is called that way, and not „CV2sd“ and „sd2CV“, respectively. Standard error always reminds me of sd/sqrt(n) or sd*sqrt(2/n) which is not what we want to plug in here...?!

Ok, maybe that your naming proposal fits your needs better. Mine was driven from the term standard deviation of error (=square root of the error variance).
What you link with this symbol is usually written as SEM = standard error of mean by me (and many others).

❝ My second question refers to the option „logscale=FALSE“. When logscale=FALSE then I wonder how the argument CV looks like. CV is actually sd/mean, but then one also requires to know something about the mean. A better argument would be the standard deviation and a look into your code reveals that in fact you directly put CV <- se. But when looking into the manual, there is no reference that it will be handled this way and moreover, in the example from sampleN.TOST you write „total CV=20%“ when putting CV=0.2 as an argument. Shouldn‘t it then be „total SD = 0.2“ (not in percent)?

You may use the mean and standard deviation the way you describe, I think. Try it by yourself.
You may also use the mean ratio (theat0) as deviation from 1 and then the CV is the ratio sd/mean. The last was the way Kem Philips has described in his basic paper, the ancestor of all power/samplesize papers on the field of BE studies. I have this adopted in my description in the manual

I must confess that I hadn't thought too much about the description in the manual if you use „logscale=FALSE“. This was only implemented for reasons of completeness for comparison with historically tables from that times as it was custom to evaluate BE studies with both log-transformed and untransformed data. But nowadays only log-transformed evaluations are done.

If you prefer untransformed evaluations (f.i. for PD parameters) the use of the Fieller CI is IMHO the appropriate method. Thus use then sampleN.RatioF() for sample size estimations.
Using sampleN.TOST() with logscale=FALSE is only an approximation since it neglects the fact that the Reference mean is only obtained as an estimate.

Naming the input parameter other than CV would inflate the parameter list which is long enough already now, I think. And it would raise the programming burden for me which was already big enough (at east for me as an bloody dabbler).

If this all don't fit your needs: The open source idea is, amongst other, take my code and do it better than I was able to do.

BTW: There is the possibility to write to the maintainer of the PowerTOST package directly. The CRAN policy deemed him to publish his mail address for that purpose :cool:

.
Having the side effect of getting some more spam than already usual. :vomit:

—
Regards,

Detlew

ElMaestro
★★★

Denmark,
2013-07-28 21:06
(3922 d 07:50 ago)

@ d_labes
Posting: # 11087
Views: 9,010

PowerTOST Usage

Post reply

Dear Detleffff,

❝ Ok, maybe that your naming proposal fits your need better. Mine was driven from the term standard deviation of error.

No sir

With all due respect, I side with Ben here. I think you should follow common naming conventions.
I am not often using PowerTOST but I think that what you are calling 'standard deviation of error' is no such thing. It is a measure of the standard deviation of the mean difference (on the log scale, for the most common use) and as such it could be termed sd or s, but definitely not Standard Error.
In practice we nned to regard the SD as a variability measure, whereas the SE is a measure of how well we have estimated the mean (slash mean difference). The two are related but different.

—
Pass or fail!
ElMaestro

d_labes ★★★ Berlin, Germany, 2013-07-28 21:30 (3922 d 07:26 ago) @ ElMaestro Posting: # 11088 Views: 9,038	Common naming conventions of EM Post reply
	Hi Anders, ❝ No sir With all due respect, I side with Ben here. I think you should follow common naming conventions. Do you remember functions `EatMyShorts <- function (x, V, T, W)` or `Apfelstrudel<-function(t, df, ta, tb, ncp)` not to speak about `I_Eat_Cadmium <- function(P, TR, CV, alpha, N)` . For the rest see my proposal for Ben: Take my code and do it better. — Regards, Detlew

ElMaestro
★★★

Denmark,
2013-07-28 21:40
(3922 d 07:15 ago)

@ d_labes
Posting: # 11089
Views: 8,971

Common naming conventions of EM

Post reply

Dear Detleff,

❝ Do you remember functions EatMyShorts <- function (x, V, T, W) or

❝ Apfelstrudel<-function(t, df, ta, tb, ncp) not to speak about I_Eat_Cadmium <- function(P, TR, CV, alpha, N) :-D .

I was young and wreckless back then. Now I have matured into an entirely different beast - bloody intelligent and handsome.

This discussion is making me hungry. Got some spare batteries I could have?

—
Pass or fail!
ElMaestro

Ben ★ 2013-07-29 19:04 (3921 d 09:52 ago) @ d_labes Posting: # 11116 Views: 8,950	PowerTOST naming issues Post reply
	Dear Detlew, Don't get me wrong, I am a big fan of PowerTOST which I could not do better! I was just curious about the background of the notation and whether I misunderstand something here. Especially regarding when to use logscale=FALSE and what it actually means. Thank you for clarifying this! Best regards, Ben

Helmut
★★★

Vienna, Austria,
2013-07-23 18:27
(3927 d 10:28 ago)

@ Compliance
Posting: # 11040
Views: 9,435

Error description?

Post reply

Hi Compliance,

❝ can any one tell us how to calculate sample size by using power-tost software.

Sure.

❝ we had tried a lot but unable to understand how to use this software.

That’s not what I call an exhaustive description of the problem. What did you try? What did not work?

Start the R-console and attach the library by typing library(PowerTOST). Type help(package=PowerTOST). The help-index opens in your preferred browser and shows a list of available functions.
Try sampleN.TOST. If you are just interested in sample size estimation, type simply ?sampleN.TOST).
On top below “Usage” you see all “arguments“ you may specify. Some are defaults; you can leave them out if your study is within the variables’ range.
Most simple case: You want to estimate* the sample size for a 2×2×2 cross-over, CV 20%, assumed T/R-ratio 95%, 80% power. Just type
sampleN.TOST(CV=0.2)
and you will get

+++++++++++ Equivalence test - TOST +++++++++++

            Sample size estimation

-----------------------------------------------

Study design:  2x2 crossover

log-transformed data (multiplicative model)



alpha = 0.05, target power = 0.8

BE margins        = 0.8 ... 1.25

Null (true) ratio = 0.95,  CV = 0.2



Sample size (total)

 n     power

20   0.834680

Note that everything in PowerTOST is given in fractions – not percentages.

If the output is too verbose for your taste, switch it off to get a data.frame:

sampleN.TOST(CV=0.2, print=F, details=F)

  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power

1    2x2  0.05 0.2   0.95    0.8   1.25          20      0.8346802          0.8

Power 90% instead of 80%:

sampleN.TOST(CV=0.2, targetpower=0.9, print=F, details=F)

  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power

1    2x2  0.05 0.2   0.95    0.8   1.25          26      0.9176333          0.9

Worse ratio:

sampleN.TOST(CV=0.2, targetpower=0.9, theta0=0.9, print=F, details=F)

  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power

1    2x2  0.05 0.2    0.9    0.8   1.25          50      0.9008663          0.9

Long half-life drug and/or study in patients? Note that the CV is CV_total and not CV_intra. Likely to be higher. 80% power is all we can afford:

sampleN.TOST(CV=0.5, targetpower=0.8, theta0=0.9, design="parallel", print=F, details=F)

    Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power

1 parallel  0.05 0.5    0.9    0.8   1.25         400      0.8007482          0.8

Sample size in the 2×2×2 above (50) larger than the clinical capacity? Try a 4-period full replicate design (TRTR|RTRT):

sampleN.TOST(CV=0.2, targetpower=0.9, theta0=0.9, design="2x2x4", print=F, details=F)

  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power

1  2x2x4  0.05 0.2    0.9    0.8   1.25          26      0.9130555          0.9

Four periods lead to unacceptable high sampling volumes or you are concerned about dropouts? Try a 3-period full replicate (TRT|RTR):

sampleN.TOST(CV=0.2, targetpower=0.9, theta0=0.9, design="2x2x3", print=F, details=F)

  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power

1  2x2x3  0.05 0.2    0.9    0.8   1.25          38      0.9066936          0.9

… or a partial replicate (TRR|RTR|RRT):

sampleN.TOST(CV=0.2, targetpower=0.9, theta0=0.9, design="2x3x3", print=F, details=F)

  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power

1  2x3x3  0.05 0.2    0.9    0.8   1.25          39      0.9131147          0.9

OK, the study is for EMA and we are allowed to widen the acceptance range for C_max only. CV with 50% is higher than the one of AUC. If we run the study in 26 subjects, how much power can we expect?

power.scABEL(CV=0.5, theta0=0.9, design="2x2x4", n=26)

[1] 0.78733

Avoid the word ‘calculate’. The input are either estimates themselves (CVs, ratios of previous studies) or assumptions (the expected ratio of the next study). You can only estimate something from uncertain input. It’s not like 2 × 2 = 4.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Compliance ★ India, 2013-07-29 07:46 (3921 d 21:09 ago) @ Helmut Posting: # 11090 Views: 8,915	Error description? Post reply
	Dear All, Thank you for the help and educating me. Regards

Sample size calculation by power-tost software [Software]

Sample size estimation with PowerTOST

PowerTOST Usage

PowerTOST naming issues

PowerTOST Usage

Common naming conventions of EM

Common naming conventions of EM

PowerTOST naming issues

Error description?

Error description?