sury
☆

India,
2019-03-19 12:22

Posting: # 20050
Views: 2,131

## Deletti tables for sample size [Power / Sample Size]

Dear All,

I want to include the deletti tables in my SOP references and i am nt able to find the reference link. can anyone please help me in this?

Thanks in advance

Edit: Category changed; see also this post #1[Helmut]
Helmut
★★★

Vienna, Austria,
2019-03-19 13:27

@ sury
Posting: # 20051
Views: 2,025

## Of historic(al) interest only

Hi sury,

» I want to include the deletti tables in my SOP references …

I don’t understand. You have already an SOP without references – what does it say? How do you estimate a sample size right now?

These tables for α 0.05 (90% CI), 70/80/90% power and
• CV 5–30% (step size 5%), T/R-ratio 0.85–1.20 (step size 0.05);
for acceptance 80.00–125.00%1
• CV 5–20% (step size 2.5%), T/R-ratio 0.925–1.075 (step size 0.025);
for acceptance range 90.00–111.11%2
• CV 15–60% (step size 5%), T/R-ratio 0.75–1.35 (step size 0.05);
for acceptance range 70.00–142.86%2
are hopelessly behind state of the art!

Since power is nonlinear, you can’t easily interpolate if you are interested in anything not given in the tables. What if you want another α (two-stage adaptive and group-sequential designs) or an acceptance range of 75.00–133.33% (applicable in some jurisdictions for Cmax)?
NB, if you are interested in reference-scaling (FDA: RSABE, EMA: ABEL) you need yet other tables (covered designs: TRR|RTR|RRT and TRTR|RTRT).3 No tables exist for other designs (e.g., TRT|RTR – which is better than the lousy partial replicate), Health Canada’s ABEL, and the FDA’s RSABE for NTIDS.

Hence, I strongly suggest to opt for software, i.e., package PowerTOST4 for R which supports all of those (plus paired and parallel designs, non-inferiority/-superiority, Fieller’s CI of ratios, dose-proportionality, …).

1. Diletti E, Hauschke D, Steinijans VW. Sample size determination for bioequivalence assessment by means of confidence intervals. Int J Clin Pharm Ther Toxicol. 1991;29(1):1–8.
2. Diletti E, Hauschke D, Steinijans VW. Sample size determination: Extended tables for the multiplicative model and bioequivalence ranges of 0.9 to 1.11 and 0.7 to 1.43. Int J Clin Pharm Ther Toxicol. 1992;30(8):287–90.
3. Tóthfalusi L, Endrényi. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Pharmaceut Sci. 2011;15(1):73–84. open access.
4. Labes D, Schütz H, Lang B. PowerTOST: Power and Sample Size Based on Two One-Sided t-Tests (TOST) for (Bio)Equivalence Studies. 2018-04-12;1.4-7.
https://cran.r-project.org/package=PowerTOST.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
sury
☆

India,
2019-03-20 05:04

@ Helmut
Posting: # 20052
Views: 1,935

## Of historic(al) interest only

» […] You have already an SOP without references – what does it say? How do you estimate a sample size right now?

we have not yet finalized the SOP, and moreover we use the SAS Software procedure "PROC POWER" for the estimation of the sample size. But however we wanted it to be more accurate sample size for that we want to include the deletti tables.

» These tables […] are hopelessly behind state of the art!
» » NB, if you are interested in reference-scaling (FDA: RSABE, EMA: ABEL) you need yet other tables (covered designs: TRR|RTR|RRT and TRTR|RTRT).3 No tables exist for other designs (e.g., TRT|RTR – which is better than the lousy partial replicate), Health Canada’s ABEL, and the FDA’s RSABE for NTIDS.

Yes

» Hence, I strongly suggest to opt for software, i.e., package PowerTOST4 for R which supports all of those (plus paired and parallel designs, non-inferiority/-superiority, Fieller’s CI of ratios, dose-proportionality, …).

yes we are thinking to opt this package. But however we have a concern whether regulatory will accept it or not. Sometime ago I have faced the concern regarding the Software validation from the regulatory. By then we are doubtfull of using this package.

BTW thanks for your reply. It has been a great help....

Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5[Helmut]
Helmut
★★★

Vienna, Austria,
2019-03-20 12:12

@ sury
Posting: # 20053
Views: 1,913

## Software validation – again and again

Hi sury,

» we have not yet finalized the SOP, and moreover we use the SAS Software procedure "PROC POWER" for the estimation of the sample size.

OK.

» But however we wanted it to be more accurate sample size for that we want to include the deletti tables.

I wonder why you were asking here for the Diletti tables. The reference is readily available in the manual of Proc POWER
Proc POWER employs Owen’s Q-function1 – as does PowerTOST by default. AFAIK, OwenQ is a still undocumented function in SAS… Proc POWER is available in SAS since v9.1 (2003). Hence, Diletti et al. wrote in 1991:

The exact form of these integrals and an algorithm for their calculation has been provide by Owen; this algorithm has been implemented to create the figures and tables in this paper.

We don’t know which software and code they used. Edgar Diletti and Volker Steinijans are retired; ask Dieter Hauschke.

» » These tables […] are hopelessly behind state of the art!
» » » NB, if you are interested in reference-scaling […]»
» Yes

For all reference-scaling methods you need simulations and have to write your own SAS-code. Expect run-times of many, many hours. The two Lászlós wrote their code in MATLAB, which is only slightly faster than SAS. Hence, for years they recommend PowerTOST themselves.

» » Hence, I strongly suggest […] package PowerTOST.
»
» yes we are thinking to opt this package. But however we have a concern whether regulatory will accept it or not.
» By then we are doubtfull of using this package.

Since PowerTOST is open-source you (or an R-specialist) can perform a white-box validation. Additionally, PowerTOST contains not only reference data sets from the literature but also scripts to validate your installation. See also this thread.
Maybe you are interested in this document.2

» Sometime ago I have faced the concern regarding the Software validation from the regulatory.

Any software used in a GCP-environment has to be validated. Have you done that with SAS?* No, I don’t mean just IQ, OQ, PQ! Good luck with commercial software where the source code (allowing white-box validation) is not accessible. You could only perform cross-validation (black-box) with reference data sets. If you don’t have more than one software at hand, you have to believe (!) that what is reported for the reference data set is correct.

1. Owen DB. A special case of a bivariate non-central t-distribution. Biometrika. 1965;52(3/4):437–46. doi:10.2307/2333696.
2. The R Foundation for Statistical Computing. R: Regulatory Compliance and Validation Issues. A Guidance Document for the Use of R in Regulated Clinical Trial Environments. Vienna, March 2018. open access.

• Stephen Senn told me this story:
He discovered that after an update of SAS the Welch-Satterthwaite’s degrees of freedom (required in parallel designs with unequal group sizes and/or unequal variances) were faulty. Scary, cause such data sets are the rule in phase III. He phoned the SAS-Institute and got the responsible software engineer on the line. After inspecting the source within minutes he confirmed the bug. However, it took SAS half a year to roll out a patch…
So much for that.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
nobody
nothing

2019-03-20 16:20

@ Helmut
Posting: # 20054
Views: 1,854

## Software validation – again and again

SCNR, although miles OT:

From your Ref. 2

R: Regulatory Compliance and Validation Issues
A Guidance Document for the Use of R in Regulated Clinical
Trial Environments
March 25, 2018
The R Foundation for Statistical Computing
c/o Institute for Statistics and Mathematics
Wirtschaftsuniversität Wien
Welthandelsplatz 1
1020 Vienna, Austria

...this unprecedented humbleness, unbelievable

Kindest regards, nobody
Helmut
★★★

Vienna, Austria,
2019-03-20 16:35

@ nobody
Posting: # 20055
Views: 1,831

## Fiaker und Apfelstrudel

Hi nobody,

» Wirtschaftsuniversität Wien
» Welthandelsplatz 1

That’s Vienna, darling. Tradition to the nth degree. Founded as “k.k. Exportakademie” in 1898 (was the bloody Austro-Hungarian Empire not interested in import?), renamed “Hochschule für Welthandel” [sic] in 1919 (highest academic degree “Diplomkaufmann”) and “Wirtschaftsuniversität Wien” in 1975.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
nobody
nothing

2019-03-20 17:34

@ Helmut
Posting: # 20056
Views: 1,815

## Fiaker und Apfelstrudel

...I should really visit your cold, windy home-sweet-home again within reasonable time

Kindest regards, nobody
Helmut
★★★

Vienna, Austria,
2019-03-20 17:54

@ nobody
Posting: # 20057
Views: 1,804

## Fiaker und Apfelstrudel

Hi nobody,

» ...I should really visit your cold, windy home-sweet-home again within reasonable time

Go for it! Ask Detlew and ElMaestro how I perform as a tour-guide.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
d_labes
★★★

Berlin, Germany,
2019-03-20 18:39

@ Helmut
Posting: # 20059
Views: 1,815

## Fiaker und Apfelstrudel

Hi nobody,

» » ...I should really visit your cold, windy home-sweet-home again within reasonable time
»
» Go for it! Ask Detlew and ElMaestro how I perform as a tour-guide.

the only thing I could say: He is the best ever!

Regards,

Detlew
ElMaestro
★★★

Belgium?,
2019-03-20 22:09

@ Helmut
Posting: # 20061
Views: 1,772

## Fiaker und Apfelstrudel

» Go for it! Ask Detlew and ElMaestro how I perform as a tour-guide.

First class tour guide service.

I could be wrong, but...
Best regards,
ElMaestro
mittyri
★★

Russia,
2019-03-20 21:09

@ Helmut
Posting: # 20060
Views: 1,781

## White-box validation

Hi Helmut,

» Since PowerTOST is open-source you (or an R-specialist) can perform a white-box validation.

Citing Wiki:

The programmer must have a deep understanding of the application to know what kinds of test cases to create so that every visible path is exercised for testing.

Well... Since PowerTOST is a Swiss army knife, it will take a lot of efforts to cover it

Kind regards,
Mittyri
Helmut
★★★

Vienna, Austria,
2019-03-21 00:19

@ mittyri
Posting: # 20062
Views: 1,767

## White-box validation

Hi mittyri,

»

The programmer must have a deep understanding of the application to know what kinds of test cases to create so that every visible path is exercised for testing.

» Well... Since PowerTOST is a Swiss army knife, it will take a lot of efforts to cover it

Yep. Your quote continues with

Once the source code is understood then the source code can be analyzed for test cases to be created.

There is no free lunch.

I have stopped reading Stephen King novels.
Now I just read C code instead.
Richard A. O'Keefe

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
Science Quotes
d_labes
★★★

Berlin, Germany,
2019-03-20 18:37
(edited by d_labes on 2019-03-20 19:15)

@ sury
Posting: # 20058
Views: 1,841

## Power of Proc Power

Dear sury,

Additionally to what Helmut has said:

» we have not yet finalized the SOP, and moreover we use the SAS Software procedure "PROC POWER" for the estimation of the sample size. But however we wanted it to be more accurate sample size for that we want to include the deletti tables.

PROC POWER doesn't allow a power calculation or a sample size estimation out of the box for study designs used mainly in bioequivalence studies, beside other f.i. for the standard 2x2 crossover design! Except if you assume no period effects present. See here.
But this assumption isn't appropriate in many cases.

You have to roll your own piece of software. See f.i. this paper.
And if you do so: You have to validate.

Regards,

Detlew
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