BE-proff
★★  

Russia,
2016-12-28 08:14

Posting: # 16892
Views: 7,697
 

 Sample Size II [Power / Sample Size]

Hi All,

Let's say I want to calculate sample size based on results of a previous study.

I have the following data:
n=20
CV=0.18 (for Cmax and AUC) ;-)
GMR1 = 0.97
GMR2=1.19

If to calculate size based on GMR1 I think it's better to use a script:

sampleN.TOST(CV=0.18, theta0=0.95)

+++++++++++ 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
True ratio = 0.95,  CV = 0.18

Sample size (total)
 n     power
16   0.820357
:ok:

if to use GMR = 1.19 we see something terrible:

sampleN.TOST(CV=0.18, theta0=1.19)

+++++++++++ 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
True ratio = 1.19,  CV = 0.18

Sample size (total)
 n     power
166   0.803570
- too many people...:no:

What to do in such situations?:confused:
mittyri
★★  

Russia,
2016-12-28 09:17

@ BE-proff
Posting: # 16893
Views: 6,992
 

 Please see the answer to your previous post

Hi BE-proff,

Out of curiosity: what is the reason not to use the detailed Helmut's answer to your previous similar question here?

Kind regards,
Mittyri
BE-proff
★★  

Russia,
2016-12-28 10:35

@ mittyri
Posting: # 16894
Views: 6,902
 

 Please see the answer to your previous post

Hi mittyri,

That was a post about pooled CV.
How would you answer the question? ;-)
mittyri
★★  

Russia,
2016-12-28 11:38

@ BE-proff
Posting: # 16896
Views: 6,927
 

 Another Master's answer

Hi BE-proff,

My answer is: 'Educated Guess'
No one will decide which GMR you should use behind your back.
Fully ACK the ElMaestro's answer below.
I'd cite another Master's post:
» If you intend the next study to be pivotal then the choice of GMR guess should reflect a ton of factors including biology, dissolution, gut feeling, Saturn's moons, your biorhythms, personal horoscope (you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?) etc but not your management's desire to save money.

Please also think about GMR = 1.19
Would you recommend to use the formulation with REAL GMR = 1.19 in practice?

Kind regards,
Mittyri
ElMaestro
★★★

Belgium?,
2016-12-28 10:52

@ BE-proff
Posting: # 16895
Views: 7,116
 

 Sample Size II

Dear BE-proff,

» I have the following data:
» n=20
» CV=0.18 (for Cmax and AUC) ;-)
» GMR1 = 0.97
» GMR2=1.19
»
» If to calculate size based on GMR1 I think it's better to use a script:
» (...) if to use GMR = 1.19 we see something terrible:
» (...) What to do in such situations?:confused:


If your product has a true GMR of 1.19 for a primary ratio, then 166 may be a sample that meets your power requirement size.
However, bear in mind that such calculations involve models with assumptions, notably a Normal distribution on the log scale. Your GMR from the trial is an estimate and not a true value; a good guess is that there is 50% chance the true GMR is worse.

In this paper, the author tried to look into the various options for situations like yours: How to use the result from one trial in the planning of the next?
The answer was: You have several options, but you do not get any easy solution that allows high power and low sample size if you try to make use of the observed GMR (and that, by the way, is also why pilot trials are not good approaches for telling if candidate formulations are so promising that a pivotal trial is merited). And if you gamble and use a GMR for planning that is closer to 1.0 than what you observed previously then you are also easily screwing yourself.

I could be wrong, but...

Best regards,
ElMaestro

"Pass or fail" (D. Potvin et al., 2008)
d_labes
★★★

Berlin, Germany,
2016-12-28 13:42

@ BE-proff
Posting: # 16897
Views: 7,062
 

 Expected power answer

Dear BE-proff, dear All,

» Let's say I want to calculate sample size based on results of a previous study.
»
» I have the following data:
» n=20
» CV=0.18 (for Cmax and AUC) ;-)
» GMR1 = 0.97
» GMR2=1.19

Taking into account that CV and GMR's of such a previous (pilot) trial are not the true values but estimates with uncertainty, as ElMaestro already pointed out. One answer to such a goal is using the so-called "expected power" implemented in PowerTOST::exppower.TOST() and expsampleN.TOST().

Let's play with your numbers step by step:
1. Taking into account uncertainty of CV, but assuming a known (true) GMR =0.95
expsampleN.TOST(CV=0.18, theta0=0.95, prior.parm = list(m=20, design="2x2"), prior.type="CV")
++++++++++++ Equivalence test - TOST ++++++++++++
       Sample size est. with uncertain CV
-------------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins = 0.8 ... 1.25
Ratio = 0.95
CV = 0.18 with 18 df

Sample size (ntotal)
 n   exp. power
18   0.823287

Not so much more than using the conventional power assuming GMR and CV known.

2. Taking into account uncertainty of CV, but assuming a true GMR =1.19
expsampleN.TOST(CV=0.18, theta0=1.19, prior.parm = list(m=20, design="2x2"), prior.type="CV")
++++++++++++ Equivalence test - TOST ++++++++++++
       Sample size est. with uncertain CV
-------------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins = 0.8 ... 1.25
Ratio = 1.19
CV = 0.18 with 18 df

Sample size (ntotal)
 n   exp. power
180   0.801466

Again slightly higher than using the conventional power.

3. Now taking into account uncertainty of CV and GMR =1.19
expsampleN.TOST(CV=0.18, theta0=1.19, prior.parm = list(m=20, design="2x2"), prior.type="both")

++++++++++++ Equivalence test - TOST ++++++++++++
  Sample size est. with uncertain CV and theta0
-------------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

Design characteristics:
df = n-2, design const. = 2, step = 2

alpha = 0.05, target power = 0.8
BE margins = 0.8 ... 1.25
Ratio = 1.19 with 18 df
CV = 0.18 with 18 df

Upper bound of expected power = 0.802418

Sample size search (ntotal)
 n   exp. power
Search for improved starting value based on nct approximation for conditional power:
4130   0.769089
4146   0.769157
4162   0.769219
4194   0.769354
4258   0.769619
4386   0.770131
...
619480   0.800000
Final search:
619480   0.800000
619478   0.800000
619476   0.800000

3 iterations
619478   0.800000


That result (!) should everyone convince that using the GMR from pilot studies with small number of subjects (or likewise from usually small stage 1 of a TSD) is not a good idea, as our captain :pirate: already stated in his post above.
It results mainly from "... there is 50% chance the true GMR is worse." And power is heavily influenced by deviations in the GMR as we already know from the power analysis functions f.i. pa.ABE()

BTW: Don't ask me for the theory behind expected power. It is something Bayesian.
If you are interested you may find a short tractatus at
https://github.com/Detlew/PowerTOST/tree/master/inst/doc
written by Ben (Benjamin Lang) who is also responsible for the implementation.

Regards,

Detlew
DavidManteigas
★    

Portugal,
2016-12-28 18:11

@ BE-proff
Posting: # 16899
Views: 6,900
 

 Sample Size and regulators

Hi all,

Just curiosity, but does anyone here had questions on sample size from regulators?

I'm asking that since in Portugal I never saw a question from regulators or ethics committees regarding sample size. They just assume we did it right :-D
d_labes
★★★

Berlin, Germany,
2016-12-28 19:24

@ DavidManteigas
Posting: # 16900
Views: 6,892
 

 Sample Size and sponsors

Dear David,

» Just curiosity, but does anyone here had questions on sample size from regulators?
»
» I'm asking that since in Portugal I never saw a question from regulators or ethics committees regarding sample size. They just assume we did it right :-D

that's also my experience. Never got a question in that direction from IEC or regulators.
But got questions from sponsors, especially if the sample size doesn't fit their budget :-D.

Regards,

Detlew
ElMaestro
★★★

Belgium?,
2016-12-28 22:22

@ d_labes
Posting: # 16901
Views: 6,926
 

 Sample Size and spongulators

Dear all,

» (...) Never got a question in that direction from IEC or regulators.

I have come across quite some members of IRBs/IECs over the past 10 years or so. I have not, however, met many who understood much about power and sample size at all. The problem is particularly pronounced at IECs where most of the members have their experience from innovator developments (or scientific literature covering this topic).
Intuition can be a real prick when it is applied to the field of bioequivalence. Personally, I have had to suck up quite a few mistakes of my own which originated in intuition, trust me.

I could be wrong, but...

Best regards,
ElMaestro

"Pass or fail" (D. Potvin et al., 2008)
mittyri
★★  

Russia,
2016-12-29 11:44

@ DavidManteigas
Posting: # 16902
Views: 6,793
 

 Sample Size and regulators

Hi David and all,

» Just curiosity, but does anyone here had questions on sample size from regulators?

some years ago all sponsors who submitted the BEQ protocols to the Russians regulators got a question: how did you calculate the sample size?
There were convinced with any answer: the code in R, values in cells in FARTSSIE, SAS code and output or even justification with some algebra.

Kind regards,
Mittyri
Helmut
★★★
avatar
Homepage
Vienna, Austria,
2016-12-29 12:39

@ DavidManteigas
Posting: # 16904
Views: 6,844
 

 Sample Size and regulators

Hi David,

» Just curiosity, but does anyone here had questions on sample size from regulators?

Never in 35+ years (both from regulators and IECs).

I share Detlew’s experience with sponsors. Too lazy to search but somewhere I posted the distribution of sample sizes of my studies. There was a sharp peak at the Babylonian 24 (two dozens were conceived a holy number). When working in a CRO at the end of the day the sponsor is always right.

Dif-tor heh smusma 🖖
Helmut Schütz
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