Bioequivalence and Bioavailability Forum

Hi Angus,

❝ I did a sample size calculation for the non replicate design (usual cross over design) using the Excel spreadsheet FARTSIE from David Dubins…

A member of the Forum since 2007.

❝ I have found this spreadsheet to be most useful in the past.

Yep, AFAIK it is still widely used.

❝ Using a desired power of 0.9, with CV of 30.05 and an anticipated ratio of 0.93. I get 67 subjects and this is more than your estimate. I wonder why?

• In your OP you stated a CV of 30.5% – not 30.05%. I assumed a T/R-ratio of 0.90 – not 0.93.
  
• The setup for conventional unscaled 2×2 ABE in FARTSSIE doesn’t help too much.
  • In [Bioequivalence, Crossover] I get n=67 with 90.11% power. Note that this would be an imbalanced design. You should round up to n=68 – as PowerTOST would do:
    sampleN.TOST(CV=0.3005, theta0=0.93, targetpower=0.9, design="2x2", details=F)
+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.9
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.93,  CV = 0.3005

Sample size (total)
 n     power
68   0.904946
    We could calculate power for n=67 as well:*
    power.TOST(CV=0.3005, theta0=0.93, n=67, design="2x2")
[1] 0.9011207
    Hey, confirmed FARTSSIE’s 90.11%… BTW, PowerTOST by default uses the exact method, where­as FARTSSIE uses an approximation based on the noncentral t-dis­tri­bution. Let’s check that:*
    power.TOST(CV=0.3005, theta0=0.93, n=67, design="2x2", method="nct")
[1] 0.9011207
    OK, the approximation works.
    Compared to a 2×2 crossover in a fully replicated design with n/2 subjects we have the same number of treatments and can expect the same power. Therefore, for un­scaled ABE we get 67/2=33.5 → 34 subjects. Let’s check that:
    sampleN.TOST(CV=0.3005, theta0=0.93, targetpower=0.9, design="2x2x4", details=F)
+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  2x2x4 replicate crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.9
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.93,  CV = 0.3005

Sample size (total)
 n     power
34   0.906647
    Bingo!
    
  • In FARTSSIE’s [Bioequivalence, Replicate] [4 period replicate (ABBA/BAAB)] [Method C2 - FDA Approach] I get n=34 with 90.12% power.
    Note 1: FDA want RTRT|TRTR not TRRT|RTTR.
    Note 2: For RSABE and (EMA’s ABEL) simulations are mandatory. Both FARTSSIE and Study Size don’t work!
• With your values the code for RSABE is
  sampleN.RSABE(CV=0.3005, theta0=0.93, targetpower=0.9, design="2x2x4", details=F)
  giving…
  ++++++++ Reference scaled ABE crit. +++++++++
           Sample size estimation
---------------------------------------------
Study design:  2x2x4 (full replicate)
log-transformed data (multiplicative model)
1e+05 studies for each step simulated.

alpha  = 0.05, target power = 0.9
CVw(T) = 0.3005; CVw(R) = 0.3005
Null (true) ratio = 0.93
ABE limits / PE constraints = 0.8 ... 1.25
Regulatory settings: FDA

Sample size
 n    power
30   0.91495
  Now we see a difference: n=30 (RSABE) and n=34 (ABE). Why? ABE assumes the CV as “carved in stone”, whereas in real life the CV might be larger → apply scaling → fewer sub­jects needed to achieve the target power.

❝ {I must try the freeware package you recommend}.

Go ahead!

❝ I do have a Study Size program from Sweden, but have not used it for this project as yet. It seems to be an excellent program. Update using Study Size for the above sample size calculation again I get 67 subjects.

Yes, but for unscaled ABE in a 2×2 design. Study Size does not work for RSABE as well. I you apply the “rule of thumb” n/2 and perform the study in 34 subjects, it will be overpowered:
power.RSABE(theta0=0.93, CV=0.3005, n=34, design="2x2x4")
[1] 0.93941
Explain to your boss why you plan to run the study in 34 subjects if 30 will give you already a power of 91.5%.

❝ There is a reference I have found…

Hey, that’s the reference I gave you in my last post.

❝ When I consult this paper I see for the fully replicate design with 4 periods that for CV of 30% and power 0.9 with GMR ratio of 0.9 that 38 subjects are estimated.

You have to look it up in Table A4, second part. For CV 30% they report n=44 for GMR 0.90 and n=23 (imbalanced: round up to 24) for GMR 0.95.

❝ So I am thinking ~ 40 subjects is needed.

Nope. 30.

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Homework:

sampleN.RSABE(CV=0.30, theta0=0.90, targetpower=0.9, design="2x2x4")
sampleN.RSABE(CV=0.30, theta0=0.95, targetpower=0.9, design="2x2x4")

Do the results match Table A4?

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• Edit: See this post and following.