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Helmut
Hero
Homepage
Vienna, Austria,
2012-01-04 15:46

Posting: # 7863
Views: 4,951
 

 Paper on RSABE/ABEL [Power / Sample Size]

Dear all,

a nice one:

László Endrényi, László Tóthfalusi
Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs
J Pharm Pharmaceut Sci 15(1), 73–84 (2011)
online

Abstract. – Purpose. To provide tables of sample sizes which are required, by the European Medicines Agency (EMA) and the U.S. Food and Drug Administration (FDA), for the design of bioequivalence (BE) studies involving highly variable drugs. To elucidate the complicated features of the relationship between sample size and within-subject variation. Methods. 3- and 4-period studies were simulated with various sample sizes. They were evaluated, at various variations and various true ratios of the two geometric means (GMR), by the approaches of scaled average BE and by average BE with expanding limits. The sample sizes required for yielding 80% and 90% statistical powers were determined. Results. Because of the complicated regulatory expectations, the features of the required sample sizes are also complicated. When the true GMR = 1.0 then, without additional constraints, the sample size is independent of the intrasubject variation. When the true GMR is increased or decreased from 1.0 then the required sample sizes rise at above but close to 30% variation. An additional regulatory constraint on the point estimate of GMR and a cap on the use of expanding limits further increase the required sample size at high variations. Fewer subjects are required by the FDA than by the EMA procedures. Conclusions. The methods proposed by EMA and FDA lower the required sample sizes in comparison with unscaled average BE. However, each additional regulatory requirement (applying the mixed procedure, imposing a constraint on the point estimate of GMR, and using a cap on the application of expanding limits) raises the required number of subjects.

[image]Regards,
Helmut Schütz 
[image]

The quality of responses received is directly proportional to the quality of the question asked. ☼
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earlybird
Junior

2012-01-10 14:11

@ Helmut
Posting: # 7893
Views: 4,036
 

 Paper on RSABE/ABEL

Dear Helmut,

thanks for this nice paper.

Does this mean we can use this paper for sample size calculation (simulations?) and put FARTSSIE in the garbage?

I have done a sample size estimation with FARTSSIE for example FDA, partial replicate, 80% power, ratio 90%, CV = 35% this result in N= 48. Whereas when I look in Table A3 I got N=37. Substantial less subjects!

Somehow strange for me, as I would guess the more constraints the higher the sample size.

Best regards,
earlybird
Ben
Regular

2012-01-12 19:22

@ earlybird
Posting: # 7918
Views: 4,040
 

 Paper on RSABE/ABEL

Dear all,

I also have some questions on this paper because I'm not that familiar with these procedures yet (sorry...). First they describe the method of EMA and state that this is "still Average Bioequivalence but with Expanding Limits" (and thus "the TOST procedure of Schuirmann can be directly applied"). Later they say that FDA uses scaled average BE instead, but for me equation [5] does not really differ from [3] and therefore (at this point) I don't understand why SABE is different from ABEL. (And hence I don't understand why the TOST procedure cannot be applied). Since the equation was equivalently restated from [3] to [5] this makes the impression – at least for me – that we have two different words (namely ABEL and SABE) for the same procedure. But I guess it's not supposed to be like this?! (BTW: the lower bound of equation [5] should be -k and not k, shouldn't it? 'cause otherwise (m_T-m_R)/s_w equals k). So where is the substantial difference here (apart of course from the additional conditions required by EMA or FDA and the different choice of k or sigma_0)?

Thank you,
Ben
Helmut
Hero
Homepage
Vienna, Austria,
2012-01-25 13:26

@ Ben
Posting: # 8000
Views: 3,896
 

 Hyslop/Howe

Dear Ben!

» […] this makes the impression – at least for me – that we have two different words (namely ABEL and SABE) for the same procedure. But I guess it's not supposed to be like this?!

For an in-depth review see the paper mentioned in this post; especially Section 4.4.2.

» […] the lower bound of equation [5] should be -k and not k, shouldn't it?

Yes. This typo was probably carried over from Eq.7 of the paper mentioned above. :-D

P.S.: You have [image].

[image]Regards,
Helmut Schütz 
[image]

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

2012-01-25 17:51

@ Helmut
Posting: # 8002
Views: 3,858
 

 Hyslop/Howe

» For an in-depth review see the paper mentioned in this post; especially Section 4.4.2.
» » […] the lower bound of equation [5] should be -k and not k, shouldn't it?
» Yes. This typo was probably carried over from Eq.7 of the paper mentioned above. :-D
» P.S.: You have [image].

Thank you very much!
d_labes
Hero

Berlin, Germany,
2012-01-25 11:12

@ earlybird
Posting: # 7998
Views: 4,004
 

 FARTSSIE on RSABE/ABEL

Dear earlybird!

» I have done a sample size estimation with FARTSSIE for example FDA, partial replicate, 80% power, ratio 90%, CV = 35% this result in N= 48. Whereas when I look in Table A3 I got N=37. Substantial less subjects!

Cave! FARTSSIE contains sW0=0.294 as regulatory constant.
But Haidar et.al had proposed sW0=0.25, switching to scaled ABE also at CV=30% (corresponds to sWR=0.294). sW0=0.294 corresponds to k=0.76..., the EMA regulatory setting. You can see this if you choose consecutive the FDA approach and the EMA approach from the drop-down box. Both methods give the same sample size.

With sW0=0.25 you will get N=29 from FARTSSIE with your settings.

Comparison to the simulated results is difficult because FARTSSSIE obviously calculates the sample size the usual way but with widened acceptance ranges (ABEL with FDA regulatory constant), whereas the simulations had used the scaled ABE criterion directly (upper 95% CI of the linearised criterion <0).
Moreover FARTSSIE uses the formulas for a balanced classical 2x2 crossover (!) correcting the obtained sample size to 0.75*n(2x2) for a 3-period replicate design with 2 sequences (not partial replicate) and the approximation of the power via non-central t-distribution. Approximate approximations :-D.

PowerTOST comes out with:
require(PowerTOST)
sampleN.TOST(CV=0.35, theta0=0.9, theta1=exp(-0.893*CV2se(0.35)), design="2x3x3", details=TRUE, method="exact")


+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  partial replicate (2x3x3)
Design characteristics:
df = 2*n-3, design const. = 1.5, step = 3

log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins        = 0.7381817 ... 1.35468
Null (true) ratio = 0.9,  CV = 0.35

Sample size search (ntotal)
 n     power
27   0.786584
30   0.824086

Exact power calculation with Owen's Q functions.


» Somehow strange for me, as I would guess the more constraints the higher the sample size.

Right guess if you look at the corrected result :cool:.

Regards,

Detlew
earlybird
Junior

2012-01-26 10:44

@ d_labes
Posting: # 8006
Views: 3,856
 

 FARTSSIE on RSABE/ABEL

Dear d_labes,

» With sW0=0.25 you will get N=29 from FARTSSIE with your settings.

OK you are right! Or as Lothar Mathäus would said: "Again what learned".

» Right guess if you look at the corrected result :cool:.

Well its not bad to have a good statistician on board ;-)

Regards,
earlybird
d_labes
Hero

Berlin, Germany,
2012-01-25 15:29
(edited by d_labes on 2012-01-25 15:52)

@ Helmut
Posting: # 8001
Views: 3,969
 

 PowerTOST vs. simulation on ABEL

Dear Helmut, dear all,

Here the results of sample size estimation using PowerTOST with expanded acceptance limits according to the EMA guidance for the 3-period partial replicate design
(example call
CV <- 0.35
# widened acceptance limits
# round to 4 decimals to take the guidance to the letter

theta1 <- round(exp(-0.76*CV2se(0.35)),4) #use 0.5 here if CV>=0.5
theta2 <- round(exp(+0.76*CV2se(0.35)),4) #use 0.5 here if CV>=0.5
sampleN.TOST(CV=CV, theta0=1.00, theta1=theta1, theta2=theta2, design="2x3x3")
) compared to the ones based on simulation:
power=80%
         0.85    0.9      0.95     1.00     1.05     1.1      1.15     1.2
  CV  sim  PT  sim  PT  sim  PT  sim  PT  sim  PT  sim  PT  sim  PT  sim  PT
 30%  194 219   53  60   27  30   22  24   26  30   45  51  104 117 >201 483
 35%  127 120   51  48   29  27   25  24   29  27   45  42   84  70 >201 189
 40%   90  84   44  42   29  27   27  24   30  27   42  39   68  60  139 114
 45%   77  66   40  36   29  27   27  24   29  27   37  33   57  51  124  84
 50%   75  57   40  36   30  27   28  24   30  27   37  33   53  45  133  69
 55%   81  66   42  42   32  30   30  30   32  30   40  39   56  54  172  81
 60%   88  75   46  48   36  36   33  33   36  36   44  45   63  63 >201  93
 65%   99  87   53  54   40  39   37  36   40  39   50  51   71  69 >201 108
 70%  109  99   58  60   45  45   41  42   45  45   56  57   80  78 >201 120
 75%  136 108   67  66   50  51   46  48   50  51   62  63   89  87 >201 135
 80%  144 120   72  75   54  57   51  51   55  54   68  69   97  99 >201 150

power=90%
         0.85    0.9      0.95     1.00     1.05     1.1      1.15     1.2
  CV  sim  PT  sim  PT  sim  PT  sim  PT  sim  PT  sim  PT  sim  PT  sim  PT
 30% >201 303   74  81   36  39   28  30   36  39   62  69  147 162 >201 666
 35%  181 165   70  66   39  36   32  30   39  36   63  57  117 108 >201 258
 40%  130 114   61  57   38  36   33  30   39  36   57  51   94  84 >201 159
 45%  132  90   55  51   37  33   33  30   38  33   51  48   85  69 >201 117
 50%  158  75   55  48   39  33   34  30   38  33   51  42   84  63 >201  93
 55%  178  90   59  54   41  39   37  36   41  39   53  51   97  72 >201 111
 60%  199 105   64  63   45  45   41  42   46  45   60  60  112  84 >201 129
 65% >201 120   72  72   51  51   46  48   51  51   67  66  125  96 >201 147
 70% >201 135   82  81   57  57   52  51   57  57   76  75  141 108 >201 165
 75% >201 150   93  90   66  66   58  57   64  63   85  84  161 120 >201 186
 80% >201 168  100 102   70  72   63  66   71  72   93  93  176 135 >201 207

Considering that:
  • PowerTOST does not consider the peculiarities of the EMA method like mixed procedure around CV=30%, additional GMR constraint etc.
  • PowerTOST gives only sample sizes for balanced designs (step size 3 here)
  • the simulated power has a simulation error assigned with it
PowerTOST does a very good job and the results are in astonishing good concordance:
  • At CV=30% the PowerTOST results are around 10% higher than the simulated ones. I guess this is due to the mixed procedure (no widening for estimated CV ≤30%, widening if estimated CV>30%, which occurs in the simulated data half to half)
  • In the GMR range 0.9 - 1.1 and CV's >30% up to 50% the PowerTOST results are around 10% to low.
  • In the GMR range 0.9 - 1.1 and CV's >50% the agreement is nearly perfect (max. diff. ±2).
  • Outside the GMR range 0.9 - 1.1 (GMR=0.85, 1.15 and 1.2) the sample sizes based on simulation are consistently much higher. I guess this is due to the additional GMR constraint which only here comes to an appreciable influence.

Regards,

Detlew
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