john john
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Spain,
2015-10-01 19:44
(3100 d 20:31 ago)

Posting: # 15513
Views: 12,088
 

 Sequential trial with B method of Potvin [Two-Stage / GS Designs]

In a sequential clinical trial conducted like a B method of Potvin, we have Cmax and AUC both not bioequivalent. Cmax has a power <80% (71.5%), and AUC>80% (84.6%).
AUC 0-30min calculated by protocol is bioequivalent.
In the protocol it was not specified how to proceed in this situation.

Can we calculate a new n and pass to the second phase? Or we must stop the trial?

Thanks


Edit: Category changed. [Helmut]
ElMaestro
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Denmark,
2015-10-01 19:58
(3100 d 20:17 ago)

@ john john
Posting: # 15514
Views: 10,572
 

 Sequential trial with B method of Potvin

Hi JJ,

❝ In a sequential clinical trial conducted like a B method of Potvin, we have Cmax and AUC both not bioequivalent. Cmax has a power <80% (71.5%), and AUC>80% (84.6%).

❝ AUC 0-30min calculated by protocol is bioequivalent.

❝ In the protocol it was not specified how to proceed in this situation.


❝ Can we calculate a new n and pass to the second phase? Or we must stop the trial?


I would go by the metric that displays the highest variance, which is usually Cmax. I suggest to proceed towards stage 2 on that basis.
However, since this was not pre-specified it is your protocol that document may be your biggest issue now; regulators may not like whatever decision you take.

Pass or fail!
ElMaestro
Helmut
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Vienna, Austria,
2015-10-01 20:13
(3100 d 20:02 ago)

@ john john
Posting: # 15515
Views: 10,537
 

 Sequential trial with B method of Potvin

Hi 2×John,

❝ In a sequential clinical trial conducted like a B method of Potvin, we have Cmax and AUC both not bioequivalent. Cmax has a power <80% (71.5%), and AUC>80% (84.6%).

❝ AUC 0-30min calculated by protocol is bioequivalent.

❝ In the protocol it was not specified how to proceed in this situation.


I assume you are talking about the interim analysis after stage 1.

❝ Can we calculate a new n and pass to the second phase? Or we must stop the trial?


That’s a stupid situation indeed. Following the scheme you could continue according to the results for Cmax, but would have to stop ’cause of AUC. Since for regulatory acceptance you have to show BE for both – and there is a chance for Cmax – well, cough, did I say before that this a stupid situation?
What you could try: Estimate the total sample size for Cmax, assume that the GMR of AUC stays the same in the pooled analysis, and calculate the CI with the higher degrees of freedom. Does the CI shrink enough? If no, think twice whether you should proceed.

Can you give us some numbers to play with? n1 (if unbalanced, nRT and nTR), GMRs, CVs.

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john john
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Spain,
2015-10-07 13:26
(3095 d 02:48 ago)

@ Helmut
Posting: # 15524
Views: 9,964
 

 Sequential trial with B method of Potvin

Hi

Sorry for the delay. I give you our numbers: n1 was 36 subjects balanced 18RT and 18TR

Cmax   CVintrasub (0.387)  Ratio(%Ref) (81.439)
               BEQ (70.162-94.529)
              Power at 20% (0.715)

AUC0-t CVintrasub (0.324)  Ratio(%Ref) (110.662)
              BEQ (97.552-125.534)
             Power at 20% (0.846)

AUC0-30       BEQ (84.314-105.609)


Thanks for your help
d_labes
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Berlin, Germany,
2015-10-07 15:49
(3095 d 00:26 ago)

@ john john
Posting: # 15525
Views: 10,024
 

 Power to the people

Hi John John

Cmax   CVintrasub (0.387)  Ratio(%Ref) (81.439)

❝                BEQ (70.162-94.529)
❝               Power at 20% (0.715)


❝ AUC0-t CVintrasub (0.324)  Ratio(%Ref) (110.662)

❝               BEQ (97.552-125.534)
❝              Power at 20% (0.846)


Whatever your power values stand for, they are not the correct ones for the Potvin TSD, method B.
You have to calculate the power at GMR=0.95, with alpha=0.0294 and CV from stage 1.

Here my results:
# Cmax
power.TOST(alpha=0.0294, CV=0.387, n=36, theta0=0.95)
[1] 0.3783821
# AUC
power.TOST(alpha=0.0294, CV=0.324, n=36, theta0=0.95)
[1] 0.5946074


Both are below the targeted 80%. Thus your problem described above doesn't exists.

Regards,

Detlew
john john
☆    

Spain,
2015-10-07 16:54
(3094 d 23:21 ago)

@ d_labes
Posting: # 15526
Views: 10,015
 

 Power to the people

Hi Detlew

❝ Here my results:

# Cmax

❝ power.TOST(alpha=0.0294, CV=0.387, n=36, theta0=0.95)

❝ [1] 0.3783821

# AUC

❝ power.TOST(alpha=0.0294, CV=0.324, n=36, theta0=0.95)

❝ [1] 0.5946074


❝ Both are below the targeted 80%. Thus your problem described above doesn't exists.


We have worked with CI of 94.12 and alpha 0.0294

Regards


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! [Helmut]
Helmut
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Vienna, Austria,
2015-10-07 18:06
(3094 d 22:09 ago)

@ john john
Posting: # 15527
Views: 10,367
 

 Software? Ethics beyond statistics…

Hi John John,

❝ We have worked with CI of 94.12 and alpha 0.0294


Which software did you use? The phrase

Power at 20%

smells of an outdated version of WinNonlin, which reports power for the FDA’s prehistoric “80/20 Rule” (i.e., power to detect a difference in least square means equal to 20% of the reference least squares mean). Since Phoenix/WinNonlin 6.4 additionally the much more relevant “Power_TOST” is reported. However, even if you have v6.4 you cannot specify a GMR of 0.95 (as required by Mme Potvin). The reported value is always given for the observed GMR. In your case it would be ex­tre­me­ly low for Cmax (⇒ 0.043) and should be calculated for a GMR of 0.95 (⇒ 0.377) – as pointed out by Detlew above.

Now for the nasty part. I recalculated your CVs and PEs from the CIs in order to increase precision. Your data make clear that Cmax is the crucial point (higher CV, worse PE).

library(PowerTOST)
n  <- 36
lo <- 0.70162
hi <- 0.94529
CV <- signif(CI2CV(lower=lo, upper=hi, n=n, design="2x2x2"), 5)
PE <- sqrt(lo*hi)
sampleN.TOST(alpha=0.0294, CV=CV, theta0=0.95, targetpower=0.8, design="2x2x2")

+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.0294, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.95,  CV = 0.38744

Sample size (total)
 n     power
74   0.802127

Potvin B (which you stated in the protocol) would mandate to initiate the second stage with 74 – 36 = 38 subjects. But: Does it make sense to still assume a GMR of 0.95 when you have observed 0.8144 (‼) in stage 1? That’s one of the drawbacks of TSDs. Generally they are not fully adaptive (i.e., re-estimate the sample size only based on the CV, not the GMR). Let’s play the devil’s ad­vo­cate and assume that both the CV and GMR in the final analysis (74 subjects) will be exactly what we observed in stage 1. Which power can we expect?

power.TOST(alpha=0.0294, CV=CV, n=74, theta0=PE, design="2x2x2")
[1] 0.05443928

Oops! Not surprising since the PE is that close to the lower limit of the acceptance range. Which sample size would we really need?

sampleN.TOST(alpha=0.0294, CV=CV, theta0=PE, targetpower=0.8, design="2x2x2")

+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.0294, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.814392,  CV = 0.38744

Sample size (total)
 n     power
6566   0.800031

I’m sure that your protocol states somewhere (not in the statistical section) that the study might be stopped by the sponsor. Think twice whether it makes sense to dose additional subjects given the information you have from the first stage (i.e., the keep-one’s-fingers-crossed approach).

In the future consider to add a futility criterion for early stopping and don’t perform TSDs if you are unsure about the GMR. Sorry, but I have to quote myself1

The entire arsenal of obtaining a reliable ‘educated guess’ (e.g. dissolution similarity for immediate release formulations of biopharmaceutics classification system class I/III drugs, established in vivo-in vitro correlation for controlled release products) should be used as well. If no reliable estimate can be derived, a—sufficiently large—pilot study should be performed. Subsequently, a TSD would still support dealing with the uncertain CV.

Be aware that futility rules deteriorate power. This was shown by Fuglsang2 for an upper total sample size, but is valid for any other rule as well. It would make sense to perform own simulations to get an idea about the impact of GMRs substantially deviating from 1.


    References:
  1. Schütz H. Two-stage designs in bioequivalence trials. Eur J Clin Pharmacol. 2015;71(3):271-81. doi:10.1007/s00228-015-1806-2
  2. Fuglsang A. Futility rules in bioequivalence trials with sequential designs. AAPS J. 2014;16(1):79–82. doi:10.1208/s12248-013-9540-0

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ElMaestro
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Denmark,
2015-10-07 23:22
(3094 d 16:53 ago)

@ Helmut
Posting: # 15528
Views: 9,907
 

 Subtraction of a df

Hi Helmut,

❝ sampleN.TOST(alpha=0.0294, CV=CV, theta0=0.95, targetpower=0.8, design="2x2x2")


Agree with every bit of your post. Though, technically I wonder if the above function call is approximative due to the lacking subtraction of a DF.
Perhaps there'd be a point in updating the package to allow for curious people and nitpickers to specify if the call forms part of a two-stage approach and needs internal subtraction of a DF.
This of course a technical digression and I apologise for borderline hijacking JJ's thread now.

Pass or fail!
ElMaestro
d_labes
★★★

Berlin, Germany,
2015-10-08 10:10
(3094 d 06:05 ago)

@ ElMaestro
Posting: # 15529
Views: 9,766
 

 df = df-1

Dear ElMaestro,

❝ ... Though, technically I wonder if the above function call is approximative due to the lacking subtraction of a DF.

❝ Perhaps there'd be a point in updating the package to allow for curious people and nitpickers to specify if the call forms part of a two-stage approach and needs internal subtraction of a DF.


Good point! And totally correct.
But I suppose that it would be hard to find any differences in estimated sample sizes using the correct df.

There is no must to use PowerTOST. Although it is termed "Gold standard" at times :cool:. But other software for SSE also lacks of this "deficiency" for nitpickers.

Regards,

Detlew
Helmut
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Vienna, Austria,
2015-10-08 17:27
(3093 d 22:48 ago)

@ john john
Posting: # 15531
Views: 9,863
 

 Potvin B: α 0.0294 in both stages

Hi John John,

Cmax   CVintrasub (0.387)  Ratio(%Ref) (81.439)

❝                BEQ (70.162-94.529)

Later you wrote:

❝ We have worked with CI of 94.12 and alpha 0.0294


I don’t think so; with your data:

library(PowerTOST)
round(100*CI.BE(alpha=0.0294, pe=0.81439, CV=0.387, n=36), 3)
 lower  upper
68.558 96.740

But:

round(100*CI.BE(alpha=0.0500, pe=0.81439, CV=0.387, n=36), 3)
 lower  upper
70.173 94.514

Talk to your statistician. I suggest to read the papers again (before designing a study & writing the pro­to­col / SAP) in order to get the analysis right.

Adding to this post:

find_alpha <- function(x) {
  require(PowerTOST)
  CI     <- CI.BE(alpha=alpha, pe=pe, CV=CV, n=n)
  closer <- CI[which.min(abs(CI - 1))]
  CI.BE(alpha=x, pe=pe, CV=CV, n=n)[names(closer)]-1
}
n     <- 36
pe    <- 0.81439
CV    <- 0.387
alpha <- 0.0294
p     <- uniroot(find_alpha, interval=c(1e-6, 0.5),
           tol=1e-8)$root
if (p < alpha) {
  cat(paste0("\n100% is not included in the ",
    "100(1\u002d2\u03b1) = ", 100*(1-2*alpha),
    "% confidence\ninterval; treatments are ",
    "significantly different (p ", signif(p, 4), ").\n\n"))
  } else {
  cat(paste0("\nTreatments are not significantly different ",
    "(p ", signif(p, 4), ").\n\n"))
}

100% is not included in the 100(1-2α) = 94.12% confidence
interval; treatments are significantly different (p 0.01289).


Do you really think that it is reasonable to continue?

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john john
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Spain,
2015-10-23 14:04
(3079 d 02:11 ago)

@ Helmut
Posting: # 15578
Views: 9,043
 

 Potvin B: α 0.0294 in both stages

Hi Helmut

We want to thank your comments and suggestions that have been a great help for the planning of our study.

Thank you !!

Best regards
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