Yura
Regular

Belarus,
2017-04-25 15:14

Posting: # 17264
Views: 6,561

## question of adjustment [RSABE / ABEL]

Dear all,
Correction of alpha is carried out by CVWR and CVWT-R (nR and nT-R, GRMR and
GRMT-R, respectively, for TRR / RTR / RRT) or only by CVWR? Since it is necessary to calculate CIT-R.
Regards
Helmut
Hero

Vienna, Austria,
2017-04-26 14:17

@ Yura
Posting: # 17267
Views: 6,047

## TIE depends on CVwR (and n)

Hi Yura,

can you please explain what you mean by the abbreviations you used?

» Correction of alpha is carried out by CVWR and CVWT-R (nR and nT-R, GRMR and
» GRMT-R, respectively, for TRR / RTR / RRT) or only by CVWR? Since it is necessary to calculate CIT-R.

The inflation of the Type I Error depends on CVwR (and to a minor extent on the sample size). CVwT – which is indeed nice to know – is not accessible in the partial replicate design.
Examples of the TIE and adjusting α for an assumed true ratio of 0.9:
1. n = 48, balanced sequences
```library(PowerTOST) scABEL.ad(CV=0.35, n=48, design="2x3x3") +++++++++++ scaled (widened) ABEL ++++++++++++          iteratively adjusted alpha    (simulations based on ANOVA evaluation) ---------------------------------------------- Study design: 2x3x3 (TRR|RTR|RRT) log-transformed data (multiplicative model) 1,000,000 studies in each iteration simulated. CVwR 0.35, n(i) 16|16|16 (N 48) Nominal alpha                 : 0.05 True ratio                    : 0.9000 Regulatory settings           : EMA (ABEL) Switching CVwR                : 0.3 Regulatory constant           : 0.76 Expanded limits               : 0.7723 ... 1.2948 Upper scaling cap             : CVwR > 0.5 PE constraints                : 0.8000 ... 1.2500 Empiric TIE for alpha 0.0500  : 0.05663 Power for theta0 0.9000       : 0.801 Iteratively adjusted alpha    : 0.04405 Empiric TIE for adjusted alpha: 0.05000 Power for theta0 0.9000       : 0.785```

2. Three dropouts
```scABEL.ad(CV=0.35, n=c(16, 14, 15), design="2x3x3") +++++++++++ scaled (widened) ABEL ++++++++++++          iteratively adjusted alpha    (simulations based on ANOVA evaluation) ---------------------------------------------- Study design: 2x3x3 (TRR|RTR|RRT) log-transformed data (multiplicative model) 1,000,000 studies in each iteration simulated. CVwR 0.35, n(i) 16|14|15 (N 45) Nominal alpha                 : 0.05 True ratio                    : 0.9000 Regulatory settings           : EMA (ABEL) Switching CVwR                : 0.3 Regulatory constant           : 0.76 Expanded limits               : 0.7723 ... 1.2948 Upper scaling cap             : CVwR > 0.5 PE constraints                : 0.8000 ... 1.2500 Empiric TIE for alpha 0.0500  : 0.05634 Power for theta0 0.9000       : 0.779 Iteratively adjusted alpha    : 0.04420 Empiric TIE for adjusted alpha: 0.05000 Power for theta0 0.9000       : 0.762```
Due to the smaller sample size in #2 the TIE is less inflated (0.05634 < 0.05663) and less adjustment is required (0.04420 > 0.4405) to preserve the patient’s risk. On the other hand the narrower CI (91.16% < 91.19%) cannot outweigh the loss in power (76.2% < 78.5%).

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
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Yura
Regular

Belarus,
2017-04-26 17:28

@ Helmut
Posting: # 17269
Views: 5,929

## TIE depends on CVwR (and n)

Hi, Helmut
Yes of course

Adjusted alpha is used to construct confidence intervals of the pharmacokinetic parameters for the index T-P?
Regards
Helmut
Hero

Vienna, Austria,
2017-04-26 18:00

@ Yura
Posting: # 17270
Views: 5,954

## TIE depends on CVwR (and n)

Hi Yura,

» Adjusted alpha is used to construct confidence intervals of the pharmacokinetic parameters for the index T-P?

What do you mean by “the index T-P”? For the EMA use the ‘Method A’ or ‘Method B’ as given in the Q&A-document. But instead of using the nominal α of 0.05 (i.e., the 100(1–2α) = 90% CI) apply the respective adjusted α. If the TIE would be inflated with α 0.05, the adjusted CI is always wider (i.e., conservative).

Cheers,
Helmut Schütz

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

Belarus,
2017-04-26 18:55

@ Helmut
Posting: # 17272
Views: 5,965

## TIE depends on CVwR (and n)

Hi, Helmut
Yes of course
We evaluate the difference between T-R, and also R-R - for expansion, if necessary. Therefore, CV T-R and CV R-R are obtained. Other CV, therefore, different alpha. What use alpha to build confidence interval difference T-R?
Regards
Yura
Regular

Belarus,
2017-04-28 11:13

@ Yura
Posting: # 17275
Views: 5,869

## TIE depends on CVwR (and n)

Hi, Helmut
Did I understand correctly, when constructing a confidence interval for T-R differences, use the adjusted alpha for R-R?
Regards
Helmut
Hero

Vienna, Austria,
2017-04-28 19:16

@ Yura
Posting: # 17277
Views: 5,934

## TIE = p(BE) at expanded limits

Hi Yura,

» Did I understand correctly, when constructing a confidence interval for T-R differences, use the adjusted alpha for R-R?

Exactly – now you got it!

In a nutshell, the Type I Error is the probability of falsely claiming BE. The TIE can be estimated by setting theta0 to one of the limits of the acceptance range. Easy for ABE (since an explicit solution exists).

```library(PowerTOST) CV  <- 0.3 des <- "2x2x4" n   <- 34 U   <- 1.25 power.TOST(CV=CV, n=n, theta0=U, design=des) # [1] 0.05```

Alternatively you can perform simulations.

```power.TOST.sim(CV=CV, n=n, theta0=U, design=des, nsims=1e7) # [1] 0.0500178```

The convergence is lousy. If you have a lot of time increase the number of simulations.
When it comes to reference-scaling no explicit formula for power exists. Hence, we need simulations. There is a complication: ABEL is a framework of decisions where the Null-hypothesis is constructed in face of the data. In other words we don’t know the expanded limits until we have calculated CVwR. Unlike in ABE the limits are random variables themselves.

```CVwR <- 0.3 reg  <- "EMA" U    <- scABEL(CV=CVwR, regulator=reg)[["upper"]] power.scABEL(CV=CVwR, n=n, theta0=U, design=des,              regulator=reg, nsims=1e6) # [1] 0.081626```

If you don’t like (or trust in) simulating the underlying statistics, with the latest version of `PowerTOST` you can simulate subject data as well.

```power.scABEL.sdsims(CV=CVwR, n=n, theta0=U, design=des,                     regulator=reg, nsims=1e6) # [1] 0.081602```

Note that in the final evaluation (i.e., the PE and its CI) the EMA’s model assumes that CVwT = CVwR which is strong meat. To get the adjusted α, and the TIEs for nominal and adjusted α:

```res  <- scABEL.ad(CV=CVwR, n=n, design=des, regulator=reg, print=FALSE) TIE0 <- res[["TIE.unadj"]] adj  <- res[["alpha.adj"]] TIE1 <- res[["TIE.adj"]] cat(TIE0, adj, TIE1, "\n") # 0.081626 0.028572 0.05```

Now imagine a study which passed with the nominal α 0.05 (90% CI):

```round(100*CI.BE(alpha=0.05, pe=0.9, CV=CV, n=n, design=des), 2) # lower upper # 82.78 97.85```

The study would still pass with the adjusted α 0.028572 (94.2856% CI) but it is a more close shave:

```round(100*CI.BE(alpha=adj, pe=0.9, CV=CV, n=n, design=des), 2) # lower  upper # 81.69  99.16```

If you want to avoid surprises increase the sample size.

```res <- sampleN.scABEL.ad(CV=CVwR, theta0=0.9, design=des,                          regulator=reg, print=FALSE) adj <- res[["alpha.adj"]] n.a <- res[["Sample size"]] cat(adj, n.a, "\n") # 0.028311 42```

Note that the TIE depends also on the sample size. Therefore, slightly more adjustment is needed (n=34: 0.028572, n=42: 0.028311). With 42 subjects you should be on the safe side.

```round(100*CI.BE(alpha=adj, pe=0.9, CV=CV, n=n.a, design=des), 2) # lower upper # 82.49 98.20```

Cheers,
Helmut Schütz

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

Belarus,
2017-04-29 13:01

@ Helmut
Posting: # 17279
Views: 5,774

## TIE = p(BE) at expanded limits

Dear Helmut
As always, you are on top
Regards
pjs
Regular

India,
2018-02-28 14:33

@ Helmut
Posting: # 18483
Views: 4,460

## TIE depends on CVwR (and n)

Dear All,

Request you to share your thoughts for the requirement for Type 1 error estimation and adjustment of alpha for below different scenarios.

» The inflation of the Type I Error depends on CVwR (and to a minor extent on the sample size).

study is conducted as partial replicate design with 60 subjects. Now CVwr has turned out to be 31% in the study. In the sample size T/R ratio was assumed to be 0.90. In the actual conducted study T/R ratio had come to 100% (product essentially similar to reference product-Hypothetical scenario). Now study is passing the SCABE criteria. Study would have also passed incase limits would not have been scaled. Essentially there would not have been difference in study conclusion if the Scaling approach would have applied or not applied. As per my understanding Type 1 error would arise incase there is difference in study conclusion when there is uncertainty in the ISCV and due to that difference in study conclusion incase different method for study conclusion is utilized (like study passing in SCABE but failing in ABE, borderline case). DO any such case require adjustment of alpha although there is borderline high variability (incases where there is maximum probability of type 1 error).

Regards
Pjs
Helmut
Hero

Vienna, Austria,
2018-02-28 14:48

@ pjs
Posting: # 18485
Views: 4,463

## TIE depends on CVwR (and n)

Dear Pjs,

» […] study is passing the SCABE criteria.

If you are referring to the FDA’s RSABE approach, there is not problem with inflation of the Type I Error if (the true) CVwR ≥30%. Only with CVwR <30% problems might be massive (see this presentation).

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
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pjs
Regular

India,
2018-03-01 07:35

@ Helmut
Posting: # 18488
Views: 4,370

## TIE depends on CVwR (and n)

Dear Helmut,

Thanks for the feedback.

Just need some clarification.

For FDA limits are scaled from 0.25 but applied at 0.294 unlike EU in which limits are scaled from 0.294.

Hence at any Swr limits would be more wider for FDA compared to EU. Hence chances of establishing BE would be more for USFDA compared to EU in the nearby CV from cutoff limit of 30%. Considering the same There is more possibility for difference in BE results when applying two different methods Scaling and ABE incase of FDA for study conclusion. Hence alpha inflation should be more for FDA instead of EU. Please correct me if i have misunderstood the concept.

Also incase of EU scaling is applicable for Cmax parameter only and not for AUC parameter in contrary to FDA for which scaling is applicable for all the primary metric. This could also play certain role in the calculation of alpha inflation.

Regards
Pjs
Helmut
Hero

Vienna, Austria,
2018-03-01 13:32

@ pjs
Posting: # 18489
Views: 4,392

## Comparing methods for (S)ABE

Hi Pjs,

your considerations are essentially correct. OK, a little bit theoretical because in all jurisdictions we need the respective region’s reference product. But yes, if we consider the same data set, the conclusions might differ if we apply different reference-scaling methods – especially in borderline cases.

What do we have now?
1. US-FDA, CFDA
RSABE for both AUC and Cmax, no clinical justification required, fixed effects model for the partial replicate design and mixed effects model for full replicate design. GMR restriction 80.00–125.00%. If swR <0.294, mixed effects model irrespective of the design.
2. EEA, Russia, EEU, Egypt, ANVISA
ABEL for Cmax (MR products additionally: Cmin, pAUCs), upper cap on scaling at CVwR 50%, clinical justification required, fixed effects model. GMR restriction 80.00–125.00%.
3. WHO
Like #3. Pilot phase for AUC. 4-period full replicate design man­datory, comparison of swT with swR (though no conditions for passing given so far).
ABEL for AUC, upper cap on scaling at CVwR 57.4%, clinical justification required, mixed effects model. GMR restriction 80.0–125.0%.
GMR of Cmax within 80.0–125.0% (no CI needed).
5. GCC member states
Widening of the acceptance limits for Cmax only (fixed and pre-specified to 75–133%), clinical justification required, CVwR >30% demonstrated in a full replicate design, GMR restriction 80.00–125.00%.
In all methods (except #4: Cmax and #5: assessed by ABE) inflation of the Type I Error is possible.

At the 2nd International Conference of the Global Bioequivalence Harmonization Initiative (Rockville, Sep 2016) an entire session was devoted to reference-scaling. No consensus reached. On the contrary. Each agency defended its concept as if it is an eternal truth. Disappointing.

BTW, we have lacking harmonization even in ABE. For NTIDs the EMA’s acceptance range is 90.00–111.11%, whereas for Health Canada it is 90.0–112.0%.

```library(PowerTOST) round(100*CI.BE(pe=1.05, CV=0.12, n=24), 2)  lower  upper  98.96 111.41```

The same study would fail for the EMA but pass for HC.

Cheers,
Helmut Schütz

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

India,
2018-03-05 14:50

@ Helmut
Posting: # 18496
Views: 4,255

## Comparing methods for (S)ABE

Hi Helmut,

Yes agree with you, harmonization should be there for evaluating BE criteria incase of HVDP or NTI drugs or any such evaluation criteria.

Have gone through some of the post related to alpha correction incase of SABE approach in the forum. In the simulations done most extreme GMR of 1.25 is assumed for the simulation and calculation of possible alpha inflation.

I would like to understand as the actual alpha adjustment would be based on actual Swr observed in the study and number of subjects, what could be the rationale of doing adjustment of alpha based on the calculation which is done on extreme GMR while for the actual study conducted T/R ratio could be very much close to unity (let's say 0.95 or 0.97). I do understand the most deviated GMR would lead to maximum probability for the alpha inflation but applying this extreme case and alpha adjustment in each and every study is required?

Regards
Pjs
Helmut
Hero

Vienna, Austria,
2018-03-05 17:40

@ pjs
Posting: # 18497
Views: 4,280

## Simulating the Null

Hi Pjs,

» Have gone through some of the post related to alpha correction incase of SABE approach in the forum. In the simulations done most extreme GMR of 1.25 is assumed for the simulation and calculation of possible alpha inflation.

Not exactly. In order to simulate the type I error we assume that the Null Hypothesis (of bio­in­equivalence) is true. In SCABE (ABEL: expanded limits, RSABE: implied limits) only if CVwR ≤30% the GMR of the Null is at 1.25 (or 0.8). Therefore, with higher CVs we have to simulate at higher GMRs as well.
Note that in ABE the Null is always at the borders of the acceptance range (0.8 and 1.25). Hence, here we don’t need simulations but can directly calculate the power (i.e., chance of passing BE = falsely rejecting the Null):

```library(PowerTOST) power.TOST(CV=0.3, theta0=1.25, design="2x2x4", n=40) # [1] 0.05```

Of course, we can simulate the TIE as well:

```power.TOST.sim(CV=0.3, theta0=1.25, design="2x2x4", n=40, nsims=1e6) # [1] 0.05004```

TOST (or the CI inclusion method) is not the most powerful test. If the sample size is very low, the TIE will be ≤5%:

```power.TOST(CV=0.3, theta0=1.25, design="2x2x4", n=12) # [1] 0.04977286```

On the other hand, a very high sample size would still preserve the nominal level:

```power.TOST(CV=0.3, theta0=1.25, design="2x2x4", n=1200) # [1] 0.05```

That’s a comforting property.

In SCABE the scaled limits (and hence the GMR which we use in simulating the Null) depend on the CVwR. Example for CVwR 40%:

``` scABEL(CV=0.4, regulator="EMA") #    lower    upper # 0.746177 1.340165 scABEL(CV=0.4, regulator="FDA") #     lower     upper # 0.7090232 1.4103911```

» I would like to understand as the actual alpha adjustment would be based on actual Swr observed in the study and number of subjects, what could be the rationale of doing adjustment of alpha based on the calculation which is done on extreme GMR while for the actual study conducted T/R ratio could be very much close to unity (let's say 0.95 or 0.97).

The observed GMR is only an estimate. We don’t know where the population’s true GMR lies. Think about the 90% CI. There is a 5% chance at each CL that the true GMR is outside. Imagine in ABE you observe a GMR of 1 with a 90% CI of 0.8–1.25. What is the TIE?

» I do understand the most deviated GMR would lead to maximum probability for the alpha inflation …

Correct.

» … but applying this extreme case and alpha adjustment in each and every study is required?

That’s maybe the best we have so far. OK, we could go even further (suggested by Molins et al.)* Simulating the Null at the scaled limits still assumes that the CVwR estimated in the study is the true value – which might not be correct. If one wants to get the most conservative adjusted α one should simulate at CVwR 30% – irrespective of what we observe (since this is the location of the maximum TIE both in ABEL and RSABE). However, there is no free lunch. Either power will be compromised or 20–25% more subjects are needed to preserve the desired power.

• Molins E, Cobo E, Ocaña J. Two‐stage designs versus European scaled average designs in bioequivalence studies for highly variable drugs: Which to choose? Stat Med. 2017;36(30):4777–88. doi:10.1002/sim.7452.

Cheers,
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. ☼
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Helmut
Hero

Vienna, Austria,
2018-03-07 16:21

@ pjs
Posting: # 18504
Views: 4,059

Hi Pjs,

extending the end of my post. No R-code yet because it requires the development-version of `PowerTOST`. Essentially we have three options:
1. Assuming that the observed CVwR is the true one.
2. Since the true CVwR is unknown, assume the worst, i.e., always adjust for a CVwR of 30%.
3. Calculate a conservative CI of the observed CVwR. If the CI includes 30%, adjust for CVwR=30%. If not adjust for the CL which is closer to 30%.
Sample sizes were estimated for a GMR of 0.9 and target power 0.8, 4-period full replicate design, and the EMA’s ABEL. `NA` denotes cases where no adjustment is necessary (since the Type I Error with the nominal α is ≤0.05).

```Adjustment based on observed CVwR (Labes and Schütz 2016):  reg design  n  CVwR TIE.nom alpha.adj TIE.adj pwr.des pwr.act  EMA  2x2x4 14 0.175 0.04988        NA      NA  0.8007  0.8007  EMA  2x2x4 18 0.200 0.04998        NA      NA  0.8007  0.8007  EMA  2x2x4 24 0.225 0.04958        NA      NA  0.8229  0.8229  EMA  2x2x4 28 0.250 0.05180   0.04825    0.05  0.8116  0.8069  EMA  2x2x4 32 0.275 0.05980   0.04148    0.05  0.8082  0.7824  EMA  2x2x4 34 0.300 0.08163   0.02857    0.05  0.8028  0.7251  EMA  2x2x4 34 0.325 0.06971   0.03418    0.05  0.8010  0.7492  EMA  2x2x4 34 0.350 0.06557   0.03630    0.05  0.8118  0.7728  EMA  2x2x4 32 0.375 0.06271   0.03782    0.05  0.8110  0.7760  EMA  2x2x4 30 0.400 0.05912   0.04024    0.05  0.8066  0.7800  EMA  2x2x4 30 0.425 0.05451   0.04454    0.05  0.8219  0.8094  EMA  2x2x4 28 0.450 0.04889        NA      NA  0.8112  0.8112  EMA  2x2x4 28 0.475 0.04114        NA      NA  0.8162  0.8162  EMA  2x2x4 28 0.500 0.03317        NA      NA  0.8143  0.8143  EMA  2x2x4 28 0.525 0.03787        NA      NA  0.8073  0.8073  EMA  2x2x4 30 0.550 0.04165        NA      NA  0.8211  0.8211  EMA  2x2x4 30 0.575 0.04420        NA      NA  0.8047  0.8047  EMA  2x2x4 32 0.600 0.04630        NA      NA  0.8101  0.8101  EMA  2x2x4 34 0.625 0.04779        NA      NA  0.8128  0.8128  EMA  2x2x4 36 0.650 0.04856        NA      NA  0.8127  0.8127 'Worst case' adjustment based on CVwR=30% (Molins et al. 2017):  reg design  n  CVwR CV.adj TIE.nom alpha.adj TIE.adj pwr.des pwr.act  EMA  2x2x4 14 0.175    0.3 0.07904   0.03022    0.05  0.8007  0.4073  EMA  2x2x4 18 0.200    0.3 0.07928   0.02988    0.05  0.8007  0.4942  EMA  2x2x4 24 0.225    0.3 0.08064   0.02927    0.05  0.8229  0.5951  EMA  2x2x4 28 0.250    0.3 0.08057   0.02910    0.05  0.8116  0.6517  EMA  2x2x4 32 0.275    0.3 0.08075   0.02904    0.05  0.8082  0.7055  EMA  2x2x4 34 0.300    0.3 0.08160   0.02864    0.05  0.8028  0.7239  EMA  2x2x4 34 0.325    0.3 0.08160   0.02864    0.05  0.8010  0.7239  EMA  2x2x4 34 0.350    0.3 0.08160   0.02864    0.05  0.8118  0.7239  EMA  2x2x4 32 0.375    0.3 0.08075   0.02904    0.05  0.8110  0.7055  EMA  2x2x4 30 0.400    0.3 0.08123   0.02888    0.05  0.8066  0.6753  EMA  2x2x4 30 0.425    0.3 0.08123   0.02888    0.05  0.8219  0.6753  EMA  2x2x4 28 0.450    0.3 0.08057   0.02910    0.05  0.8112  0.6517  EMA  2x2x4 28 0.475    0.3 0.08057   0.02910    0.05  0.8162  0.6517  EMA  2x2x4 28 0.500    0.3 0.08057   0.02910    0.05  0.8143  0.6517  EMA  2x2x4 28 0.525    0.3 0.08057   0.02910    0.05  0.8073  0.6517  EMA  2x2x4 30 0.550    0.3 0.08123   0.02888    0.05  0.8211  0.6753  EMA  2x2x4 30 0.575    0.3 0.08123   0.02888    0.05  0.8047  0.6753  EMA  2x2x4 32 0.600    0.3 0.08075   0.02904    0.05  0.8101  0.7055  EMA  2x2x4 34 0.625    0.3 0.08160   0.02864    0.05  0.8128  0.7239  EMA  2x2x4 36 0.650    0.3 0.08173   0.02852    0.05  0.8127  0.7454 Conservative adjustment based on 99.9% CI of observed CVwR:  reg design  n  CVwR lower CL upper CL CV.adj TIE.nom alpha.adj TIE.adj pwr.des pwr.act  EMA  2x2x4 14 0.175   0.1022   0.4536 0.3000 0.07818   0.03072    0.05  0.8007  0.4096  EMA  2x2x4 18 0.200   0.1237   0.4407 0.3000 0.07944   0.03005    0.05  0.8007  0.4935  EMA  2x2x4 24 0.225   0.1475   0.4300 0.3000 0.08040   0.02933    0.05  0.8229  0.5952  EMA  2x2x4 28 0.250   0.1683   0.4503 0.3000 0.08122   0.02886    0.05  0.8116  0.6513  EMA  2x2x4 32 0.275   0.1892   0.4737 0.3000 0.08130   0.02860    0.05  0.8082  0.7018  EMA  2x2x4 34 0.300   0.2082   0.5088 0.3000 0.08163   0.02857    0.05  0.8028  0.7251  EMA  2x2x4 34 0.325   0.2251   0.5547 0.3000 0.08163   0.02857    0.05  0.8010  0.7251  EMA  2x2x4 34 0.350   0.2420   0.6014 0.3000 0.08163   0.02857    0.05  0.8118  0.7251  EMA  2x2x4 32 0.375   0.2560   0.6641 0.3000 0.08130   0.02860    0.05  0.8110  0.7018  EMA  2x2x4 30 0.400   0.2694   0.7334 0.3000 0.08102   0.02888    0.05  0.8066  0.6777  EMA  2x2x4 30 0.425   0.2856   0.7864 0.3000 0.08102   0.02888    0.05  0.8219  0.6777  EMA  2x2x4 28 0.450   0.2979   0.8680 0.3000 0.08122   0.02886    0.05  0.8112  0.6513  EMA  2x2x4 28 0.475   0.3136   0.9263 0.3136 0.07365   0.03238    0.05  0.8162  0.6668  EMA  2x2x4 28 0.500   0.3291   0.9864 0.3291 0.06893   0.03485    0.05  0.8143  0.6814  EMA  2x2x4 28 0.525   0.3446   1.0480 0.3446 0.06639   0.03625    0.05  0.8073  0.6965  EMA  2x2x4 30 0.550   0.3646   1.0730 0.3646 0.06362   0.03748    0.05  0.8211  0.7421  EMA  2x2x4 30 0.575   0.3800   1.1360 0.3800 0.06183   0.03838    0.05  0.8047  0.7580  EMA  2x2x4 32 0.600   0.4000   1.1610 0.4000 0.05905   0.04008    0.05  0.8101  0.8035  EMA  2x2x4 34 0.625   0.4198   1.1890 0.4198 0.05430   0.04416    0.05  0.8128  0.8464  EMA  2x2x4 36 0.650   0.4397   1.2170 0.4397 0.04819        NA      NA  0.8127  0.8127```

As you can see, power is compromised (`pwr.des` = achieved power in sample size estimation, `pwr.act` = actual power if the study is evaluated with the adjusted α). IMHO, power <0.7 is not desirable.
Molin’s approach is extremely conservative. Imagine an observed CVwR of 100%. According to ABEL we will employ the maximum expansion (69.84–143.19%) of the BE limits and the decision will practically lead by the GMR-re­striction (80.00–125.00%). But how likely is a true CVwR of 30%? Less than 10–15! The adjusted α (4-period full replicate, n 68) will be 0.02748 and power 0.7161. Borderline.

Will it help to use a less strict CI of CVwR?

```Conservative adjustment based on 99.0% CI of observed CVwR:  reg design  n  CVwR lower CL upper CL CV.adj TIE.nom alpha.adj TIE.adj pwr.des pwr.act  EMA  2x2x4 14 0.175   0.1135   0.3535 0.3000 0.07818   0.03072    0.05  0.8007  0.4096  EMA  2x2x4 18 0.200   0.1359   0.3603 0.3000 0.07944   0.03005    0.05  0.8007  0.4935  EMA  2x2x4 24 0.225   0.1604   0.3660 0.3000 0.08040   0.02933    0.05  0.8229  0.5952  EMA  2x2x4 28 0.250   0.1822   0.3895 0.3000 0.08122   0.02886    0.05  0.8116  0.6513  EMA  2x2x4 32 0.275   0.2039   0.4146 0.3000 0.08130   0.02860    0.05  0.8082  0.7018  EMA  2x2x4 34 0.300   0.2240   0.4471 0.3000 0.08163   0.02857    0.05  0.8028  0.7251  EMA  2x2x4 34 0.325   0.2423   0.4863 0.3000 0.08163   0.02857    0.05  0.8010  0.7251  EMA  2x2x4 34 0.350   0.2605   0.5261 0.3000 0.08163   0.02857    0.05  0.8118  0.7251  EMA  2x2x4 32 0.375   0.2763   0.5758 0.3000 0.08130   0.02860    0.05  0.8110  0.7018  EMA  2x2x4 30 0.400   0.2914   0.6292 0.3000 0.08102   0.02888    0.05  0.8066  0.6777  EMA  2x2x4 30 0.425   0.3090   0.6725 0.3090 0.07533   0.03144    0.05  0.8219  0.6875  EMA  2x2x4 28 0.450   0.3231   0.7326 0.3231 0.07043   0.03402    0.05  0.8112  0.6755  EMA  2x2x4 28 0.475   0.3402   0.7787 0.3402 0.06698   0.03590    0.05  0.8162  0.6924  EMA  2x2x4 28 0.500   0.3573   0.8257 0.3573 0.06493   0.03691    0.05  0.8143  0.7083  EMA  2x2x4 28 0.525   0.3742   0.8736 0.3742 0.06322   0.03784    0.05  0.8073  0.7255  EMA  2x2x4 30 0.550   0.3952   0.9005 0.3952 0.05981   0.03969    0.05  0.8211  0.7744  EMA  2x2x4 30 0.575   0.4121   0.9487 0.4121 0.05704   0.04200    0.05  0.8047  0.7946  EMA  2x2x4 32 0.600   0.4330   0.9759 0.4330 0.05217   0.04695    0.05  0.8101  0.8410  EMA  2x2x4 34 0.625   0.4539   1.0040 0.4539 0.04565        NA      NA  0.8128  0.8128  EMA  2x2x4 36 0.650   0.4747   1.0330 0.4747 0.03821        NA      NA  0.8127  0.8127```

Only a little.

Cheers,
Helmut Schütz

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