Bioequivalence and Bioavailability Forum • Type 1: n2=2 (EMA), no interim power (NL?)

Helmut
★★★

Vienna, Austria,
2015-02-13 14:29
(3716 d 18:04 ago)

Posting: # 14415
Views: 6,594

Type 1: n2=2 (EMA), no interim power (NL?) [Two-Stage / GS Designs]

Simulators,

I explored “type 1” designs derived from Potvin’s Method B (T/R 0.95, target power 80%). As posted previously Pocock’s α_adj 0.0294 is unnecessarily conservative (and might be too liberal for Method C); 0.0304 suits pretty well (largest inflation of the TIE 0.050111; n.s. >0.05). Since EMA in their Q&A-document (Rev.7) stated a minimum n₂ of 2¹ and sometimes Dutch regulators seemingly don’t like² interim power (for “type 2” TSDs only?), I gave it a try. I obtained an α_adj of 0.0310 with a maximum TIE of 0.050229 (n.s. >0.05).

Empiric TIE; I = modified Potvin 0.0304, II = EMA/NL (?) 0.0310.

           12             24             36             48             60      

CV     I      II      I      II      I      II      I      II      I      II   

0.1  0.0304 0.0409  0.0302 0.0378  0.0303 0.0366  0.0303 0.0358  0.0302 0.0352

0.2  0.0474 0.0497  0.0324 0.0387  0.0303 0.0366  0.0303 0.0358  0.0302 0.0352

0.3  0.0453 0.0455  0.0488 0.0493  0.0405 0.0423  0.0328 0.0370  0.0304 0.0353

0.4  0.0358 0.0355  0.0448 0.0449  0.0501 0.0502  0.0468 0.0471  0.0416 0.0427

0.5  0.0321 0.0322  0.0353 0.0353  0.0434 0.0434  0.0500 0.0498  0.0494 0.0493

0.6  0.0310 0.0310  0.0320 0.0321  0.0343 0.0345  0.0419 0.0417  0.0485 0.0484

0.7  0.0304 0.0304  0.0315 0.0315  0.0316 0.0316  0.0337 0.0337  0.0397 0.0397

0.8  0.0302 0.0301  0.0310 0.0310  0.0309 0.0309  0.0313 0.0313  0.0330 0.0330

0.9  0.0300 0.0300  0.0309 0.0309  0.0309 0.0309  0.0308 0.0308  0.0311 0.0311

1.0  0.0300 0.0300  0.0308 0.0308  0.0307 0.0307  0.0307 0.0307  0.0307 0.0307

Whereas TIEs of EMA’s approach are similar at high CVs, we see higher inflation of the TIE at low to moderate CVs (the main application of TSDs). Though the patient’s risk is still maintained – why all that fuzz‽

Empiric power; I = modified Potvin 0.0304, II = EMA/NL (?) 0.0310.

           12             24             36             48             60     

CV     I      II      I      II      I      II      I      II      I      II   

0.1  0.9775 0.9912  1.0000 1.0000  1.0000 1.0000  1.0000 1.0000  1.0000 1.0000

0.2  0.8411 0.8483  0.8816 0.9037  0.9571 0.9693  0.9889 0.9922  0.9975 0.9984

0.3  0.7845 0.7865  0.8306 0.8314  0.8366 0.8437  0.8551 0.8714  0.9017 0.9177

0.4  0.7520 0.7524  0.8040 0.8038  0.8227 0.8235  0.8305 0.8301  0.8303 0.8331

0.5  0.7366 0.7364  0.7824 0.7824  0.8063 0.8063  0.8194 0.8179  0.8248 0.8257

0.6  0.7287 0.7297  0.7738 0.7738  0.7908 0.7908  0.8029 0.8029  0.8153 0.8153

0.7  0.7251 0.7251  0.7695 0.7695  0.7853 0.7853  0.7930 0.7930  0.8028 0.8028

0.8  0.7233 0.7233  0.7689 0.7689  0.7830 0.7830  0.7882 0.7882  0.7963 0.7963

0.9  0.7207 0.7207  0.7672 0.7672  0.7808 0.7808  0.7874 0.7874  0.7923 0.7923

1.0  0.7191 0.7191  0.7670 0.7670  0.7802 0.7802  0.7854 0.7854  0.7924 0.7924

Slightly higher power at low to moderate CVs.

Alfredo García told me that he suggested the BSWP a minimum stage 2 sample size of 12 in order “to get a good estimate of the variance“.
Deficiency letter of the MEB (2011) about Method C: “Confidence intervals were adapted based upon the power of the pharmacokinetic variable. In this case for C_max the power was below 80% and confidence intervals were adapted to 94.12%, instead of the usually applied 90%. However, adapting the confidence intervals based upon power is not acceptable and also not in accordance with the EMA guideline. Confidence intervals should be selected a priori, without evaluation of the power.”
(my emphases)
Bonus question: Is interim power acceptable for “type 1” TSDs?

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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d_labes
★★★

Berlin, Germany,
2015-02-13 15:53
(3716 d 16:40 ago)

@ Helmut
Posting: # 14417
Views: 5,364

Type 1: no interim power (NL?)

Post reply

Dear Helmut,

❝ Bonus question: Is interim power acceptable for “type 1” TSDs?

If not, use power.2stage.fC() with arguments (powerstep = FALSE, method="B", fClower=0, ...) and simsalabim interim power has vanished :cool:

!

Note: The results are totally equal to powerstep = TRUE since this step is now substitutionally done (implicitly) by the sample size estimation step.

BTW: This n2=2 at minimum is totally incomprehensible to me. One of the arguments was if not used alpha will be inflated. Seems you have shown that the opposite is true.

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2015-02-13 16:22
(3716 d 16:11 ago)

@ d_labes
Posting: # 14418
Views: 5,475

Type 1: no interim power (NL?)

Post reply

Dear Detlew,

❝ ❝ Bonus question: Is interim power acceptable for “type 1” TSDs?

❝

❝ If not, use power.2stage.fC() with arguments (powerstep = FALSE, method="B", fClower=0, ...) and simsalabim interim power has vanished :cool: !

That’s what I’ve done.

[image]

One interpretation of the MEB’s statement would be that interim power is not acceptable for “type 2” TSDs (aka variants of Method C) but still for “type 1”. Since interim power is the root of the decision tree in “type 2” TSDs it cannot be dropped – bad luck.
Beheaded Justitia standing firm.

❝ BTW: This n2=2 at minimum is totally incomprehensible to me.

I don’t get it as well.*

❝ One of the arguments was if not used alpha will be inflated.

I’m not sure. The Q&A stated only:

From the perspective of type I error control it is considered that there is no minimal number of subjects to be included in the second stage of a two-stage design, so long as it can be demonstrated that the type I error of the study is controlled [sic].

I would rather say, the BSWP had the sequence × stage term in mind (to perform a test for poolability or what?):

However, the analysis model for analysing the combined data also needs to be considered.
To fit this model it is necessary to have in each stage at least one patient in each sequence – so a minimum of two patients in each stage of the study, but more if both happen to be randomised to the same sequence.

❝ Seems you have shown that the opposite is true.

Since Alfedo García suggested to ask questions concerning TSDs directly to the BSWP I’m currently preparing an open letter. I will clearly state that I will make the answer public. I’m sick of lacking transparency (<span lang="de"> “Im stillen Kämmerlein.” </span> = on the Q.T.)…

Edit: I compared a more detailed matrix (n₁: 12, 14, 16, 18, 20, 22, 24, 30, 36, 42, 48, 54, 60, 70 and CV: 0.1, 0.12, 0.14, 0.16, 0.18, 0.2, 0.25, 0.3, 0.35, 0.4, 0.5, 0.6, 0.7, 0.8) without and with this “minimum n₂ = 2” requirement for both “types”. Empiric TIE and power were identical to the fifth decimal… What a waste of time.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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