Helmut
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2015-02-13 13:29

Posting: # 14415
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 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 αadj 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 αadj 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.


  1. 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“.
  2. 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 Cmax 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?

Cheers,
Helmut Schütz
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d_labes
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Berlin, Germany,
2015-02-13 14:53

@ Helmut
Posting: # 14417
Views: 3,842
 

 Type 1: no interim power (NL?)

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
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2015-02-13 15:22

@ d_labes
Posting: # 14418
Views: 3,848
 

 Type 1: no interim power (NL?)

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.

:crying:

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.

Cheers,
Helmut Schütz
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