Bioequivalence and Bioavailability Forum • EMA: Q&A update (Two-Stage designs)

Helmut
★★★

Vienna, Austria,
2013-03-08 15:47
(4835 d 20:45 ago)

Posting: # 10174
Views: 13,459

EMA: Q&A update (Two-Stage designs) [BE/BA News]

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Dear all,

yesterday EMA’s PK working party published Rev. 7 of the Q&A document. According to the new #14:

The expected analysis for the combined data in a two-stage design is ANOVA with terms for stage, sequence, sequence × stage, subject(sequence × stage), period(stage), formulation.
This model can be fitted provided that in each stage, there is at least one subject randomised to each sequence. This does not supersede the requirement for at least 12 subjects overall.
A term for a formulation × stage interaction should not be fitted.

If you have a Two-Stage study underway, amend your SAP. :-D

Note 1: The CI in the pooled analysis is not affected if compared to a model without ~~subject(sequence × stage)~~ sequence × stage. For Potvin’s Example 2 I got p ~~0.7689~~ 0.1539.*
Bonus question: What if p <0.05?

Note 2: Phoenix/WinNonlin-users: Such a setup was already needed for an ‘all fixed-effects’ model.
Model Specification > Fixed Effects > Stage+Sequence+Sequence*Stage+Subject(Sequence*Stage)+Period(Stage)+Treatment

Typos corrected. THX to Detlew – see this post.

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
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ElMaestro
★★★

Denmark,
2013-03-08 16:12
(4835 d 20:20 ago)

@ Helmut
Posting: # 10175
Views: 11,142

EMA: Q&A update (Two-Stage designs)

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Hi Helmut,

❝ yesterday EMA’s PK working party published Rev. 7 of the Q&A document. According to the new #14:

The expected analysis for the combined data in a two-stage design is ANOVA with terms for stage, sequence, sequence × stage, subject(sequence × stage), period(stage), formulation.
❝
This model can be fitted provided that in each stage, there is at least one subject randomised to each sequence. This does not supersede the requirement for at least 12 subjects overall.
❝
A term for a formulation × stage interaction should not be fitted.

If you have a Two-Stage study underway, amend your SAP. :-D

Thanks for posting this.
Given that they request those sequence-related fixed factors it sounds to me like they implicitly are assuming that all two-stage studies are crossovers. While it is of course true that Potvin & Montague so far only studied those cases I can't believe the intention is to eliminate an option for parallel 2-stage studies. But what do I know?!?

—
Pass or fail!
ElMaestro

d_labes
★★★

Berlin, Germany,
2013-03-08 16:40
(4835 d 19:52 ago)

@ Helmut
Posting: # 10176
Views: 11,447

EMA: Q&A update (Two-Stage designs)

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Dear Helmut!

❝ yesterday EMA’s PK working party published Rev. 7 of the Q&A document. According to the new #14:

The expected analysis for the combined data in a two-stage design is ANOVA with terms for stage¹, sequence², sequence × stage³, subject(sequence × stage)⁴, period(stage)⁵, formulation⁶.
❝
This model can be fitted provided that in each stage, there is at least one subject randomised to each sequence. This does not supersede the requirement for at least 12 subjects overall.
❝
A term for a formulation × stage interaction should not be fitted.

If you have a Two-Stage study underway, amend your SAP. :-D

Numbering by me

First: Thanx for this valuable information! Indeed I have a 2-stage study under way.

Second: From Potvin et.al.:
"If the individual ln-transformed data are to be used in the analysis instead of the differences, then the error term derived from the GLM ANOVA model including
sequence², stage¹, period(stage)⁵, treatment⁶, subject(sequence × stage)⁴
will give the appropriate s2 term."
Thus the emphasis should be at sequence × stage :-P

❝ Note 1: The CI in the pooled analysis is not affected if compared to a model without subject(sequence × stage)...

Typo? If you fit without subject(sequence × stage) you would omit totally the subjects effects! This will heavily affect the CI I guess.
If you meant sequence × stage you are totally right. Since stage and sequence are between-subjects effects the additional inclusion of the sequence × stage interaction is only a further breakdown of the subjects effect. The question is why the mighty oracle want us to include such a term :confused:

.

BTW: Where did your p-value came from?

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2013-03-08 17:43
(4835 d 18:49 ago)

@ d_labes
Posting: # 10177
Views: 11,018

Almighty miraculous oracle

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Dear Detlew!

❝ First: Thanx for this valuable information! Indeed I have a 2-stage study under way.

You are not alone. ;-)

❝ Second: From Potvin et.al.:

❝ "If the individual ln-transformed data are to be used in the analysis instead of the differences, then the error term derived from the GLM ANOVA model including

❝ sequence², stage¹, period(stage)⁵, treatment⁶, subject(sequence × stage)⁴

❝ will give the appropriate s2 term."

❝ Thus the emphasis should be at sequence × stage :-P .

Yep. Doesn’t the order of factors influence the analysis in SAS as well (aka type III limbo)?

❝ ❝ Note 1: The CI in the pooled analysis is not affected if compared to a model without subject(sequence × stage)...

❝

❝ Typo? If you fit without subject(sequence × stage) you would omit totally the subjects effects! This will heavily affect the CI I guess.

❝ If you meant sequence × stage you are totally right.

Sure – bloody typo; corrected.

❝ Since stage and sequence are between-subjects effects the additional inclusion of the sequence × stage interaction is only a further breakdown of the subjects effect. The question is why the mighty oracle want us to include such a term :confused: .

Maybe Señor García-Arieta’s footprints? See the quoted (d) in this post.

❝ BTW: Where did your p-value came from?

Grml; duno…

Model Specification and User Settings

       Dependent variable : Response

                Transform : LN

              Fixed terms : int+Stage+Sequence+Sequence*Stage+Subject(Sequence*Stage)+

                            Period(Stage)+Treatment



Class variables and their levels

                  Subject : 1  2  3  4  5  6  7  8  9  10

                            11 12 13 14 15 16 17 18 19 20

                    Stage : 1  2

                 Sequence : RT TR

                   Period : 1  2

                Treatment : R  T



Diagnostics

       Total Observations :           40

        Observations Used :           40

 Obs. Missing Model Terms :            0

              Residual SS :     0.780224

              Residual df :           17

        Residual Variance :    0.0458956



Partial Tests of Model Effects

            Hypothesis  Numer_DF  Denom_DF      F_stat     P_value

----------------------------------------------------------------------

                   int         1        17   1088.59       0

                 Stage         1        17     17.3504     0.000648307

              Sequence         1        17      0.369037   0.551559

        Sequence*Stage         1        17      2.22777    0.153875

Sequence*Stage*Subject        16        17     24.9524     1.04115E-08

          Stage*Period         2        17      0.967076   0.400153

             Treatment         1        17      0.0454252  0.833759

Now what? Will the mighty oracle not accept pooling since stages are highly significant different? Would not be the first time ignoring Potvin et al.

Does not require poolability criteria (or at least should know whether results from both stages are poolable before sample analysis, i.e. base poolability on study conduct such as subject demographics, temporal considerations, use of same protocol, use of same site, etc., rather than a statistical test of poolability).

(my emphases)

P.S.: In the mixed-effects model I used in my previous studies [fixed: Sequence, Stage, Period(Stage), Treatment and random: Subject(Sequence × Stage)] p for stage is 0.403286…

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
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d_labes
★★★

Berlin, Germany,
2013-03-12 13:12
(4831 d 23:20 ago)

@ Helmut
Posting: # 10190
Views: 10,770

Miraculouser oracle

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Dear Helmut, dear All!

❝ ...

❝ Partial Tests of Model Effects

❝ Hypothesis Numer_DF Denom_DF F_stat P_value

❝ ----------------------------------------------------------------------

❝ int 1 17 1088.59 0

❝ Stage 1 17 17.3504 0.000648307

❝ Sequence 1 17 0.369037 0.551559

❝ Sequence*Stage 1 17 2.22777 0.153875

❝ Sequence*Stage*Subject 16 17 24.9524 1.04115E-08

❝ Stage*Period 2 17 0.967076 0.400153

❝ Treatment 1 17 0.0454252 0.833759

Seems to me like all the F-tests are done with MSE as denominator.
My beasty SAS gives almost the same:

Source                  DF     Type III SS     Mean Square    F Value    Pr > F



treatment                1      0.00208481      0.00208481       0.05    0.8338

period(stage)            2      0.08876896      0.04438448       0.97    0.4002

sequence                 1      0.01436992      0.01436992       0.31    0.5831

stage                    1      0.79630537      0.79630537      17.35    0.0006

sequence*stage           1      0.10224489      0.10224489       2.23    0.1539

subjec(sequen*stage)    16     18.32323177      1.14520199      24.95    <.0001

The question is: Are these tests appropriate?

Like the test for the sequence effect in the classical 2x2x2 crossover I would suppose to test stage and sequence as between-subject effects and also the new introduced interaction sequence*stage with subject(stage*sequence) as denominator. But I'm not quite sure.

The as bogus suspected RANDOM statement in Proc GLM may assist is in getting the 'right' F-tests. But as always when the Almighty miraculous oracle prophesies difficulties are just around the corner (at least for statistical sermons).

Formulating RANDOM stage sequence subject(sequence*stage) / test;
gives me the anticipated denominator

Source                    DF     Type III SS     Mean Square    F Value    Pr > F

treatment                  1        0.002085        0.002085       0.05    0.8338

period(stage)              2        0.088769        0.044384       0.97    0.4002

subjec(sequen*stage)      16       18.323232        1.145202      24.95    <.0001

Error: MS(Error)          17        0.780224        0.045896





Source                    DF     Type III SS     Mean Square    F Value    Pr > F

  sequence                 1        0.014370        0.014370       0.01    0.9122

* stage                    1        0.796305        0.796305       0.70    0.4166

  sequence*stage           1        0.102245        0.102245       0.09    0.7689

Error                     16       18.323232        1.145202

Error: MS(subjec(sequen*stage))

* This test assumes one or more other fixed effects are zero.

But! The F-test for stage is only valid if sequence*stage is assumed zero.

Formulating RANDOM stage sequence sequence*stage subject(sequence*stage) / test;
gives:

Source                    DF     Type III SS     Mean Square    F Value    Pr > F

treatment                  1        0.002085        0.002085       0.05    0.8338

period(stage)              2        0.088769        0.044384       0.97    0.4002

subjec(sequen*stage)      16       18.323232        1.145202      24.95    <.0001

Error: MS(Error)          17        0.780224        0.045896



Source                    DF     Type III SS     Mean Square    F Value    Pr > F

sequence                   1        0.014370        0.014370       0.16    0.7743

Error                 0.7141        0.062612        0.087676

Error: 1.014*MS(sequence*stage) - 0.014*MS(subjec(sequen*stage)) - 22E-16*MS(Error)



Source                    DF     Type III SS     Mean Square    F Value    Pr > F

stage                      1        0.796305        0.796305       7.79    0.2190

Error                      1        0.102245        0.102245

Error: MS(sequence*stage)



Source                    DF     Type III SS     Mean Square    F Value    Pr > F

sequence*stage             1        0.102245        0.102245       0.09    0.7689

Error                     16       18.323232        1.145202

Error: MS(subjec(sequen*stage))

No warning, but ... Rather wild denominators in the F-tests for sequence and stage!
Especially unique for sequence with non-interger df's :surprised:

.

Any opinion out there?

BTW: The whole mess is "für die Katz" (strictly for the birds). The confidence intervals are not affected at all.

with sequence*stage 101.454363  (88.445194 ... 116.377016)

without             101.454363  (88.445194 ... 116.377016)

—
Regards,

Detlew