Bioequivalence and Bioavailability Forum • CHMP PKWP Doc: recode of Period required?

randombadger
☆

UK,
2011-11-28 19:45
(5326 d 22:20 ago)

Posting: # 7742
Views: 6,519

CHMP PKWP Doc: recode of Period required? [Regulatives / Guidelines]

Hi,

For higher order studies (i.e. 3x3, 4x4 etc) I understand that the PKWP want us to make comparisons using a data subset (e.g. T2 vs T1) excluding the data from the treatments that are not relevant for the comparison in question (e.g. T1).

So, the analysis done is basically a 2-way crossover study for each treatment comparison.

However, how are the the order of treatments incorporated into the statistical model? Are the actual periods ignored hence recoded e.g. for the comparison between R and T2 for a subject assigned to R|T1|T2 treatment sequence, is Period 1 data regarded as “period 1” data and Period 3 data regarded as “period 2” data in the analysis or can the original Period be used in the model?

Thanks!

ElMaestro
★★★

Denmark,
2011-11-28 20:15
(5326 d 21:50 ago)

@ randombadger
Posting: # 7743
Views: 5,696

CHMP PKWP Doc: recode of Period required?

Post reply

Hi RB,

❝ However, how are the the order of treatments incorporated into the statistical model? Are the actual periods ignored hence recoded e.g. for the comparison between R and T2 for a subject assigned to R|T1|T2 treatment sequence, is Period 1 data regarded as “period 1” data and Period 3 data regarded as “period 2” data in the analysis or can the original Period be used in the model?

My personal, unqualified, subjective, random and wrong view is that data need to be recoded to a 2,2,2-BE design. Any sequence is where T was before R is coded TR, else RT (for the relevant treatment pair). Period levels accordingly boiled down to 1 or 2. I am aware that I may be starting a war now. I am not in any way advocating that this 'makes sense' in every way, but I do believe it does in one way.

—
Pass or fail!
ElMaestro

Helmut
★★★

Vienna, Austria,
2011-11-29 03:15
(5326 d 14:49 ago)

@ ElMaestro
Posting: # 7745
Views: 5,699

Potlatch

Post reply

Ahoy!

Rough seas ahead, matey? Read this post first.

❝ […] I am aware that I may be starting a war now.

As I learned from Martin you can only do statistics if you understand the data-generating process. Have we administered three formulations – yes. In how many periods – three. You get the point?

I did some recoding in the past – but only acting in self-defense since I had no confidence-interval based nonparametric method for t_max in my toolbox. Currently my rank order is:

Full model: Code everything as it happened in the study. Yes, three treatments in three periods, six sequences. Full stop.
EMA’s: Bad style. Jury out, verdict pending.
Recoding: The wonderful thing with the cross-over is that we can forget period-effects (meaning out); what if P1≠P2≠P3 and some responses are shifted from one period to another? Pray for balance!

Tried recoding; too late to send the file to my QAU. Errors possible as usual.

T1 only
T1/R: 113.31% [101.57% – 126.41%] CI width 24.84% CV: 14.86% GLSM: 6.08 (R), 6.89 (T1)
T2 only
T2/R: 104.38% [ 89.83% – 121.28%] CI width 31.45% CV: 20.49% GLSM: 6.08 (R), 6.35 (T2)

Results for T1 similar to the full model and for T2 to EMA’s. Now what? :smoke:

Overview

CIs
Full model EMA’s Recoded 2×2 T1/R 101.35% – 126.67% 103.44% – 124.12% 101.57% – 126.41% T2/R 93.37% – 116.69% 90.51% – 120.37% 89.83% – 121.28%
CVs
Full model EMA’s Recoded 2×2 T1/R 15.93% 12.23% 14.86% T2/R —"— 19.23% 20.49%
GLSMs identical; might not be the case if imbalanced! Detlew assumed that already a while ago.

Dropped subject 12:

CIs
Full model EMA’s Recoded 2×2 T1/R 97.76% – 122.45% 101.22% – 119.59% 99.14% – 120.26% T2/R 90.43% – 113.27% 87.31% – 115.02% 86.63% – 115.34%
CVs
Full model EMA’s Recoded 2×2 T1/R 15.25 10.44% 12.35% T2/R —"— 17.35% 18.38%
GLSMs
Full model EMA’s Recoded 2×2 R 6.20 NA NA T1 6.78 NA NA T2 6.27 NA NA R 6.19 6.28 T1 6.81 6.85 R 6.21 6.23 T2 6.22 6.22

As expected we get different GLSMs for the separated evaluations in EMA’s method and after recoding. But since the data are not presented… :angry:

Ignorance is bliss.

Smooth sailin’, an’ fair winds t’ ye! :pirate:

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Helmut
★★★

Vienna, Austria,
2011-11-28 21:41
(5326 d 20:24 ago)

@ randombadger
Posting: # 7744
Views: 6,305

No recoding; but…

Post reply

Hi randombadger!

❝ For higher order studies (i.e. 3x3, 4x4 etc) I understand that the PKWP want us to make comparisons using a data subset (e.g. T2 vs T1) excluding the data from the treatments that are not relevant for the comparison in question (e.g. T1).

Reading in between the lines it’s clear that EMA likes Williams’ designs (e.g., 6×3) – not Latin squares (3×3). See the GL p22: “[…] (3 treatment, 3 period, 6 sequence design).”

No recoding should be done. See the complied Q&A-document from last year’s joint EGA/EMA workshop:

Q In the case of a 3-arm study with two reference products what does “excluding the data” mean?
If the data from one (or more) treatment arm(s) is (are) removed from ANOVA (eg, removing the data for a USA comparator product) and thus effectively considering it as a two arm study then the true sequences and periods are modified.
Answer
In studies with more than two treatment arms (eg, a three period study including two references, one from the EU and another from the USA; or a four period study including test and reference in fed and fasted conditions; or 2 test products and one reference provided one of the test products is the final ‘to be marketed’ formulation), the analysis for each comparison should be conducted excluding the data from the treatments that are not relevant to the comparison in question. However, the treatment, groups, sequences and periods should have their original values maintained in the analysis, and not have the values modified. For example an observation made in period 3 should still be coded as period 3, not have the period changed to “2” because the results for that subject in one of the earlier periods has now be removed.

David Brown (MHRA) gave the following example:

If we exclude the (irrelevant) data from the US test product,
we get this data-set
SUB SEQ PRD FRM 1 1 1 T 1 1 2 A 2 3 1 A 2 3 2 T 3 6 2 A 3 6 3 T 4 2 1 T etc.
which can be analysed as usual in PROC GLM with terms for
sequence, subject (sequence), period and formulation. (© Crown copyright 2005)

❝ So, the analysis done is basically a 2-way crossover study for each treatment comparison.

Not really. I would call it three-way with missing observations. ;-)

Not sure whether this approach (essentially ignoring part of the story) is valid. The jury is out; no verdict^* yet (search the forum).

Let’s look at an example (Chow & Liu, Table 10.3.13; 6×3 Williams’ design, analysis on log-data):


Sequence Subject Period  AUC Formulation

RT2T1       1       1   5.68     R

RT2T1       1       2   4.21     T2

RT2T1       1       3   6.83     T1

RT2T1       2       1   3.60     R

RT2T1       2       2   5.01     T2

RT2T1       2       3   5.78     T1

T1RT2       3       1   3.55     T1

T1RT2       3       2   5.07     R

T1RT2       3       3   4.49     T2

T1RT2       4       1   7.31     T1

T1RT2       4       2   7.42     R

T1RT2       4       3   7.86     T2

T2T1R       5       1   6.59     T2

T2T1R       5       2   7.72     T1

T2T1R       5       3   7.26     R

T2T1R       6       1   9.68     T2

T2T1R       6       2   8.91     T1

T2T1R       6       3   9.04     R

T1T2R       7       1   9.68     T1

T1T2R       7       2   8.91     T2

T1T2R       7       3   9.04     R

T1T2R       8       1   4.63     T1

T1T2R       8       2   7.23     T2

T1T2R       8       3   5.06     R

T2RT1       9       1   7.25     T2

T2RT1       9       2   7.88     R

T2RT1       9       3   9.02     T1

T2RT1      10       1   5.00     T2

T2RT1      10       2   7.84     R

T2RT1      10       3   7.79     T1

RT1T2      11       1   4.63     R

RT1T2      11       2   6.77     T1

RT1T2      11       3   5.72     T2

RT1T2      12       1   3.87     R

RT1T2      12       2   7.62     T1

RT1T2      12       3   6.74     T2

Complete model (all effects fixed: Sequence+Subject(Sequence)+Period+Formulation)
T1/R: 113.31% [101.35% – 126.67%] CI width 25.32% T2/R: 104.38% [ 93.37% – 116.69%] CI width 23.32% CV: 15.93% GLSM: 6.08 (R), 6.89 (T1), 6.35 (T2)
Formulation T2 or T1 excluded
T1/R: 113.31% [103.44% – 124.12%] CI width 20.68% CV: 12.23% GLSM: 6.08 (R), 6.89 (T1) T2/R: 104.38% [ 90.51% – 120.37%] CI width 29.87% CV: 19.23% GLSM: 6.08 (R), 6.35 (T2)

If I take the full model as the ‘Gold Standard’ results according to EMA’s method are liberal for T1 (passes, while BE in the full model fails) and conservative for T2.

That’s why I said »EMA is a serious risk to public health!« last year. Wasn’t diplomatic, I know.

^* Innocent = conservative, guilty = liberal.

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

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Science Quotes

d_labes
★★★

Berlin, Germany,
2011-11-29 11:49
(5326 d 06:16 ago)

@ Helmut
Posting: # 7746
Views: 5,688

No recoding; but…

Post reply

Dear Discu-Tanten!

Helmut: Two posts - excellent and comprehensive as always. Nearly nothing left to add.

But to me throw in my own two cents into the gladiator's arena:

I had the same preferences:

❝ 1. Full model: Code everything as it happened in the study. Yes, three treatments in three periods, six sequences. Full stop.

❝ 2. EMA’s: Bad style. Jury out, verdict pending.

❝ 3. Recoding: The wonderful thing with the cross-over is that we can forget period-effects; what if P1≠P2≠P3 and some responses are shifted from one period to another? Pray for balance!

To 1.: Intuitively this approach is for me the preferred, as said "Code everything as it happened". But of course it has pre-conditions. Not at least the variance homogeneity.

To 3.: IMHO especially the argument of period effects not considered adequate if recoding of the periods is done speaks against it.

To 2.: Regarding the evaluation pairwise (not considering the rest of the data) I'm meanwhile not totally convinced that this is bad style.

Having in mind Stephen Senn's basic estimator approach¹⁾:
Calculate the difference (of log-transformed metrics) you are interested in via intra-subject contrasts and analyse them as sequence group stratified mean (intercept of an ANOVA with sequence as effect) goes along the same line. Senn calls this approach "simple and fairly robust", don't know exactly whatever robust here means.

And having in mind some simulation results coming soon ;-)

¹⁾ Stephen Senn
Cross-over Trials in Clinical Research
Second edition, Chapter 5.4.1
John Wiley, Chichester 2002

—
Regards,

Detlew

ElMaestro
★★★

Denmark,
2011-11-29 12:39
(5326 d 05:26 ago)

@ d_labes
Posting: # 7747
Views: 5,714

No recoding; but…

Post reply

Dear d_labes,

❝ Having in mind Stephen Senn's basic estimator approach:

❝ Calculate the difference (of log-transformed metrics) you are interested in via intra-subject contrasts and analyse them as sequence group stratified mean (intercept of an ANOVA with sequence as effect) goes along the same line. Senn calls this approach "simple and fairly robust", don't know exactly whatever robust here means.

Was this said in specific reference to equivalence crossover trials? I ask because I mainly think of Senn as the God of superiority statistics, while at the same time I reckon that for equivalence stats certain aspects are sometimes completely contrary to superiority stats. A good example is ITT which is the conservative population for superiority while the conservative population for equivalence is PP. I thus wonder if this robustness, whatever it is, applies equally to superiority and equivalence?

—
Pass or fail!
ElMaestro

Helmut
★★★

Vienna, Austria,
2011-11-29 15:07
(5326 d 02:58 ago)

@ ElMaestro
Posting: # 7749
Views: 5,620

No recoding; but…

Post reply

Hi ElMaestro!

❝ ❝ […] Senn calls this approach "simple and fairly robust", don't know exactly whatever robust here means.

❝

❝ Was this said in specific reference to equivalence crossover trials?

Chapter 5.4.1 gives a method for obtaining the CI (+ an example).

❝ I thus wonder if this robustness, whatever it is, applies equally to superiority and equivalence?

No idea (gut feeling: doesn’t matter). Walnut-size brain, etc.

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Helmut
★★★

Vienna, Austria,
2011-11-29 14:57
(5326 d 03:07 ago)

@ d_labes
Posting: # 7748
Views: 5,670

No recoding; but…

Post reply

Dear Simul-Ants!

❝ To 1.: Intuitively this approach is for me the preferred, as said "Code everything as it happened". But of course it has pre-conditions. Not at least the variance homogeneity.

Right. Like in RT|TR and EMA’s crippled model for replicate designs. ;-)

❝ To 2.: Regarding the evaluation pairwise (not considering the rest of the data) I'm meanwhile not totally convinced that this is bad style.

Hhm.

❝ Having in mind Stephen Senn's basic estimator approach […]

The quote comes from the end of chapter 5.4.2 and continues with: “It is not optimal.” I have to read chapter 5 again. Asked him for help.

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes