Bioequivalence and Bioavailability Forum • ICH M13A complex study designs missing data and data excluded

kimhuang
☆

China,
2025-03-04 09:12
(30 d 02:06 ago)

Posting: # 24380
Views: 750

ICH M13A complex study designs missing data and data excluded [Regulatives / Guidelines]

ICH M13A Q&A 2.9: When is it appropriate to remove data from statistical analysis for BE assessment?

In a 2-way crossover design, if data from one period are excluded, the subject should not be included in the statistical analysis. In more complex study designs, removal of subject data from only one period may not result in the complete removal of the subject from the statistical analysis.

I have 2 questions:

1. For 4*4 William's design, if the subject only completes one period, should it be excluded from BE evaluations? How many periods must each subject complete to include the data for BE evaluating?

2. For PK parameter analysis, can at least one period data to be included in PK parameter analysis?

Edit: Please follow the Forum’s Policy. Q&A document linked. [Helmut]

Helmut
★★★

Vienna, Austria,
2025-03-04 10:24
(30 d 00:54 ago)

@ kimhuang
Posting: # 24381
Views: 650

ICH M13A: Two-at-a-Time

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Hi kimhuang,

❝ 1. For 4*4 William's design, if the subject only completes one period, should it be excluded from BE evaluations?

Yes – not informative in a fixed effect model.

❝ How many periods must each subject complete to include the data for BE evaluating?

Two relevant ones. ICH M13A recommends – without naming it as such – the ‘Two-at-a-Time’ approach in Section 2.2.3.1:

In studies with more than two treatment arms, e.g., a four-period study […], the analysis for each comparison should be conducted excluding the data from the treatment arms that are not relevant for the comparison in question.

In a 4-treatment Williams’ design you obtain Incomplete Block Designs (IBDs) for the pairwise comparisons.
As an example one of the six possible Williams’ designs (with the treatments \(\small{\text{A, B, C, D}}\)) gives for the comparisons \(\small{\text{A}}\,vs.\text{B}\) and \(\small{\text{C}}\,vs.\text{D}\) these IBDs (\(\small{\color{Red}\bullet}\) denotes excluded data):

\(\small{\begin{array}{c|cccc}
s/p & \text{I} & \text{II} & \text{III} & \text{IV}\\\hline
1 & \text{A} & \text{C} & \text{B} & \text{D}\\
2 & \text{B} & \text{A} & \text{D} & \text{C}\\
3 & \text{C} & \text{D} & \text{A} & \text{B}\\
4 & \text{D} & \text{B} & \text{C} & \text{A}\\
\end{array}}{\color{Blue}\mapsto}
\begin{array}{c|cccc}
s/p & \text{I} & \text{II} & \text{III} & \text{IV}\\\hline
1 & \text{A} & {\color{Red}\bullet} & \text{B} & {\color{Red}\bullet}\\
2 & \text{B} & \text{A} & {\color{Red}\bullet} & {\color{Red}\bullet}\\
3 & {\color{Red}\bullet} & {\color{Red}\bullet} & \text{A} & \text{B}\\
4 & {\color{Red}\bullet} & \text{B} & {\color{Red}\bullet} & \text{A}\\
\end{array}{\color{Blue}\wedge}\small{\begin{array}{c|cccc}
s/p & \text{I} & \text{II} & \text{III} & \text{IV}\\\hline
1 & {\color{Red}\bullet} & \text{C} & {\color{Red}\bullet} & \text{D}\\
2 & {\color{Red}\bullet} & {\color{Red}\bullet} & \text{D} & \text{C}\\
3 & \text{C} & \text{D} & {\color{Red}\bullet} & {\color{Red}\bullet}\\
4 & \text{D} & {\color{Red}\bullet} & \text{C} & {\color{Red}\bullet}\\
\end{array}}\)

In each of the two resulting IBDs you exclude subjects with incomplete data (only one treatment).
Say, one subject in sequence \(\small{\text{B A D C}}\) dropped out after the second period. Fine for \(\small{\text{A}}\,vs.\text{B}\), but the subject has to be excluded for \(\small{\text{C}}\,vs.\text{D}\) (no relevant data). Another subject in sequence \(\small{\text{D B C A}}\) dropped out after the third period. Keep for \(\small{\text{C}}\,vs.\text{D}\), but the subject has to be excluded for \(\small{\text{A}}\,vs.\text{B}\) (only data of \(\small{\text{B}}\)).

❝ 2. For PK parameter analysis, can at least one period data to be included in PK parameter analysis?

Not sure what you mean. Can you reword / elaborate?
In a mixed effects model you could include the data but the result will be very similar (often identical) to a fixed effects model of complete data only (ANOVA).

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Helmut Schütz

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kimhuang
☆

China,
2025-03-07 01:46
(27 d 09:31 ago)

@ Helmut
Posting: # 24382
Views: 496

ICH M13A: Two-at-a-Time

Post reply

Dear Helmut,

Thank you very much for your reply, ICH M13A has a very clear description, thank you very much for sharing the case of missing data processing for multiple treatment groups.

❝ ❝ 2. For PK parameter analysis, can at least one period data to be included in PK parameter analysis?

❝ Not sure what you mean. Can you reword / elaborate?

❝ In a mixed effects model you could include the data but the result will be very similar (often identical) to a fixed effects model of complete data only (ANOVA).

My so-called PK parameter analysis refers to the simple descriptive statistics of PK parameters (such as AUC, Cmax, Tmax, etc. for mean, standard deviation, median, minimum value, maximum value, etc.), which does not involve the BE evaluation between the two treatment, whether PK descriptive analysis set and BE evaluation set must be consistent?

BTW, in FDA draft guidance «Statistical Approaches to Establishing Bioequivalence Guidance for Industry» about handling missing data, it is described as "Statistical methods for handling missing data include complete case analysis, available case analysis, weighting methods, imputation, and model-based approaches... An available case analysis could be done using SAS PROC MIXED, which uses all observed data (e.g., in a two-way crossover study, uses all subjects with one or two complete periods of data)... Approaches for handling missing data and the statistical methods for the primary BE analysis (e.g., GLM vs. MIXED) should be pre-specified in the study protocol or SAP.".
Will FDA guidance be updated with the ICH M13A statistical perspective? Or will FDA accept the two pre-specified missing data handling methods?

Thank you very much!
Looking forward to your reply again.

Helmut
★★★

Vienna, Austria,
2025-03-07 09:45
(27 d 01:32 ago)

@ kimhuang
Posting: # 24383
Views: 481

ICH M13A: Descriptive statistics

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Hi kimhuang,

❝ My so-called PK parameter analysis refers to the simple descriptive statistics of PK parameters (such as AUC, Cmax, Tmax, etc. for mean, standard deviation, median, minimum value, maximum value, etc.), which does not involve the BE evaluation between the two treatment, whether PK descriptive analysis set and BE evaluation set must be consistent?

According to ICH M13A Section 2.2.3.2 you can use a model with all effects fixed of the per protocol data for assessing BE or a mixed effects model of all data (even if only one period). A mixed effects model (1) is preferred by the FDA, Health Canada, and China’s CDE, whereas a model with all effects fixed (2) of the per protocol data is preferred in all other jurisdictions. Theoretically both methods should be acceptable but I suggest not to lure assessors out of their comfort zone.
Therefore, the short answer to your question: Yes. Always give appropriate location and dispersion statistics reflecting the distributional properties, i.e., for log-transformed PK metrics the geometric mean and CV instead of the arithmetic mean…

Descriptive statistics of all data. Easy.
Descriptive statistics of all data and of the per protocol data (only complete ones).

State in the text that the point estimate of the treatment effect from the BE model will be close but not identical to the ratio of geometric means of treatments. In a mixed effects model it is based on Restricted Maximum Likelihood (REML). This statement avoids questions from assessors equipped with a pocket calculator. :-D

❝ BTW, in FDA draft guidance «Statistical Approaches to Establishing Bioequivalence Guidance for Industry»…

❝ Will FDA guidance be updated with the ICH M13A statistical perspective? Or will FDA accept the two pre-specified missing data handling methods?

I guess both but will prefer the latter. ICH M13A gives no details in Section 2.2.2.2, only:

Summary statistics to be reported include number of observations, geometric mean, coefficient of variation, median, arithmetic mean, standard deviation, minimum, and maximum.

—
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

kimhuang ☆ China, 2025-03-08 06:55 (26 d 04:23 ago) @ Helmut Posting: # 24385 Views: 441	ICH M13A: Descriptive statistics Post reply
	Dear Helmut: I understand, I will continue to pay attention to the requirements of different regulatory, thank you again!