Bioequivalence and Bioavailability Forum

graveendranath ☆ 2009-09-23 11:13 (6105 d 22:44 ago) Posting: # 4235 Views: 10,356	Balaam's design [General Statistics] Post reply
	Dear all, We are going to conduct one study using Balaam's design `Period ------------- Sequence 1 2 ------------------------- 1 T T 2 R R 3 R T 4 T R` Using these design, can we calculate Intra CV for Reference and Intra CV for Test separately? If yes plz tell me the ANOVA design. Edit: Category changed, reformatted using BBCode. [Helmut] — Rgds Raveendranath

Helmut
★★★

Vienna, Austria,
2009-09-23 14:47
(6105 d 19:10 ago)

@ graveendranath
Posting: # 4236
Views: 9,003

Balaam's design

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Dear Raveendranath!

❝ […] Balaam's design […] can we calculate Intra CV for Reference and Intra CV for Test separately?

Yes, because you have repeated administrations in the the first two sequences.

❝ If yes plz tell me the ANOVA design.

You gave the design already yourself. :confused:

I would guess that for FDA and EMEA applications you are on slippery ground (they expect 3- or 4-period replicate designs). On the other hand ANVISA states Balaam’s design in their guideline. Don’t ask me about sample size estimations – no idea…

For the evaluation see:

S-C Chow and J-p Liu
Design and Analysis of Bioavailability and Bioequivalence Studies
Marcel Dekker, New York, pp 257-266 (3^rd ed. 2008)

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

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d_labes
★★★

Berlin, Germany,
2009-09-24 18:13
(6104 d 15:44 ago)

@ Helmut
Posting: # 4244
Views: 9,158

Balaam's design, sample size

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Dear Helmut,

❝ [...] On the other hand ANVISA states Balaam's design in their guideline. Don't ask me about sample size calculations - no idea…

For the sample size calculation have a look into

K.-W. Chen, S.-C. Chow and G. Li
A Note on Sample Size Determination for Bioequivalence Studies with Higher-order Crossover Designs
J. Pharmacokinetics and Biopharmaceutics, Vol. 25, No. 6, p753-765 (1997)

It comes out that the sample size needed for the Balaam's design is approx. twice that of a common classical 2x2 cross-over.

—
Regards,

Detlew

graveendranath
☆

2009-09-25 14:23
(6103 d 19:34 ago)

@ d_labes
Posting: # 4250
Views: 8,703

Balaam's design

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Dear D.Labes,

Can you please explain the SAS procedure for ANOVA.

I tried with the following procedure.

proc glm data=one outstat=tanova;

class trt per seq sub;

model lncmax lnAUCt lnAUCi= seq sub(seq) per trt/ ss3 CLPARM ALPHA=0.1;

test h= seq e=sub(seq)/htype=3 etype=3; 

lsmeans trt /stderr pdiff out=lsmean;

run;

But I didn't get Intra CV for test & Reference separately.

Kindly suggest the correct procedure.

Edit: Reformatted using BBCode. [Helmut]

—
Rgds
Raveendranath

d_labes
★★★

Berlin, Germany,
2009-09-29 16:44
(6099 d 17:13 ago)

@ graveendranath
Posting: # 4268
Views: 8,732

Balaam's design, intra-subject variances

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Dear Raveendranath,

❝ I tried with the following procedure.

❝

❝ proc glm data=one outstat=tanova;

❝ class trt per seq sub;

❝ [...]

❝ run;

❝

❝ But I didn't get Intra CV for test & Reference separately.

Correct. There is no way to specify different residuals for groups within Proc GLM. This is because all estimates and tests rely not on such different variabilities but only on the pooled error MSE.

You have two options:

Use the sequence group TT and RR to calculate differences T-T or R-R within each subject of the corresponding sequence group, respectively. The variance of these differences have the expectation 2*sigma²_{within T} for the sequence group TT and 2*sigma²_{within R} for the sequence group RR. So you can estimate the intra-subject variance by simply calculating the sample variance of the appropriate differences. This method is sometimes called "Method of moments". To get rid of the factor 2 you can start the calculations by
(T1-T2)/sqrt(2) and (R1-R2)/sqrt(2).
Use Proc MIXED instead of Proc GLM. The code in Appendix E of the FDA guidance "Statistical approaches ..." works also for the Balaam design. But the standard estimation method for Proc MIXED is REML (resticted maximum likelihood est.) and is somewhat different to the least square estimation within Proc GLM. For balanced designs and no missing values the differences are only marginal.
Since the FDA model is in most cases somewhat over-specified you can consider the simpler model of the between subject variances with compound symmetry.
In this model the subject by treatment interaction is considered as zero.

BTW: My recommended code for Proc GLM is found here. :cool:

BTW2: What was the reason that you performed your study according to the Balaam design? Just to cite from the FDA guidance:
" ... For the majority of drug products, two-period replicated crossover designs such as the Balaam design (which uses the sequences TR, RT, TT, and RR) should be avoided ...".

—
Regards,

Detlew

graveendranath ☆ 2009-09-30 15:59 (6098 d 17:59 ago) @ d_labes Posting: # 4275 Views: 8,556	Balaam's design, intra-subject variances Post reply
	Dear d_labes, Thank you for your valuable information. — Rgds Raveendranath

Helmut
★★★

Vienna, Austria,
2009-09-25 17:44
(6103 d 16:13 ago)

@ d_labes
Posting: # 4251
Views: 8,792

Balaam's design, sample size

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Dear Detlew,

❝ ❝ Don't ask me about sample size calculations - no idea...

❝ For the sample size calculation have a look into

❝ K.-W. Chen, S.-C. Chow and G. Li (1997)

Oh, thanks for the refresher!

❝ It comes out that the sample size needed for the Balaam's design is approx. twice that of a common classical 2x2 cross-over.

Do I miss something here? :confused:

For delta -5% (PE 95%), power 80% for the conventional 2×2 design Diletti et al. (1991) give sample sizes of 7 (10% CV), 19 (20%), and 39 (30%), whereas for Balaam’s design* according to Table V of Chen et al. (p 761) sample sizes are given with 20 (CV 10%), 72 (20%), and 156 (30%).

Balaam LN. A Two-Period Design with t² Experimental Units. Biometrics 1968;24(1):61–73. doi:10.2307/2528460.

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

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d_labes ★★★ Berlin, Germany, 2009-09-28 13:58 (6100 d 19:59 ago) @ Helmut Posting: # 4258 Views: 8,641	Balaam's design, sample size doubled one more time Post reply
	Dear Helmut, uups, you have caught me red handed! My statement came from the factor 2 in the sample size formula on page 757, containing the number of subjects per sequence. But I forgot here we have four sequences compared to two of the classical 2x2 cross-over. Lesson learned: Think twice and check ones assumptions before touting it half-cooked to the audience. Sorry. — Regards, Detlew

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