Bioequivalence and Bioavailability Forum

Dear Helmut,

We too heard this type of design and we are also planning for the study as per the sponsor's request.

Here we got the type like Partial scaled average Replicate Bioequivalence study. In this study, we had two treatments forming 3 period 3 sequence design as follows:

1) T R R
2) R T R
3) R R T

Now my question is:

Then what is the difference between an Scaled average Replicate 3-way cross over study with the above stated one?

Please clarify me regarding this.

Thanks in advance.

Dear Helmut, dear all,

❝ I've heard this term for the first time at the recent Workshop at Ahmedabad. Yes, it's a 3-period replicate design.

Taking the Holy Bible^[1] of cross-over designs the best known 3-period replicate design has the name 3-period dual design with the two sequences

TRR
RTT

In the FDA Guidance an other 3-period replicate design is recommended:

TRT
RTR

But nowhere it is named "partial replicate design".

I have found this term in discussions (FDA and others) about scaled average bioequivalence. But here it denominates a one-sequence design with replication of the reference only, for instance

TRR.

To answer the original question:
If the design is a 3-period design with more then one sequence, to my knowledge the SAS code for the evaluation of average bioequivalence does not depend on the specific design used in replicate studies, provided you will go with restricted maximum likelihood estimation (Proc MIXED in "The power to know").

The code recommended in the FDA guidance was discussed already in breadth on this forum. See for instance this thread and others (use search!).
Let me give it here again for your convienience.

Proc MIXED data=YourData method=REML alpha=0.1;
  class treatment period sequence subject;

  model Y= treatment period sequence / ddfm=satterth;     
  random treatment /subject=subject type=FA0(2) G;
  repeated /group=treatment subject=subject type=simple;

  ODS output LSMeans=_LSMeans Diffs=_CI;

  lsmeans treatment/diff cl alpha=0.1;
run;

Y is the pharmacokinetic target (eventually log transformed f.i. for AUC, Cmax). The ODS output statement saves you the least square means and the 90% confidence intervals in SAS datasets for further processing, f.i. to back transform them into the original scale if your target was log-transformed.
Be aware that SAS always gives you the difference (and 90% confidence interval) in least square means in lexicographic order, namely R-T if you code your treatments as R(eference) and T(est).
So do not forget to change the sign in subsequent processing!

But there are variants of this code (covariance structure other than FA0(2), other ddfm=denominator degrees of freedom) and there are complete other models to choose from!
See for instance ^[2] and ^[3].

If it is an ominous one-sequence design I think we have no sequence and period effects in the model.?

1. B Jones and MG Kenward
   Design and Analysis of Cross-over Trials
   Chapman & Hall/CRC, Boca Raton, Chapter 4 (2^nd ed. 2003)
   
2. Patterson and Jones
   Replicate Designs and Average, Individual, and Population Bioequivalence
   GSK BDS Technical Report 2002 – 01 (part I)
   GSK BDS Technical Report 2002 – 05 (part II)
   
3. S.A. Willavize and E.A. Morgenthin
   Comparison of models for average bioequivalence in replicate crossover designs
   Pharmaceut. Stat. Vol.5 (3), p. 201 - 211 (2008) published online 24 May 2006

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Edit: Updated URLs. [Helmut]