Bioequivalence and Bioavailability Forum

Dear Essar,

in order to continue with the nomenclature generally used in BE studies I have re-aranged your table. Periods (P1-P3) in columns, and Sequences/Groups (S1-S3) in rows:
┌────┬────────────┐
│    │ P1  P2  P3 │
├────┼────────────┤
│ S1 │ T1  T2  R  │
│ S2 │ T2  R   T1 │
│ S3 │ R   T1  T2 │
└────┴────────────┘

❝ Now, please let me know whether my design is right? Is it approprirate to name this study as "3-treatment, 3-period, 3-sequence crossover Bioequivalence study"?

Question #1: no
Question #2: yes

❝ Can there be other designs to compare T1 and T2 with R in a single BE study?

Yes, explanations following:
Your design is not balanced in respect to all effects in the model, in other words, 3 combinations of treatments are missing. The chance of regulatory acceptance of a 3×3 is close to zero.
The plainest design you may apply is a Williams' design (3-treatment, 3-period, 6-sequence):
┌────┬────────────┐
│    │ P1  P2  P3 │
├────┼────────────┤
│ S1 │ T1  T2  R  │
│ S2 │ T2  R   T1 │
│ S3 │ R   T1  T2 │
│ S4 │ T1  R   T2 │
│ S5 │ T2  T1  R  │
│ S6 │ R   T2  T1 │
└────┴────────────┘
If you want to extract paired comparisons (e.g., for the nonparametric method) you will fail with your design (3×3), but succeed with the given one (6×3).

Since we are leaving the novice's level now, I would suggest you some further reading (not cheap, but every cent worth):

• B Jones and MG Kenward
  Design and Analysis of Cross-Over Trials
  Chapman & Hall, Boca Raton, (2^nd Ed 2003)
  
• S-C Chow and J-p Liu
  Design and Analysis of Bioavailability and Bioequivalence Studies
  Marcel Dekker, New York, (2^nd Ed 2000)

❝ Also, please let me know how you calculate the no of subjects required for this type of a study.

Have a look at

RP Qu
Sample Size and Power Calculation for High Order Crossover Design
Bio/Pharma Quarterly 9(1), 9-14 (March 2003)
which is available online (277kB PDF).

Good Luck!