Bioequivalence and Bioavailability Forum

Hi Kumarnaidu,

❝ For the product like Valsartan + Amlodipine or Telmisartan + Amlodipine, is it possible to plan a analysis with 3 way design for Valsartan/Telmisartan and 2 way design for Amlodipine in same study.

❝ For e.g. if we plan a 3 way Partial replicate in 48 subjects (RTR/TRR/RRT).

I guess you are aiming at reference-scaling (Reference-scaled Average Bioequivalence [RSABE] or Average Bioequivalence with Expanding Limits [ABEL]) because valsartan and telmisartan are highly variable. In a FDC with telmisartan, S-am­lo­dipine was reported to be highly variable as well.¹ Since this was a 4-period full replicate design with the FDC vs. the monos, unexpectedly the high variability was only observed in the FDC (the mono showed only CV_w≈10%).

❝ For Val/Telm, sample size will be 48 (All three period) …

Based on what (CV_wR, T/R-ratio, target power)? Method of scaling (FDA: RSABE, EMA and all others: ABEL)? Note that for the EMA you can expand the limits only for C_max. Hence, the sample size would be driven by the variability of AUC.

❝ … and for Amlodipine, sample size will be 32 (First two period and with sequence RTR and TRR only).

Given what you wrote above, I can’t follow you. Which CV_w and T/R-ratio did you assume, which power were you targeting, which drop­out-rate did you anticipate?

❝ Is there any statistical issues with such design?

Statistically, none. From a regulatory perspective, indeed.

❝ I know the ideal way is to analyse both Val and Aml in same way.

Exactly. As Divyen pointed out, it is ethically not acceptable to dose subjects and not use their data. Hence, use all data of both drugs in all periods in the statistical analyses.

There is a massive problem with the FDA’s RSABE in the partial replicate design if \(\small{s_\text{wR}<0.294}\) because the study has to be assessed for – con­ventional, unscaled – ABE.

• The model with the the FDA’s covariance structure in the guidances is over-specified.² Therefore, the optimizer may fail to converge (independent from the software) and you get no (‼) result at all.
  Remedy in SAS-lingo: Instead of FA0(2) specify FA0(1), CSH, or CS.³ Since that is not given in the guidances, state it unambigously in the SAP or – likely better – initiate a controlled correspondence with the OGD.
  
• An alternative is one of the 3-period 2-sequence full replicate designs (TRT|RTR or TRR|RTT). Then you can keep the FDA’s covariance structure and there will be no issues with convergence.⁴

NB, there are no problems with the EMA’s ABEL (evaluated by an ANOVA with all effects fixed and assuming \(\small{s_\text{wR}^2\equiv s_\text{wT}^2}\)).

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1. Kang WY, Seong SJ, Ohk B, Gwon M-R, Kim BK, La S, Kim H-J, Cho S, Yoon Y-R, Yang DH, Lee HW. Pharmacokinetic and bioequivalence study of a telmisartan/S-amlodipine fixed-dose combination (CKD-828) formulation and coadministered telmisartan and S-amlodipine in healthy subjects. Drug Des Devel Ther. 2018; 12: 545–53. doi:10.2147/DDDT.S156492. Free Full text.
   
2. The model tries to estimate the within-subject variances of both reference and test (\(\small{\widehat{\sigma}_\text{wR}^2}\), \(\small{\widehat{\sigma}_\text{wT}^2}\)). Where \(\small{\widehat{\sigma}_\text{wR}^2}\) can be estimated in any reference-replicated design, \(\small{\widehat{\sigma}_\text{wT}^2}\) cannot be estimated in a partial replicate design since the test is only administered once. Even if you are lucky and the model converges, \(\small{\widehat{\sigma}_\text{wT}^2}\) will be plain nonsense. For details see this article.
   
3. FA0(2) = No Diagonal Factor Analytic with two factors, FA0(1) = No Diagonal Factor Analytic with one factor, CSH = He­te­ro­genous Com­pound-Symmetry, CS = Com­pound-Symmetry.
   
4. Since both treatments are replicated, the within-subject variances of reference \(\small{\widehat{\sigma}_\text{wR}^2}\) and test \(\small{\widehat{\sigma}_\text{wT}^2}\) can be estimated.

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PS: Why is the bloody partial replicate design still so popular? Beyond me.