Bioequivalence and Bioavailability Forum

Dear all,

I had a closer look into

García-Arieta A, Morales-Alcelay S, Herranz M, de la Torre-Alvarado JM, Blázquez-Pérez A, Suá­rez-Gea M^aL, Álvarez C. Investigation on the need of multiple dose bioequivalence studies for pro­longed-release generic products. Int J Pharm. 2012;423(2):321–5. doi:10.1016/j.ijpharm.2011.11.022.

The authors reviewed all studies of prolonged release products submitted to the Spanish Agency since 2000. In Table 3 they reported the outcome (single dose and multiple dose) of six cases where the MD study failed on C_min,ss.¹ Values are given for C_τ (SD) and C_min,ss (MD).

Case   design     n   CV%     PE        90% CI       Conclusion   BE?  SD/MD agrees?
  6  SD  fasted  55  33.05  145.57  131.21  161.50  inequivalent   no      yes      
     MD  fasted  33  60.13  146.30  125.48  170.59  inequivalent   no               
  7  SD  fasted  34  47.48  125.15  103.99  150.62  inconclusive   no      yes      
     MD  fasted  34  38.11   83.86   72.09   97.56  inconclusive   no               
  8  SD  fasted  35  45.50  119.37  100.15  142.27  inconclusive   no      yes      
     MD  fasted  42  27.84  120.32  108.83  133.03  inconclusive   no               
  9  SD  fed     24  49.57   89.31   70.79  112.67  inconclusive   no      yes      
     MD  fed     24  54.32   80.38   62.47  103.42  inconclusive   no               
 10  SD  fasted  28  50.33  112.28   90.40  139.41  inconclusive   no      yes      
     MD  fasted  59  35.32  119.19  107.25  132.46  inconclusive   no               
 11  SD  fed     23  23.96   92.08   81.67  103.82  equivalent    yes       no      
     MD  fed     28  38.49   84.43   71.27  100.02  inconclusive   no               

Interesting that in case 6 (MD fasted) the sample size does not agree with the overview given in Table 1 (33 vs. 35). Is this a typo or why were two subjects in this study dropped from the com­parison? I recalculated the CV from the reported CI & sample size of all studies. One discrepancy is evident: Case 6, MD (reported 60.13%, calculated 38.05%).²

I am not a friend of post-hoc power, but evidently none [sic] of the studies was sufficiently powered (\(\tilde{x}\) 11.84%, quartiles: 3.25–13.35%) to demonstrate BE of minimum con­cen­tra­tions – not unexpected, since at the time of submission C_min was not a strict requirement. Even if designed for an expected ratio of 95%, only three of the studies would have a power of ≥80%. In five of six cases C_τ (SD) correctly predicted the result of C_min,ss (MD). In case 11 variability after MD in­creased substantially (from SD 24% to 38%). We cannot conclude the product is bio­inequivalent in steady state; it would only need an extremely large sample size of 260 subjects to demonstrate BE in a 2×2 cross-over (or 78 in a 4-period full replicate with reference-scaling). In other words the failed prediction of BE from SD might be a false positive as well.
Although in case 7 both SD and MD failed, the deviation of the ratio from 100% reversed (SD 125%, MD 84%). Would be interesting which type of formulation this one was. Never seen anything like this in 30+ years. Or a coding error?³

The authors concluded that C_τ (SD) is a poor predictor of C_min,ss (MD):

[…] in […] six cases […] the multiple dose study was the only design [sic] able to detect the differences and, therefore, it was essential when comparing the in vivo performance of prolonged release products.
Regarding the predictive value of C_τ, one case in Table 3 shows that it is predictive of the bioequivalence failure of C_min,ss, but in the other five cases, the results are not predictive or as sensitive as C_max,ss or C_min,ss.

On the contrary, I would say all studies – except case 11 – failing on C_τ (SD) failed on C_min,ss (MD) as well. The re­main­ing case was extremely underpowered. Actually, the authors confirmed (‼) in real examples that C_τ is indeed a reliable predictor of multiple dose performance of prolonged release formulations. It might not have been the authors’ intention, but in fact, these findings do not refute but rather support the work by Pai­xão et al.⁴ I consider it bad science if conclusions contradict the data.
IMHO, a clear case for commenting lines 612–615 of the draft guideline.

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1. Would have been nice to know how many studies passed. Without this number the relevance of the authors’ findings cannot be set into perspective, i.e., estimate the false positive rate.
   
2. library(PowerTOST)
cat(sprintf("%.2f%%", 100*CI2CV(lower=1.2548, upper=1.7059, n=33)), "\n")
   
3. Edit March 2018: Acc. to an e-mail exchange with Alfredo: No.
   
4. Paixão P, Gouveia LF, Morais JAG. An alternative single dose parameter to avoid the need for steady-state studies on oral extended-release drug products. Eur J Pharmaceut Biopharmaceut. 2012;80(2):410–7. doi:10.1016/j.ejpb.2011.11.001.