Bioequivalence and Bioavailability Forum

Salam Mahmoud,

❝ Please, advise on sample size estimation and setting of BE limits in the following situations where ISV for Cmax and AUC are far apart.

You have to demonstrate BE for both. Since in your example C_max seems to be highly variable I assumed a T/R-ratio of 0.9 (and not the observed despite that it is close to 1) and the same for AUC. Target power 80%.
Two options for the EMA:

1. Reference-scaling acceptable (widening of the limits for C_max clinically justifiable), RTRT|TRTR design.
   
       Design method metric   GMR    CV     LL     UL  n  power  GMRlo
 RTRT|TRTR   ABEL   Cmax 0.900 0.336 0.7799 1.2822 34 0.8040   <NA>
 RTRT|TRTR    ABE    AUC 0.900 0.202 0.8000 1.2500 34 0.9613 0.8717

Regulator: EMA (ABEL applicable if CVwR of Cmax >0.3).
PK metric ruling the sample size: Cmax
Sample size: 34 (ABEL, power: 0.8040)
Power of AUC (ABE): 0.9613
Lowest GMR of AUC which will give power 0.8: 0.8717
Total number of treatments in study: 136
   
   
2. Reference-scaling not acceptable (conventional ABE)
   
   
   1. RTRT|TRTR design.
      
          Design method metric   GMR    CV     LL     UL  n  power  GMRlo
 RTRT|TRTR    ABE   Cmax 0.900 0.336 0.8000 1.2500 50 0.8132   <NA>
 RTRT|TRTR    ABE    AUC 0.900 0.202 0.8000 1.2500 50 0.9938 0.8586

PK metric ruling the sample size: Cmax
Sample size: 50 (ABE, power: 0.8132)
Power of AUC (ABE): 0.9938
Lowest GMR of AUC which will give power 0.8: 0.8586
Total number of treatments in study: 200
      
      
   2. TR|TR design.
      
      Design method metric   GMR    CV     LL     UL  n  power  GMRlo
  RT|TR    ABE   Cmax 0.900 0.336 0.8000 1.2500 98 0.8046   <NA>
  RT|TR    ABE    AUC 0.900 0.202 0.8000 1.2500 98 0.9928 0.8593

PK metric ruling the sample size: Cmax
Sample size: 98 (ABE, power: 0.8046)
Power of AUC (ABE): 0.9928
Lowest GMR of AUC which will give power 0.8: 0.8593
Total number of treatments in study: 196
      

For the FDA you could try reference-scaling (no justification needed, applicability depends on s_wR). RTRT|TRTR design.

    Design method metric   GMR    CV     LL     UL  n  power  GMRlo
 RTRT|TRTR  RSABE   Cmax 0.900 0.336 0.7468 1.3390 28 0.8064   <NA>
 RTRT|TRTR  RSABE    AUC 0.900 0.202 0.8000 1.2500 28 0.9168 0.8984

Regulator: FDA (RSABE applicable to PK metrics with CVwR ≥0.3).
PK metric ruling the sample size: Cmax
Sample size: 28 (RSABE, power: 0.8064)
Power of AUC (RSABE): 0.9168
Lowest GMR of AUC which will give power 0.8: 0.8810
Total number of treatments in study: 112

For ABE the outcome is the same as for the EMA’s 2.a and 2.b. above.

You can see that the variability of C_max (even for reference-scaling) drives the sample size. However, you get an incentive. Power for AUC will be (much) higher than the target. Hence, its T/R-ratio can deviate more from 1 than expected (as shown above in the column GMRlo) or its CV can be higher whilst still maintaining the target level.