Bioequivalence and Bioavailability Forum

Dear DLabes!

❝ Statistical analysis, page 13 (lines 504-505)

❝ A nonparametric analysis is not acceptable.

❝

❝ This cannot be discussed seriously without crying.

❝ Moreover in the text any statistical analysis of t_max has be gone.

Some more background information…
Quoting an e-mail I received from Walter Hauck: “Also interesting that they now say they will not accept non-parametric analyses. That seems a step backwards.”
I talked to a lot of regulators at the EGA-CMP(h)-Symposium in Paris last week and what we already suspected is true: Nonparametrics are evil, therefore t_max had to eliminated from the PK-metrics as well. We all know that t_max is a lousy metric for the rate of absorption, but on the other hand it served well in thousands of studies in the past. Although introduced as a metric for ‘early exposure’ by the http://www.fda.gov/cder/guidance/5356fnl.pdf FDA in 2003, to my knowledge there’s no empirical evidence that this metric performs better than t_max.

Schall and Luus (1992)¹ have shown that in the one-compartment open model the difference in t_max, and the ratio of the C_max/AUC ratio of two drug formulations are equivalent characteristics for the comparison of the absorption rate. In two- or higher compartment models these relationships hold approximately. This provides a powerful argument for the use of the observed C_max/AUC ratio, rather than t_max, as a mesure for the rate of absorption, because it is well-known that C_max/AUC can be observed with higher precision than t_max.
Midha et al. (1994)² suggested that mean AUC_tmax may not be a reliable basis for estimation of relative extent [sic!] of absorption because the within-subject variabilities of the partial areas over the first few hours after dose tend to be very high, but decline rapidly to become stable at some point that may fall before or after mean-t_max.
Midha et al. (1993)³ showed that high within-subject variability increases the likelihood of failure of 90% confidence intervals to fall within preset bioequivalence limits in simulations in which the true ratio of geometric means was set at unity.
In a retrospective analysis of 11 BE studies early partial areas showed high variability which stabilized at about 2×t_max, which lead the authors to their often quoted statement: “Once absorption is over, formulation differences no longer apply.”⁴

1. R Schall and HG Luus
   Comparison of absorption rates in bioequivalence studies of immediate release drug formulations
   Int J Clin Pharm Ther Toxicol 30/5, 153–9 (1992)
   
2. Midha KK, Hubbard JW, Rawson MJ, and L Gavalas
   The application of partial areas in the assessment of rate and extent of absorption in bioequivalence studies of conventional release products: Experimental evidence
   Eur J Pharm Sci 2, 351–63 (1994)
   
3. Midha KK, Hubbard JW, Yeung PKF, Ormsby E, McKay G, Hawes EM, Korchinski ED, Gurnsey T, Rawson M, and R Schwedes
   Application of Replicate Design
   In: KK Midha and HH Blume
   Bio-International: Bioavailability, Bioequivalence and Pharmacokinetics
   medpharm Scientific Publishers, Stuttgart, pp 53–68 (1993)
   
4. Midha KK, Hubbard JW, and MJ Rawson
   Retrospective evaluation of relative extent of absorption by the use of partial areas under plasma conentration versus time curves in bioequivalence studies on conventional release products
   Eur J Pharm Sci 4, 381–4 (1996)

If partial AUC truncated at reference’s t_max will become a main target parameter (according to statements at the EGA-Symposium no widening of the acceptance range of 0.80-1.25 will be considered), this metric will lead to exceptionally high sample sizes because of its intrinsic variability.

In the following two examples from my database (IR formulations, clinical claim on C_max/t_max). Both of them showed very low to moderate CV_intra on both AUC and C_max, and were suitably powered in order to be able to demonstrate BE for C_max.

Example 1:
Original evaluation
Median t_max (ref.) 1.5h
Additive model (nonparametric)
Hodges-Lehman estimate: ±0.00h (100%)
Moses CI: -0.25, +0.25 (85.0%, 115%)
Conclusion: BE
New evaluation
pAUC_1.5
Multiplicative model (parametric)
GMR: 90.1%
CI: 75.0%, 110.1%
CV_intra 26.4% (AUC_t 13.3%, C_max 17.0%)
Conclusion: not BE

Example 2:
Median t_max (ref.) 1.5h
Additive model (nonparametric)
Hodges-Lehman estimate: +0.26h (116%)
Moses CI: ±0.00, +0.50 (100%, 130%)
Conclusion: not BE
pAUC_1.5
Multiplicative model (parametric)
GMR: 66.1%
CI: 53.1%, 82.0%
CV_intra 29.7% (AUC_t 6.33%, C_max 9.43%)
Conclusion: not BE

Power to show BE for partial AUC was clearly insufficient, even in example 1. CV_intra for the partial AUC was thrice that of C_max and almost five times that of AUC_t in example 2.

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Edit: FDA-link corrected to latest archived copy. [Helmut]