Bioequivalence Studies With Pharmacokinetic Endpoints for Drugs Submitted Under an Abbreviated New Drug Application

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Term	Definition
AUC	Area under the curve
$AUC_{0-\infty}$	Area under the curve extrapolated to infinity
$AUC_{0-t}$	Area under the curve from time zero to the last measurable time point
$AUC_{0-\tau}$	Area under the curve for one dosing interval at steady state
$C_{avSS}$	Average plasma concentration at steady state
$C_{max}$	Maximum plasma concentration
$C_{maxSS}$	Maximum plasma concentration during the dosing interval at steady state
$C_{minSS}$	Minimum plasma concentration at steady state
Enantiomers	Two stereoisomers that are mirror images but nonsuperimposable. Same physical properties except: (1) direction of polarized light rotation, (2) interactions with optical isomers of other compounds.
pAUC	Area under the curve between two specific time points
$\lambda_z$	Terminal or elimination rate constant
Racemate	Mixture of two enantiomers in equal proportion (optically inactive). Different melting point, solubility, or boiling point than pure enantiomers. Pharmaceuticals may be racemates or pure enantiomers with different potency.
$T_{max}$	Time to maximum observed plasma concentration
$t_{1/2}$	Half-life

III. ESTABLISHING BIOEQUIVALENCE

A. Pharmacokinetic Studies

4. Study Designs

FDA recommends that applicants use (1) a two-period, two-sequence, two-treatment, single-dose crossover study design, (2) a single-dose parallel study design, or (3) a single-dose replicate study design for BE studies.
The BE studies generally should be conducted on the highest strength of the drug product, unless safety considerations preclude the use of that dose in study subjects.
The general recommendations for study designs provided in Appendix A should be considered in designing studies. FDA recommends that applicants use the average BE method of analysis with these study designs.
For most dosage forms that release a drug intended to be systemically available, FDA recommends that applicants perform a two-period, two-sequence, two-treatment, single-dose, crossover study using either healthy subjects or other populations, as appropriate.
In this design, each subject should receive each treatment (the test and the reference product) in a random order.
A replicate crossover study design (either partial or fully replicate) is appropriate for drugs whether the reference product is a highly variable drug or not.
A replicate design can have the advantage of using fewer subjects compared to a non-replicate design, although each subject in a replicate design study would receive more treatments.

6. Steady-State Studies

When safety considerations suggest using patients who are already receiving a medication, often the only approach to establish BE without disrupting a patient’s ongoing treatment is in a steady state study.
If a steady-state study is used, we recommend that applicants carry out appropriate dosage administration and sampling to demonstrate the attainment of steady state.

9. Pharmacokinetic Measures of Rate and Extent of Absorption

a. Rate of absorption (peak exposure)

For both single-dose and steady-state studies, FDA recommends that applicants assess the rate of absorption by measuring the Cmax obtained directly from the data (i.e., without interpolation).
$T_{max}$ can also provide important information regarding the rate of absorption.
Applicants should evaluate $T_{max}$ differences between their product and the reference product for any clinical implications.

b. Extent of absorption (total exposure)

For single-dose studies, FDA recommends that the indicators for the extent of absorption be both of the following: - Area under the plasma, serum, or blood concentration-time curve from time zero to time t ($AUC_{0-t}$), where t is the last time point with a measurable concentration - Area under the plasma, serum, or blood concentration-time curve from time zero to time infinity ($AUC_{0-inf}$), where: - $AUC_{0-inf} = AUC_{0-t} + C_t/λ_z$ - $C_t$ is the last measurable drug concentration - $λ_z$ is the terminal or elimination rate constant calculated according to an appropriate method

For steady-state studies, FDA recommends that the indicator for the extent of absorption be the area under the plasma, serum, or blood concentration-time curve over a dosing interval at steady state ($AUC_{0-tau}, where tau is the length of the dosing interval).

c. Partial exposure

FDA recommends that sufficient quantifiable samples be collected to allow adequate estimation of the pAUC

APPENDIX A: GENERAL DESIGN AND DATA HANDLING OF BIOEQUIVALENCE STUDIES WITH PHARMACOKINETIC ENDPOINTS

Pharmacokinetic information in submissions:

We recommend that applicants provide the following PK information in their submissions: - Plasma or other acceptable matrix concentrations and time points (both actual and nominal sampling time points). - Subject, period, sequence, treatment. - Intersubject, intrasubject, and/or total variability, if available. - For single-dose BE studies: $AUC_{0-t}, AUC_{0-inf}$, AUC truncated or partial AUCs if applicable, and Cmax. In addition, report the following supportive information: $T_{max}, K_{el}$ and $t_{1/2}$. - For steady-state BE studies: AUC0-tau and CmaxSS. In addition, report CminSS (lowest concentration in a dosing interval), CavSS (average concentration during a dosing interval), degree of fluctuation [$(C_{maxSS}-C_{minSS})/C_{avSS}], swing [(C_{maxSS}-C_{minSS})/C_{minSS}$], and $T_{max}$. - Additional analysis may be needed in certain cases to ensure that the two products are bioequivalent.

Statistical information for $AUC_{0-t}, AUC_{0-inf}$, and $C_{max}$:

We recommend that applicants provide the following statistical information for $AUC_{0-t}, AUC_{0-inf}$, and $C_{max}$: - Geometric means - Arithmetic means - Geometric mean ratios and their corresponding 90 percent confidence intervals and/or 95 percent upper confidence bound, as applicable

We also recommend that applicants provide logarithmic transformation for measures used for BE demonstration and consult the guidance for industry Statistical Approaches to Establishing Bioequivalence (February 2001).

Confidence interval values for unscaled average bioequivalence anaylses:

For unscaled average bioequivalence analyses, to pass a confidence interval limit of 80 to 125 percent, the rounded confidence interval value should be at least 80.00 percent and not more than 125.00.

We thus recommend that when applicants evaluate the confidence interval to assess bioequivalence using an unscaled average bioequivalence analysis during the development program, applicants round confidence interval values to two digits after the decimal point.

APPENDIX B: METHOD FOR STATISTICAL ANALYSIS USING THE REFERENCE946 SCALED AVERAGE BIOEQUIVALENCE APPROACH: HIGHLY VARIABLE DRUGS

For highly variable drugs, a mixed scaling approach is used. Namely, the reference-scaled procedure is used for specific PK parameters that have a within subject variability of the reference product ( $s_{WR}$ ) ≥ 0.294, and the two one-sided tests procedure is used for PK parameters with WR s < 0.294. In other words, if AUC ($AUC_{0-t}^{47}$ and $AUC_{0-inf}$, as applicable) and $C_{max}$ have different WR 952 s values, different BE analysis should be conducted.

The following are the steps that can be followed to carry out the statistical analysis for the reference-scaled average bioequivalence assessment for highly variable drugs:

Step 1

Determine $s_{WR}$, the within-subject standard deviation of the reference product, for the 958 pharmacokinetic (PK) parameters including AUC and $C_{max}$.

If $s_{WR} < 0.294$, use the two one-sided tests procedure to determine bioequivalence (BE) for the individual PK parameter(s).
If $s_{WR} ≥ 0.294$, use the reference-scaled procedure to determine BE for the individual PK parameter(s).

\[s^2_{WR} = \frac{\sum^m_{i=1} \sum^{n_i}_{j=1}(D_{ij} - \bar{D}_i)^2}{2(n-m)}\]

i = number of sequences m used in the study
- [m=3 for partially replicate design: TRR, RTR, and RRT;
- m=2 for fully replicate design: TRTR and RTRT]
j = number of subjects within each sequence
T = Test product
R = Reference product
$D_{ij} = R_{ij1} – R_{ij2}$ (where 1 and 2 represent replicate reference treatments)
$\bar{D}_i = \frac{\sum^{n_j}_{j=1} D_{ij} }{n_i}$
$n = \sum^m_{i=1}n_i$(i.e., total number of subjects used in the study, while ni is number of subjects used in sequence i)
Step 2

Determine the 95% upper confidence bound48 for:

$( \bar{Y}_T - \bar{Y}_R )^2 - \theta s^2_{WR}$

$\bar{Y}_T$ and $\bar{Y}_R$ are the means of the ln-transformed PK endpoint (AUC and/or $C_{max}$) obtained from the BE study for the test and reference products, respectively.
$\theta = (\frac{ln(1.25)}{\sigma_{W0}})^2$ (scaled average BE limit).
$\sigma_{W0} = 0.25$ (regulatory constant).
Step 3.

For the test product to be bioequivalent to the reference product, both of the following conditions must be satisfied for each PK parameter tested:

The 95% upper confidence bound for $( \bar{Y}_T - \bar{Y}_R )^2 - \theta s^2_{WR}$ must be ≤ 0 (numbers should be kept to a minimum of four significant figures for comparsion).
The point estimate of the Test/Reference geometric mean ratio must fall within [0.8000, 1.2500].
PROC GLM should be used for partially replicate (3-way) BE studies
PROC MIXED should be used for fully replicate (4-way) BE studies

[FDA] Bioequivalence Studies With Pharmacokinetic Endpoints

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