Transcript Criteria for Evaluating Bio- inequivalence among Drug Products Using Multiple PK Endpoints

Criteria for Evaluating Bioinequivalence among Drug
Products Using Multiple PK
Endpoints
Qian H. Li
QMR/OB/OPASS/CDER, FDA
Introduction
• Why multiple PK endpoints?
– Bioequivalence between drugs are
established by comparing the rate and extent
of drug absorption, which are represented by
Cmax, AUCt, and AUC.
– Bioequivalence for generic drug approvals
has evolved to use AUCt, AUC, and Cmax .
– Bio-inequivalence can be established if any
one of the PK endpoints are inequivalent in
truth.
October 20, 2004
ACPS Meeting
2
Outline
– Criterion for bio-inequivalence using one PK
endpoint
– Strategies for assessing bio-inequivalence
using three PK endpoints
• Available approaches
• Power comparison to show bio-inequivalence
– Recommendations
October 20, 2004
ACPS Meeting
3
Definitions for One Endpoint
• Ratios of geometric means µT/µR,
– µT the geometric mean of the test product
– µR the geometric mean of the reference product
• Bioequivalence interval [80%, 125%]
• Bio-inequivalence [0, 80%) or (125%, )
µT/µR
Bio-inequivalence
Region
October 20, 2004
80%
125%
Bioequivalence
Interval
ACPS Meeting
Bio-inequivalence
Region
4
Test for Bio-inequivalence
• Hypotheses for testing bio-inequivalence:
H0: 80%  µT/µR 125% vs. HA: µT/µR < 80% or µT/µR >125%
• Perform 2 one-sided tests
–
–
–
–
H01: µT/µR ≥80% vs. HA1: µT/µR < 80%
H02: µT/µR ≤125% vs HA2: µT/µR >125%
Only need to reject either null
The significance level for each one-sided test is controlled at
0.05
• CRITERION: Reject bioequivalence when the
two-sided 90% CI lies completely in either of the
two bio-inequivalence regions
October 20, 2004
ACPS Meeting
5
Error Discussion for
Bio-inequivalence Criterion
• Using 2-sided 90% CI, the error rate is protected
at 5% if a 2-sequence and 2-way balanced
crossover trial has
– >20 subjects and
– Within subject standard deviation < 0.7
• Using 2-sided 90% CI, the error rate may be
higher than 5% if
– Sample size is <20 or
– Variance is large
– Using 2-sided 95% CI
October 20, 2004
ACPS Meeting
6
Definitions with Three Endpoints
AUC
Inequivalence
Region
125%
125%
80%
AUCt
Equivalence
Region 125%
Cmax
October 20, 2004
ACPS Meeting
7
Criterion for Bioequivalence with
3 PK endpoints
• Criterion: the 2-sided 90% CIs for the
ratios of all three endpoints have to be
within [80%, 125%]
• The error rate of wrongfully rejecting bioinequivalence is protected at 5% level.
October 20, 2004
ACPS Meeting
8
Bio-inequivalence with Three
Endpoints
• Looking for strategies that
– Control the error rate of wrongfully rejecting
bioequivalence at the rate of 5%
– Control the error rate under all correlation
structures since the correlation structure is
unknown
– Assume the variances of test statistics are not
large (0.3)
October 20, 2004
ACPS Meeting
9
A Common Misconception
• Claim bio-inequivalence when one of the
three PK endpoints satisfies the bioinequivalence criterion for one endpoint;
• Inflate error rate of wrongfully rejecting
bioequivalence
0.147 if independent
0.082 if highly correlated (correlation is about 0.9)
(Note: the error rate is calculated when  is 0.1)
• Not acceptable
October 20, 2004
ACPS Meeting
10
A Tough Criterion
• Claim bio-inequivalence if all the three PK
endpoints satisfy the bio-inequivalence
criterion.
• Tightly control the error rate under all
correlation structures for the three PK
endpoints.
• Usually does not provide adequate power
• Not recommended
October 20, 2004
ACPS Meeting
11
Strategy I
• Pre-specify one of the three PK endpoints for
bio-inequivalence testing.
– For example, test AUCt only, ignore the other two.
– Need to pre-specify the endpoint in study protocols
– Controls error rate.
• Ideal for scenarios when one knows that a
specific one PK endpoint is more likely to show
bio-inequivalence than others
• May have poor power if the wrong endpoint is
chosen
October 20, 2004
ACPS Meeting
12
Strategy II
• Bonferroni correction:
– Ex: Using 2-sided 96.7% confidence intervals (CIs)
instead of 2-sided 90% CIs
– If one of the three 96.7% CIs fall in the bioinequivalence regions, then demonstrate bioinequivalence
– Other possible versions
– Distribution independent
• Ideal for scenarios when one knows that one PK
endpoint is more likely to demonstrate bioinequivalence than others, but do not believe
that all endpoints have good power.
October 20, 2004
ACPS Meeting
13
Strategy III
• Three confidence intervals with different lengths,
a variation to the approach that requires all three
endpoints to satisfy the bio-inequivalence
criterion of one endpoint.
– Control error rate at 5%
– Derived based on simulation study and distribution
dependent
– Ex: (94%, 80%, 65%)
• Ideal for scenarios when
– one has no idea which PK endpoint is more likely
than others to show bio-inequivalence and
– All three PK endpoints are inequivalent
October 20, 2004
ACPS Meeting
14
Power Examples
• Scenario I: only one endpoint has
good power to demonstrate bioinequivalence
– AUCt=5%, AUC=20%, Cmax=90%
Strategies
Power under Correlation Structures
(0.9, 0.8, 0.7)
(0.99, 0.99, 0.99)
Pre-specify
5-90%
5-90%
Bonferroni
78.4%
78.6%
Varying CIs
(94, 80, 65)
17.7%
17.7%
October 20, 2004
ACPS Meeting
15
Power Examples
• Scenario II: All three endpoints have
reasonable power
– AUCt=60%, AUC=70%, Cmax=80%
Strategies
Power under Correlation Structures
(0.9, 0.8, 0.7)
(0.99, 0.99, 0.99)
Pre-specify
60-80%
60-80%
Bonferroni
71.8%
64.4%
Varying CIs
(94, 80, 65)
73.6%
72.5%
October 20, 2004
ACPS Meeting
16
Power Examples
• Scenario III: All three endpoints have
equal power
– AUCt=80%, AUC=80%, Cmax=80%
Strategies
Power under Correlation Structures
(0.9, 0.8, 0.7)
(0.99, 0.99, 0.99)
Pre-specify
80%
80%
Bonferroni
78.0%
67.4%
Varying CIs
(94, 80, 65)
82.2%
75.4%
October 20, 2004
ACPS Meeting
17
Recommendations
• When one knows which endpoint is more likely to show bioinequivalence, Strategy I should be used.
– Pre-specify the endpoint in study protocols, use this endpoint to test bioinequivalence
– Use a two-sided 90% CI
• When one knows that one endpoint may have good power, but do
not believe that all of them have good power, use Strategy II,
Bonferroni correction.
– An example of Bonferroni correction is to use a two-sided 96.7% CI.
• When one believes that all three endpoints could have reasonable
power to show bio-inequivalence, Strategy III could be a good
choice.
– An example of varying CIs is (94%, 80%, 65%) if normally distributed
October 20, 2004
ACPS Meeting
18