Background Information for Advisory Committee for
Pharmaceutical Science
Concept and Criteria of BioINequivalence
Introduction
Bioequivalence
is defined as “the absence of a significant difference in the rate and extent
to which the active ingredient or active moiety in pharmaceutical equivalents
or pharmaceutical alternatives becomes available at the site of drug action
when administered at the same molar dose under similar conditions in an
appropriately designed study...”. To evaluate
bioequivalence, the U.S. Food and Drug Administration (FDA) has employed a
testing procedure termed the two
one-sided tests procedure ([i])
to determine whether the average values for the pharmacokinetic measures from
the test and reference products are comparable.
This procedure involves the calculation of a confidence interval for the
ratio between the average values of the test and reference product. FDA considers a test product to be
bioequivalent to a reference product if the 90% confidence interval of the
geometric mean ratio of AUC and Cmax between the test and reference
fall within 80-125% ([ii]).
Recently, the FDA has
received several studies intended to show bio-inequivalence between two drug
products, for example an innovator company might conduct a study to challenge
FDA’s approval of generic versions of its drug product. Although there has not
been a formal definition of the concept of bio-inequivalence in the regulation,
intuitively, the concept of bio-inequivalence is not hard to perceive, given
the well-defined concept of bioequivalence. However, there are no clear
criteria to guide sponsors in conducting bio-inequivalence studies and FDA
reviewers in assessing the validity of such bio-inequivalence studies. Because
of a lack of a clear definition of bio-inequivalence, there has been some
confusion and misunderstanding by the public.
Many questions arise when
evaluating a bio-inequivalence claim. A typical question is if it is
appropriate to claim bio-inequivalence when the two-sided 90% confidence
intervals for the ratios of the PK endpoints do not fall inside the
bioequivalence interval? There are numerous literature reports that claim
bio-inequivalence based on a failed bioequivalence study without identification
of the causes of the study failure. There are many ways that a bioequivalence
study can fail, including an insufficient number of subjects. Many products
that were claimed to be bio-inequvialent in the literature might well be
bioequivalent if the studies were conducted appropriately. Therefore, it is
imperative to develop and establish a bio-inequivalence criterion to clarify
confusion and misunderstanding in the public.
In these presentations, we
first introduce the concept of bio-inequivalence and present a statistical
explanation for the proposed criterion to assess bio-inequivalence. We then
discuss several statistical strategies to assess bio-inequivalence studies with
three pharmacokinetic endpoints (Cmax, AUCt and AUC¥). The goal is to propose a set of criteria that are
scientifically sound, statistically valid, and easy to use and to provide
sufficient information to stimulate discussion on the evaluation of
bio-inequivalence.
The concept of bio-inequivalence and test criteria
FDA’s bioequivalence criteria require the
90% confidence interval of the ratio of the geometric means of the test and
reference drug products to be within the bioequivalence interval [80%, 125%].
The definition of the bio-inequivalence region then is simply the region that
lies outside the bioequivalence interval, i.e., (0, 80%) or (125%,
∞). Now the question is why a
study failing to show bioequivalence cannot be used to claim bio-inequivalence.
Once this question is answered, it will be a little easier to understand the
statistical criteria proposed for bio-inequivalence claims.
To answer this question, we
need to understand statistically how the criteria for bioequivalence are
formed. To test bioequivalence, the null hypothesis is set to be the
bio-inequivalence region and the alternative hypothesis to be the
bioequivalence interval. The goal is to
see if bio-inequivalence can be rejected so that we may conclude that
bioequivalence is true. For this purpose, it is important for the probability
of an error that wrongfully rejects bio-inequivalence, and therefore falsely
concludes bioequivalence, to be small. This error is usually controlled at the
level of 0.05, which is the so-called significance level or the type I error
rate. To reject the bio-inequivalence region, we need to perform two one-sided tests,
each controlling the type I error rate at the level of 0.05. The maximum error rate in the two tests are actually controlled at the level
of 0.05. The statistical criteria for rejecting bio-inequivalence and claiming
bioequivalence are to have two-sided 90% confidence intervals (for the
geometric mean ratio for each of the three PK endpoints) that are each within
the bioequivalence interval. This procedure based on 90% confidence intervals
is identical to carrying out the two one-sided tests described above.
To address whether failing to
show bioequivalence demonstrates bio-inequivalence, we need to understand that
in a bioequivalence test we usually do not control the error of wrongfully
failing to conclude bioequivalence. If this error were controlled at a very low
level, this would be equivalent to having very high power in a bioequivalence
test. In order for both the significance level and power to be controlled at
high level, a large sample size will generally be required, which will increase
the cost of the study. For example, if we set the power to be 85%, and assuming
the variance is 0.04, the sample size required is about 22, given the ratio of
the two geometric means deviates from 1 by no more than 5%. In this case, the
test could have about a 15% chance to fail to show bioequivalence even when the
two drugs are truly equivalent. If the variance is larger than 0.04 and the
ratio of the two geometric means deviates from 1 by more than 5% but still
within the bioequivalence interval, the power could be much lower than 85% for
the given sample size of
22. That is, the chance of failing to show bioequivalence would
be much higher than 15% even when the two drugs are equivalent. Therefore,
because there is less control over the probability of failing to show
bioequivalence, it is inappropriate to use a study that fails to show
bioequivalence to claim bio-inequivalence.
Then why should
the bio-inequivalence criterion be that the upper (lower) limit of the
two-sided 90% CI should be less (greater) than 80% (125%)? As mentioned before, usually it is not
realistic to control both types of errors, i.e., wrongfully rejecting
bio-inequivalence and bioequivalence. A reasonable study only tightly controls
one type of error. Therefore when testing for bio-inequivalence, we would like
to control the error of wrongfully rejecting bioequivalence to be small. To be
consistent with the bioequivalence testing, the error rate is also chosen at
the level of 0.05. To reject bioequivalence, we also need to perform two one-sided
tests, however, the level of each test may need to be
0.05. For one of the two tests to be
significant at the 0.05 level, either the upper limit of the two-sided 90% CI
has to be less than 80% or the lower limit to be above 125%.
Theoretically, it is possible for the
type I error to reach 0.10 when a two-sided 90% CI is used to assess
bio-inequivalence. However, this is true only when the variance of the
estimated treatment difference (the ratio of geometric means) is very large.
For typical crossover bio-inequivalence trials, such a large variance may not
be a realistic possibility. Therefore, the type I error rate should be
maintained at the level of 0.05 when two-sided 90% CI is used.
The above figure illustrates
the different possible outcomes. A study with the two-sided 90% confidence
interval completely between 80-125% demonstrates bioequivalence and allows
market access. A study with the two-sided 90% confidence interval completely
outside 80-125% demonstrates bio-inequivalence and may be grounds for market
exclusion. A study with the point estimate within 80-125% but the two-sided 90%
confidence interval outside of 80-125% fails to demonstrate bioequivalence. A
study with the point estimate outside 80-125% but the two-sided 90% confidence
interval overlapping 80-125% fails to demonstrate bio-inequivalence. Both of
the failing cases would require studies with larger sample sizes to draw a
definitive regulatory conclusion.
Evaluating the three PK endpoints collectively:
As mentioned earlier, based
on the interpretation of regulation, FDA usually requires three pharmacokinetic
endpoints (Cmax, AUCt, and AUC¥) to show bioequivalence. All the two-sided 90% confidence intervals
for the ratios of the geometric means for the three pharmacokinetic endpoints
must be within the bioequivalence interval to demonstate bioequivalence. If the
90% confidence interval for just one of the three pharmacokinetic endpoints
does not fall completely within the bioequivalence interval, the study has not
demonstrated that the two drugs are bioequivalent. However, the statistical
criteria for testing bio-inequivalence using all the three pharmacokinetic endpoints
will not be as simple. Here we discuss several strategies that potentially can
be used for assessing bio-inequivalence using three pharmacokinetic endpoints. The evaluation of the strategies is based on
both the error rate of wrongfully rejecting bioequivalence and power for
detecting bio-inequivalence under various correlation structures.
One strategy that seems
intuitive is to have at least one of the three pharmacokinetic endpoints
satisfy the statistical criteria for bio-inequivalence, i.e., the upper (lower)
limit of the two-sided 90% CI to be less (greater) than 80% (125%). However,
this strategy could potentially inflate the error rate of wrongfully rejecting
bioequivalence above the level of 0.05 if the three pharmacokinetic endpoints
are not highly correlated.
The second strategy that is
just the opposite of the first one discussed above is to require all the three
pharmacokinetic endpoints to satisfy the statistical criteria for
bio-inequivalence. This strategy can certainly control the error rate of
wrongfully rejecting bioequivalence under all correlation structures. However,
it may not always provide adequate power under alternatives that are of
interest.
The third strategy that could
protect the error rate of wrongfully rejecting the bioequivalence is to
pre-specify one pharmacokinetic endpoint for bio-inequivalence testing. For
example, one could pre-specify AUCt and completely ignore the results
of the other two pharmacokinetic endpoints. However, this strategy only has
good power when AUCt is the endpoint most likely to demonstrate
bio-inequivalence. If only Cmax of the two drugs were bioinequivalent, then
pre-specifying AUCt would give the test zero power to detect bio-inequivalence.
It is possible to develop a
compromise approach. Instead of requiring all the three pharmacokinetic endpoints
to satisfy the statistical criteria for bio-inequivalence with two-sided 90%
confidence intervals as the measurement, we could have flexible width of the
one-sided confidence intervals, while controlling the error rate at the level
of 0.05 under all correlation structures. For example, it is possible to have
one pharmacokinetic endpoint use a two-sided 92% confidence interval (slightly
wider than 90% confidence interval) to show bio-inequivalence, while the second
pharmacokinetic endpoint uses a two-sided 86% confidence interval (narrower
than 90% confidence interval) and the third pharmacokinetic endpoint uses
two-sided 80% confidence interval (much narrower than 90% confidence
interval). For this strategy, it does
not matter which pharmacokinetic endpoints uses which confidence interval. The
advantage of this strategy is to use narrower confidence intervals to increase
power to show bio-inequivalence, although at the cost of slightly widening one
pharmacokinetic endpoint’s confidence interval. Notice this strategy is
developed using the assumption of a normal distribution. If the normal
assumption is inadequate, it is possible to derive slightly different widths of
confidence intervals under other distributions.
Summary
of Bio-inequivalence discussions on April 14, 2004 ACPS Meeting
At the
1.
Does the ACPS agree with the distinction between
demonstrating bioINequivalence and failure to demonstrate bioequivalence?
Committee’s comments: The Committee
felt that there was a need to establish criteria for bioINequivalence
evaluation and the criteria should not be just as failure of the bioequivalence
test. The members argued it was important to focus on the clinical relevance
with the therapeutic index. The Committee discussed both Area under the Curve
(AUC) and Cmax as metrics important for bioequivalence and bioINequivalence.
2.
Does the ACPS recommend a preferred method for
evaluating the three pharmacokinetic endpoints for bioINequivalence?
·
If bioINequivalence is demonstrated for any one
pharmacokinetic endpoint, then bioINequivalence is demonstrated for the
products.
·
BioINequivalence must be demonstrated for all three
pharmacokinetic endpoints for bioINequivalence to be demonstrated for the
products.
·
There should be one pre-selected pharmacokinetic endpoint
used for bioINequivalence testing. If so, which one?
·
The three pharmacokinetic endpoints should be evaluated
for bioINequivalence with statistical corrections to the level of significance
for each endpoint in order to maintain an overall significance level of 0.05.
Committee’s comments:
The Committee agreed on a
general understanding of bioINequivalence to move forward by recognizing it is
not a simple matter. In addition, the members felt this is an important
concept, especially how it applies to the entire regulatory scenario. There was
no consensus at this point as to a final criteria pertaining to the three
pharmacokinetic endpoints.
Outline
of Bioinequivalence discussion for Oct. 20 ACPS Meeting
The discussion on bioinequivalence will be focused on using
three PK endpoints, AUCt, AUC¥,
and Cmax, to establish bioinequivalence between drug products. We will discuss
strategies and recommendations under different scenarios for assessing bio-inequivalence
using three PK endpoints.
If one of the three PK
endpoints fail to satisfy the equivalence interval [80%, 125%], by definition,
the bioequivalence is false and bioinequivalence is true. To test bioinequivalence using three PK
endpoints, we would also like to control the error rate of wrongfully rejecting
bioequivalence at the level of 5%.
As mentioned before, it is
tempting to claim bioinequivalence between two drug products if one of the
three endpoints demonstrates inequivalence by showing that a two-sided 90% CI
falls in the bioinequivalence regions. This strategy could potentially inflate
the overall type I error of wrongfully rejecting bioequivalence. For example, the
error rate can be as high as 14.7% if no correlation exists (ρ=0), about 8.2%
when pairwise correlation is 0.90, and 5.9% when the three endpoints are highly
correlated (ρ=0.99), given the variance of test statistics is not too
large. Therefore, this strategy is not acceptable for assessing bioinequivalence
using three endpoints.
However, if one is certain
that one PK endpoint could have the highest power to demonstrate inequivalence
among the three, it is possible to pre-specify the PK endpoint to test for bioinequivalence
using one PK endpoint at the level of 5%. This strategy will protect the error
rate of wrongfully rejecting bioequivalence at the level of 5% and perform well
if we know, at the design stage of study protocol, which PK endpoint is most
likely to demonstrate bioinequivalence. Pre-specifying one PK endpoint is
important in this strategy in order to protect the error rate. The disadvantage
of this strategy is that it could end up having low power if the pre-specified
PK endpoint in fact does not have high power to show inequivalence.
If one can not pre-specify a
PK endpoint, three PK endpoints should be used to demonstrate bioinequivalence.
For this scenario, the strategy that requires all three two-sided 90% CIs to fall
outside the equivalence interval should not be recommended. Though this
strategy protects the error rate tightly, it is overly stringent to show
bioinequivalence in most situations. An enhanced approach for this scenario is
to use unequal width of CIs, such as 92%, 86%, 80% for the three CIs. This
approach controls the error rate at 5% level regardless the correlation
structure of the three endpoints, and can have enhanced power for the
situations that all three PK endpoints may have some power to demonstrate bioinequivalence,
but it is uncertain which one would have the best power.
In this presentation, we will
explain that so far there is not a universally powerful approach that can be
used to evaluate three PK endpoints for bioinequivalence. The sponsor of the
bioinequivalence studies should be able to make their own choice in selecting a
strategy in evaluating bioinequivalence. However, the choice must be
pre-specified in bioinequivalence study protocol before study is conducted.
Discussion Topic for ACPS Meeting
What is your
preferred method for evaluating the three pharmacokinetic parameters for bioinequivalence?
· If bioinequivalence is demonstrated for any one pharmacokinetic
parameter that is prespecified, then bioinequivalence is demonstrated for the
products.
· Bioinequivalence must be demonstrated for all three
pharmacokinetic parameters for bioinequivalence to be demonstrated for the
products, where the error rate is controlled at 5%.
· FDA should allow sponsors of bioinequivalence studies
to make their own choice on picking up strategies; sponsors should prespecify
the choice in study protocols before the study is conducted.