**Background
Information for Advisory Committee Meeting
**

**On ****April 14, 2004**

**Criteria for
Establishing Bio-inequivalence between Two Drug Products**

**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 C_{max} 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 parameters 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 concepts 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 parameters (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 parameters) 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
parameters collectively:**

As
mentioned earlier, based on the interpretation of regulation, FDA usually
requires three pharmacokinetic parameters (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 parameters must be within the bioequivalence interval to
demonstate bioequivalence. If the 90% confidence interval for just one of the
three pharmacokinetic parameters 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 parameters will not be as simple. Here we
discuss several strategies that potentially can be used for assessing
bio-inequivalence using three pharmacokinetic parameters. 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 parameters 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 parameters 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 parameters 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 parameter for bio-inequivalence
testing. For example, one could pre-specify AUCt and completely ignore the results
of the other two pharmacokinetic parameters. However, this strategy only has
good power when AUCt is the parameter 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 parameters 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 parameter use a
two-sided 91% confidence interval (slightly wider than 90% confidence interval)
to show bio-inequivalence, while the second pharmacokinetic parameter uses a
two-sided 87% confidence interval (narrower than 90% confidence interval) and
the third pharmacokinetic parameter uses two-sided 80% confidence interval
(much narrower than 90% confidence interval).
For this strategy, it does not matter which pharmacokinetic parameters
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 parameter’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.

We
would like to note here that it might not be necessary to control all the
correlation structures, as it may be very unlikely for the three
pharmacokinetic parameters to be highly correlated (the correlation coefficient
is above 0.99). For the strategy with flexible confidence intervals discussed
above, the error inflation occurs at correlation structures that are highly
correlated. If it is possible to show that the three pharmacokinetic parameters
are unlikely to have correlation higher than 0.99, the strategy can be further
relaxed.

In summary, this meeting will introduce and clarify the concepts of bioequivalence, bio-inequivalence, failing to demonstrate bioequivalence, and failing to demonstrate bio-inequivalence. We will explain the statistical criteria used to claim bio-inequivalence for one pharmacokinetic parameter. We will present the pros and cons of several strategies to collectively evaluate the three pharmacokinetic parameters. Our main focus for the discussion of bio-inequivalence criteria is on statistical issues related to power and error. Other statistical issues, such as an inadequate statistical model, study design, as well as conduct of the studies, may also impact bioequivalence and bio-inequivalence testing.

**April 14,
2004**

Do you agree with the distinction between demonstrating bio-inequivalence and failure to demonstrate bioequivalence?

What is your preferred method for evaluating the three pharmacokinetic parameters for bio-inequivalence?

- If bio-inequivalence is demonstrated for any
one pharmacokinetic parameter, then bio-inequivalence is
demonstrated for the products.
- bio-inequivalence must be demonstrated
for all three pharmacokinetic parameters
for bio-inequivalence to be demonstrated for the products.
- There should be one preselected pharmacokinetic parameter
used for bio-inequivalence testing. If so, which one?
- The three pharmacokinetic parameters should be
evaluated for bio-inequivalence with statistical corrections to the
level of significance for each parameter in order to maintain an
overall significance level of 0.05.

[i] D.J. Schuirmann. A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. J. Pharmacokinet. Biopharm. 15: 657-680 (1987).

[ii]