Statistical Information from the June 1999 Draft Guidance and Statistical Information for In Vitro Bioequivalence Data Posted on August 18, 1999

Administrative draft guidance, not enacted legislation. This captured publisher edition preserves the listed document and attachments; later developments are not independently consolidated.

Statistical Information from the June 1999 Draft Guidance
and
Statistical Information for In Vitro Bioequivalence Data Posted on
August 18, 1999
Statistical analysis method recommendations for in vitro nonprofile bioequivalence data, to
accompany the draft guidance for industry entitled Bioavailability and Bioequivalence Studies for
Nasal Aerosols and Nasal Sprays for Local Action (April 2, 2003), are under development. At a
later time, the analysis methods will be posted. Until these methods are prepared, two documents,
both in need of updating, are being made available in the present document. These documents are
the original statistical information taken from the earlier June 1999 draft of this guidance, and also
from the added Statistical Information for In Vitro Bioequivalence Data material posted on August
18, 1999. The subsequent implementation will include the estimation of within canister (between
life stage) component of variance.
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FROM THE DRAFT JUNE 1999 GUIDANCE
IX. 	STATISTICAL ANALYSES
B. 	IN VITRO BE DATA: NONPROFILE ANALYSES USING A CONFIDENCE
INTERVAL APPROACH
Nonprofile analyses should be applied to the following tests: (1) dose or spray content uniformity
through container life; (2) droplet size distribution; (3) spray pattern; and (4) priming and/or
repriming, when this information is specified in the labeling.
1. 	Study Protocol
Data for the BE criterion should be based on testing a suitable number of bottles or canisters from
each of three batches of the T and R drug products. Each bottle or canister should be tested for the
measure (parameter) of interest at beginning and end, or beginning, middle, and end of unit life, as
indicated in section V and Table 1. Rather than evaluate performance at each life stage separately,
a criterion is recommended that combines the multiple life stages. In doing so, the multiple life
stages are considered as providing measures of the same underlying quantity. The recommended
criterion considers deviations from uniformity across bottle or canister life stages; results are
ideally uniform. Lack of uniformity between life stages should be treated as another variance
component in the criterion.
For suspension formulation nasal sprays and solution formulation and suspension formulation nasal
aerosols, the number of canisters or bottles (units) of product to be studied should not be fewer than
30 for each of the test and reference products (i.e., no fewer than 10 from each of three batches).
For solution formulation nasal sprays, no fewer than 10 units from each of the three batches or
three sublots should be studied. The number of units is a function of T to R product means and
variances. Estimates of these mean differences and variances will necessitate pilot studies.
2. 	Criterion for Comparisons, Confidence Interval, and Bioequivalence Limit
The equivalence approach for nonprofile tests relies on (1) a criterion to allow the comparison, (2)
a confidence interval for the criterion, and (3) a BE limit for the criterion.
a. 	Criterion for comparison
The in vitro population BE criterion and BE limit are:
2 	2 	2
(μ 	− μ 	) 	+ 	(σ 	− σ 	)	T 	R 	T 	R
2 ≤ 	θ
σ R
where:
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:T, :R 	= 	T and R means (log scale)
FBT, FBR 	= 	between batch T and R standard deviations (log scale)
FCT, FCR 	= 	between canister T and R standard deviations (log scale)
F2R 	= 	F2BR + F2CR + F2LR
F2T 	= 	F2BT + F2CT + F2LT
FLT, FLR 	= 	within T and R canister between life stage standard deviation
2 	= 	in vitro BE (upper) limit
The overall means for the two formulations should be averaged over all bottles or canisters, life
stages (except for priming and repriming evaluations), and batches.
The general approach should be to calculate a 95 percent upper bound for the criterion. If this
upper bound is less than or equal to the upper limit, 2, the test product may be judged to be
bioequivalent to the reference product at the 5 percent level. The criterion will be further discussed
in the guidance for industry on In Vivo Bioequivalence Studies Based on Population and Individual
Bioequivalence Approaches (draft December 1997), when finalized. A population, rather than
average, bioequivalence criterion is recommended in order to estimate whether the test product may
be more variable than the reference product. The test product should be as or more consistent in
the delivery of drug than is the reference product. An individual BE approach is not appropriate for
in vitro data because there are no subjects, thus no subject-by-formulation interaction.
b. 	Determining a 95 percent upper bound
CDER recommends that a method of moments approach be used for estimating the means
and variances needed to determine the population bioequivalence criterion. Approaches based on
restricted maximum likelihood (REML) may be used in special cases. For determining the 95
percent upper bound, CDER recommends using a method analogous to one proposed for individual
bioequivalence (Hyslop, Hsuan and Holder 1998).
c. 	Specification of the population BE upper limit
The general form of the upper limit, 2, is analogous to the form of the population BE criterion,
which is
(mean difference in natural log scale)2 + variance terms
comparison variance
The corresponding form for the upper limit is then
(average BE limit in natural log scale)2 + variance terms offset
scaling variance
This formula contains three values to be specified: (1) average BE limit, (2) variance terms offset,
(3) and scaling variance. These values will be specified when this guidance is finalized based on
simulation work now in progress.
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Average BE Limit
Due to the low variability of in vitro measurements, at the present time CDER recommends that the
limit not be larger than 90/111 (i.e., the ratio of geometric means would fall within 0.90 and 1.11).
A value of 0.90 is tentatively recommended as the average BE limit. This value should be used in
calculating the population BE limit (refer to 2 in the equation in section IX.B.2.a, above).
Variance Terms Offset
This value arises to allow some difference among the total variances that may be inconsequential.
In this regard, the variance terms offset is analogous to the average BE limit. The variance terms
offset also helps correct for the effect on power and sample size for the need to estimate the
variances. Because of the low variability of in vitro measurements, the variance terms offset,
denoted ,P in the draft guidance on In Vivo Bioequivalence Studies Based on Population and
Individual Bioequivalence Approaches (December 1997), when finalized, should be taken as 0.0.
CDER is also considering ,P equal to 0.01.
Scaling Variance
This value adjusts the BE criterion depending on the reference product variance. When this
variance is greater than the scaling variance, FT0 2, the limit is widened. When this variance is less
than the scaling variance, the limit is narrowed.
Mixed scaling should be employed for in vitro studies, as described in the draft guidance on In Vivo
Bioequivalence Studies Based on Population and Individual Bioequivalence Approaches
(December 1997), when finalized. With mixed scaling, when the reference variance in the study is
less than the scaling variance, the population BE criterion should be modified to its constant-scaled
form:
2 	2 	2
(μ 	− 	μ 	) 	+ 	(σ 	− 	σ 	)T 	R 	T 	R
σ 2
T0
Mixed scaling is used to avoid penalizing test products for cases with very low reference variance.
It is CDER's current intent to select FT0 for in vitro studies so that most studies will use constant
scaling and thus, that FT0 will be at least 0.10.
The upper limit may be interpreted by reference to a population distance ratio (PDR). The PDR is
the ratio of the test-reference distance (in the log scale) to the reference-reference distance. In
contrast to individual BE, the distances for population BE are based on administration to separate
individuals (further details will be provided in the guidance for industry on In Vivo Bioequivalence
Studies Based on Population and Individual Bioequivalence Approaches (draft December 1997),
when finalized. The population BE criterion, denoted by PBC, is related to the PDR by
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1
PDR = 

 1 	+ PBC 


2
2
Substituting the BE limit 2 for PBC expresses the upper limit in the PDR scale. The specification
of 0.90 for the average limit, 0.0 for the variance offset, and 0.10 for the scaling standard deviation
corresponds to an upper limit for PDR of 1.25.
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STATISTICAL INFORMATION FOR IN VITRO
BIOEQUIVALENCE DATA
(Originally posted August 18, 1999)
BIOAVAILABILITY AND BIOEQUIVALENCE STUDIES FOR NASAL AEROSOLS AND
NASAL SPRAYS FOR LOCAL ACTION
IN VITRO NONPROFILE BIOEQUIVALENCE DATA:
POPULATION BIOEQUIVALENCE - PARALLEL DESIGNS
Method for Statistical Test of Population Bioequivalence Criterion
Since three batches are not sufficient to reliably estimate the between batch component of variance,
the total variances are estimated as the between canister variance of the "super-batch" consisting of
the three batches combined. In addition, this initial implementation does not include the estimation
of within canister (between life stage) component of variance.
Criterion:
Following the method developed by Hyslop, Hsuan, and Holder (1999) for the individual
bioequivalence criterion, we propose the following method for testing this criterion. The procedure
involves the computation of a test statistic which is either positive (does not conclude population
bioequivalence) or negative (concludes population bioequivalence). This method is based on the
work of Howe (1974) and Ting et al. (1990). The method outlined below assumes equal numbers
of canisters per batch, and that three batches for each product will be combined as one "super-
batch" for each product for analysis.
Notation:
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:
: 	Number of canisters per batch, for T and R products
: 	Number of batches of T and R products
: 	Mean difference of T and R products
: 	Total variance of T and R products
Regulatory constants

Linearized Criteria:
, 	for σR > σT0
, 	for σR ≤ σT0
Estimating the Linearized Criteria:
Begin by computing the separate means and variances for the log of the measure of each product.
Since three batches is not sufficient to reliably estimate the between batch component, the total
variances are estimated as the between canister variance of the "super-batch" consisting of the three
batches combined. Compute the total sum of squares for each product and denote them as SSTT
Estimate the overall means of each product and compute:
and SSTR . Compute: 	and 	(Searle).
.
To test for population bioequivalence, compute the 95% upper confidence bound of either the
reference-scaled or constant-scaled linearized criterion. The procedure for computing this is
described in the next paragraphs. If this upper bound is negative, conclude population
bioequivalence. If the upper bound is positive, do not conclude population bioequivalence.
95% Upper Confidence Bounds of Components:
Use the estimated total variance for T and for R based on
lT*nT-1 and
lR*nR -1 degrees of freedom
where nT and n R are the number of canisters in each of the T and R batches and
lT,
lR are the number
of batches of each product.
Using methods developed by Lee and Gurland for the Behrens-Fisher problem and the estimation
method provided by Lee and Fineberg, compute two-sided confidence interval for 	based on the
total variances.
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using the two-sided interval obtained for	Let 	,
which is described above (Hsu et al, 1994).
Let 	, compute
Let E2rs= 	, compute
Let E2cs= 	, compute
For each component above, also compute 	.
95% Upper Confidence Bounds for Linearized Criteria:
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References
Howe W.G., “Approximate confidence limits on the mean of X+Y where X and Y are two tabled
independent random variables”. J Amer Statist Assoc, 69:789-794, 1974.
Hsu J.C., J.T.G.Hwang, H.-K. Liu, and S.J. Ruberg, “Confidence intervals associated with tests for
bioequivalence”. Biometrika, 81: 103-114, 1994.
Hyslop T., F. Hsuan, D.J. Holder, "A small-sample confidence interval approach to assess
individual bioequivalence," Submitted, 1999.
Lee A.F.S., J. Gurland, "Size and power of test for equality of means of two normal populations
with unequal variances," J Amer Statist Assoc, 70, 933-941, 1975.
Lee A.F.S., N.S. Fineberg, "A fitted test for the Behrens-Fisher problem," Comm Statist- Theory
Meth, 20, 653-666, 1991.
Searle S.R., Linear Models. John Wiley and Sons, New York, 1997.
Ting N., R.K. Burdick, F.A. Graybill, S. Jeyaratnam, T.-F.C.Lu, “Confidence intervals on linear
combinations of variance components that are unrestricted in sign”. J Statist Computation and
Simulation, 35, 135-143, 1990.
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