Statistical Information from the June 1999 Draft Guidance 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accompany the draft guidance for industry entitled Bioavailability and Bioequivalence Studies for 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. 
5383stats.doc 
04/10/03  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
T R  T R     
  2 
R 
where: 
5383stats.doc 
04/10/03  : , : =  T and R means (log scale) 
T R 
F , F   =  between batch T and R standard deviations (log scale) 
BT BR 
F , F   =  between canister T and R standard deviations (log scale) 
CT CR 
F2   =  F2  +  F2  +  F2
R BR CR LR 
F2   =  F2  +  F2  +  F2
T BT CT LT 
F , F =  within T and R canister between life stage standard deviation 
LT LR 
 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. 
5383stats.doc 
04/10/03  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 ,  in the draft guidance on In Vivo Bioequivalence Studies Based on Population and 
P
Individual Bioequivalence Approaches (December 1997), when finalized, should be taken as 0.0. 
CDER is also considering ,  equal to 0.01. 
P
Scaling Variance 
This value adjusts the BE criterion depending on the reference product variance.  When this 
variance is greater than the scaling variance, F 2, the limit is widened.  When this variance is less 
T0  
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
      +      
T R  T R 
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  F  for in vitro studies so that most studies will use constant 
T0
scaling and thus, that F  will be at least 0.10. 
T0
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 
5383stats.doc 
04/10/03  1 
 PBC
 2 
PDR
 =
  1
 +
 

 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. 
5383stats.doc 
04/10/03  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: 
:  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 
5383stats.doc 
04/10/03  Linearized Criteria: 
,    for  >  
R  T0 
,    for    
R  T0 
 
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 SST
T 
and SST . Compute:  and  (Searle). 
R    
Estimate the overall means of each product and compute: 
. 
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 l*n -1 and l*n -1 degrees of freedom 
T T R R
where n and n  are the number of canisters in each of the T and R batches and l,l are the number 
T  R T  R
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. 
5383stats.doc 
04/10/03  Let  ,  using the two-sided interval obtained for 
   
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: 
5383stats.doc 
04/10/03  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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