Drug Information Journal, Vol. 35, pp.

865–874, 2001 0092-8615/2001

Printed in the USA. All rights reserved. Copyright  2001 Drug Information Association Inc.

GUIDELINES ON DISSOLUTION
PROFILE COMPARISON

GUDRUN FREITAG
Ruhr-Universität Bochum, Abteilung für Medizinische Informatik, Biometrie und Epidemiologie,
Bochum, Germany

This article presents a short review on guidelines for dissolution profile testing, particu-
larly focusing on the recommendations regarding statistical methods for assessing profile
similarity. In this context, the guidelines on in vitro/in vivo correlations and on granting
biowaivers are outlined briefly. The comparison of two dissolution profiles can be per-
formed in different ways. There are many model-dependent and model-independent proce-
dures suggested in the methodical literature. Current guidelines primarily recommend
the application of a method based upon the f2 statistic as a measure of the similarity of
two dissolution curves, though this procedure has often been criticized recently. The goal
of this article is to give a survey of the current guidelines, including a description and
discussion of the recommended methods for data analysis.

Key Words: Dissolution profiles; Equivalence testing; In vitro/in vivo correlation; Bio-
waivers

INTRODUCTION main applications of dissolution testing are for

oral dosage forms, but it is also used for other
THE DISSOLUTION characteristics under
drug delivery routes, for example, for transder-
physiological conditions of a solid dosage
mal delivery.
form of a drug are influential on its in vivo
In the development stage of a new drug
absorption. Thus, the in vitro dissolution may
product building up certain dissolution speci-
be relevant for the prediction of the in vivo
fications is commonly required; these can
performance of a drug product. The impor-
then be used as a yardstick for quality control
tance of the dissolution properties depends par-
of the drug product. Usually, the dissolution
ticularly upon the release form of the drug
specifications are constructed from the range
product, for example, whether it is an immedi-
of dissolution values found in the lot used in
ate release or an extended release product, and
the pivotal (in vivo) bioavailability study, or
on the solubility and permeability properties
from the range of values found from different
of the drug product. In vitro dissolution testing,
lots produced during the development phase.
that is, the determination of the rate and extent
Based upon those specifications, dissolution
of drug release in an in vitro experiment, is
testing can then be used for assessing the lot-
well established as a monitoring technique for
to-lot quality of a drug product, for ensuring
the performance of a drug product, and it is
a continuous drug product quality and per-
routinely used in the development and quality
formance after certain minor postapproval
control of drugs and medicinal products. The
manufacturing changes (eg, minor changes
in formulation, or in the scale-up of the man-
Reprint address: Gudrun Freitag, Ruhr-Universität Bo- ufacturing process), and for guiding the de-
chum, Abteilung für Medizinische Informatik, Biomet- velopment of new formulations of the drug
rie und Epidemiologie, D-44780, Bochum, Germany. substance.
865
866 Gudrun Freitag

For the approval of generic drugs, or GENERAL RECOMMENDATIONS

of drugs that have undergone larger postap-
Most of the guidelines considered here deal
proval changes, conducting bioavailability/
with the conduct of BA/BE studies for ge-
bioequivalence (BA/BE) studies, in which
neric drug products or for drug products hav-
the rate and extent of drug absorption in hu-
ing undergone certain postapproval changes,
mans is evaluated and must be shown to be
for example, in the manufacturing procedure
equivalent to the approved reference product,
of the drug (see, for example, 1–10). For
is generally required. In vitro dissolution
each type of change, the FDA guidances pro-
testing usually must be performed as comple-
vide detailed recommendations on:
mentary to the in vivo bioavailability investi-
gations. Here the comparison of dissolution
• The different levels of change (there are
profiles, that is, of dissolution measurements
always up to three levels of change to be
at multiple time points, is required. In certain
distinguished; Level 1 changes are smallest
situations, when a high in vivo/in vitro corre-
and Level 3 changes are greatest,
lation can be shown, dissolution similarity
• The chemistry, manufacturing, and controls
becomes a potential surrogate for in vivo
tests required for each level of change,
bioequivalence. Then dissolution testing can
• The in vitro dissolution tests and the in
be of use for achieving biowaivers, that is,
vivo BE tests required for each level of
for rendering BA/BE studies unnecessary, if
change, and
equivalence of in vitro dissolution profiles
• The necessary documentation that should
can be shown.
support the change.
Here I present only general, that is, no
product specific, (draft) guidelines on disso-
For dissolution testing, there are always quite
lution profile comparison from the United
precise specifications on:
States Food and Drug Administration (FDA)
and the Committee for Proprietary Medicinal
• The number of individual dosage units of
Products (CPMP). I restrict attention to rec-
test and reference products, usually chosen
ommendations on solid oral dosage forms
as n1 = n2 = 12,
and on topical dermatological drug products.
• The number of sampling time points and
Furthermore, I briefly present guidelines
the corresponding sampling schedule (in
concerning the development of in vivo/in
general more than one time point is re-
vitro correlations and the granting of bio-
quired, except for special cases such as de-
waivers. On the other hand, I would like to
scribed eg, in 2), and
emphasize that pharmacological aspects,
• The different testing conditions that must
methods for the optimization of dissolution
be analyzed, for example, different dissolu-
conditions or for the setting of dissolution
tion media, different pH values, the dissolu-
specifications, or requirements on quality
tion apparatus, different agitation rates,
control are not examined in this review.
temperature, and so forth.
In the next section, I outline some general
recommendations on dissolution testing to be
These requirements mainly depend on the
found in the guidelines under consideration.
dosage form(s) under investigation.
Then I deal with the statistical methods for
dissolution profile comparison that are rec-
ommended in the guidelines. In the section DISSOLUTION PROFILE
after that, I provide an overview on the rec- COMPARISON
ommendations on in vivo/in vitro correla-
Dissolution Profile Data
tions, then focus on the aspect of granting
biowaivers. The recommendations are briefly The data for the comparison of two dissolu-
discussed in the last section. tion profiles are usually of the following
Guidelines on Dissolution Profile Comparison 867

form. There are i = 1, . . . , n1 dosage units of comparison of two single curves, but it can
the reference product and j = 1, . . . , n2 units also be applied to the comparison of several
of the test product under investigation. In curves from two samples, given that all units
cases of equal sample sizes we define n := are tested at the same sampling time points.
n1 = n2. For each unit, the dissolution percent- No distributional assumptions have to be
ages are measured at p different time points made for applying the method. The f2 factor
tk, k = 1, . . . , p. is calculated from the group means of the
Let Xki, Ykj denote the percentage of drug dissolution profiles at each sampling time
dissolved from dosage unit i for the reference point. More precisely, it is given by a func-
drug and for dosage unit j for the test drug, tion of the weighted average of the squared
respectively. The vectors of means at the dif- differences of the group means,
ferent time points for each group shall be
denoted by µX and µY, that is, µX = (µX1, . . . ,
µXp), with µXk = EXk. The corresponding vari-
ance-covariance matrices are denoted by ΣX
冉 冋
f2 = 50 log10 100 1 +
1
p
p

∑
k=1
册冊
wk(X̄k − Ȳk)2
−
1
2 ,

and ΣY, and the elements of their main diago- where the wk are optional weight factors.
nals by σX2k and σY2k, k = 1, . . . , p, respec- Guidelines referring to this statistic always
tively. The vectors of the sample means are assume equal weights wk = 1, k = 1, . . . , p.
given by X̄ = (X̄1, . . . , X̄p) and Ȳ = (Ȳ1, . . . , A value of f2 close to 100 indicates strong
Ȳp), respectively. SX and SY shall denote the similarity of the two mean curves. If the
variance-covariance matrices for the two mean difference at each time point is equal
samples, and the pooled sample variance- to 10 points and the weights are equal to 1,
covariance matrix is given by Sp := (n1 + a value of about 50 is obtained for f2. This
n2 − 2)−1((n1 − 1)SX + (n2 − 1)SY). has lead to the decision rule (the “f2 method”)
recommended in all guidelines proposing the
use of f2 (see, for example, 2), where similar-
Methods for Data Analysis
ity of the curves may be concluded if f2 ∈
The comparison of dissolution profiles can [50,100].
be based upon either model dependent meth- The FDA guidance on immediate release
ods, that is, on fitting a specific dissolution products (2) specifies the sampling schedule
curve to the data of each sample and the for obtaining multipoint dissolution profiles
subsequent comparison of the parameters of in different situations, with the restriction
the two fitted curves, or on model indepen- “until either 90% of drug is dissolved or an
dent methods, where the two profiles are asymptote is reached.” No further conditions
compared only at the observed time points. are given for the use of the f2 method. In the
Most of the guidelines on dissolution pro- FDA guidance on immediate release products
file comparison primarily recommend the (4), the f2 method is suggested for profile
use of the (model independent) f2 method comparison when three to four or more disso-
(see, for example, 2,4,5,8–11). They differ lution time points are available. Only one
at most in the additional requirements for measurement should be considered after 85%
the application of the f2 method or in the dissolution of both products. In addition to
specification of the sampling schedule for the that, it is required “to allow the use of mean
different dosage forms. If dissolution testing data, the percent coefficient of variation at
must be performed in different media, the the earlier time points (eg, up to 15 minutes)
profile comparisons are always allowed to be should not be more than 20%, and at other
performed independently for each medium. time points not more than 10%.”
The f2 method is based upon the similarity The FDA guidance on modified release
factor f2 suggested by Moore & Flanner (12). products (5) recommends that for calculating
Originally this statistic was proposed for the f2 only one point past the plateau of the pro-
868 Gudrun Freitag

files be used. Furthermore, “the average dif- DM = √(X̄ − Ȳ)TS −1

p (X̄ − Ȳ). (3.1)
ference at any dissolution sampling time
point should not be greater than 15% between This approach is suggested, for example, in
the changed . . . and the . . . unchanged drug Tsong et al. (13). It is closely related to the
product dissolution profiles.” It is stated that concept of two-sided equivalence testing (us-
“an f2 value less than 50 does not necessarily ing confidence intervals) in BA/BE studies.
indicate lack of similarity,” and the possibil- The use of Mahalanobis distance instead of f2
ity of the submission of “an appropriate justi- is recommended by FDA (4) for the situation
fication” is pointed out. In such instances, when the “within batch variation is more than
it is required that “this justification should 15% CV,” that is, when the percent coeffi-
include additional data to support the claim cient of variation is larger than 15%.
of similarity, as well as supporting statistical A similarity limit must be determined in
analysis (eg, 90% confidence interval anal- terms of multivariate statistical distance (ie,
ysis).” the Mahalanobis distance) based upon inter-
The CPMP draft note for guidance (9) batch differences in dissolution from refer-
requires a minimum of three time points. Fur- ence batches. However, no exact procedure
thermore, not more than one mean value of for calculating this similarity limit is given.
>85% dissolved should be included. The In practice, this might be done via the calcu-
“standard deviation of the mean should be lation of confidence intervals based upon
<10% from second to last time point.” The suitable data from standard approved batches.
following special situation is distinguished: Tsong et al. (13) suggest using the limit
“In cases where more than 85% of the drug √[Dg]TS p−1[Dg], with [Dg] as the 1x p vector
is dissolved within 15min, the dissolution with all entries equal to a prespecified limit
profiles may be accepted as similar without Dg for the maximum tolerable difference at
further mathematical evaluation.” each time point. The use of Sp is questionable,
The FDA draft guidance (11) does not however, since this yields a similarity limit
restrict the use of the f2 method, but simply depending on the test batches under investi-
states that “in instances where dissolution gation.
profile comparisons are recommended, f2 cri- For the true multivariate statistical dis-
teria should be used.” tance between test and reference batches, the
The FDA guidance (4) recommends using FDA guidance (4) requires the calculation
the f1 difference factor suggested by Moore & of a 90% confidence interval. There are no
Flanner (12) in addition to f2. The f1 statistic further details given regarding how to obtain
represents a measurement of the relative er- this confidence interval. Referring to Tsong
ror between the two mean curves, et al. (13), this could be done, for example,
by calculating a 90% confidence region for

f1 = 100 再冋∑
p

k=1
*X̄k − Ȳk*册'冋∑ 册冎
p

k=1
X̄k .
the true difference between the mean vectors,
µX − µY, as

Clearly, a value of f1 close to 0 indicates

the similarity of the two mean curves. The
CR = y:再 n1n2
(n1 + n2)
[(y − (X̄ − Ȳ))TS p−1
guidance recommends considering values up
to 15 for f1 as indicating the similarity of two
mean profiles; we will call this procedure the 冎
(y − (X̄ − Ȳ))] ≤ Fp,n1+n2−1,0.90
f1 method.
Under the assumption of normality, an- and subsequently determining the minimum
other (‘model independent’) method is based and the maximum multivariate statistical dis-
upon the use of the Mahalanobis distance tance to the original from the elements of
between two vectors of normally distributed CR. Here Fp,n1+n2−1,0.90 denotes the 90th percen-
random variables, tile of the F distribution with degrees of free-
Guidelines on Dissolution Profile Comparison 869

dom p and n1 + n2 − 1. For a given similarity procedure is also suggested in Sathe et al.
limit and a 90% confidence region for µX − (16).
µY, the test batch is considered similar to the A special model-dependent procedure is
reference batch if the upper confidence limit recommended for release testing in the FDA
is less than or equal to the similarity limit. guidance on Scale-Up and Post-Approval
In the following, this procedure will be called Changes (SUPACs) for nonsterile semisolid
the multivariate statistical distance method. preparations (3). A linear model is chosen
The FDA guidance (5) only mentions the for the plots “amount of drug released per
possibility of using other model independent unit area vs. square root of time.” Hence,
methods than f2. Thereby, it refers to the par- the comparison of two drug products can be
ticulars in FDA (4), hence also to the mul- performed with help of the release rates (that
tivariate statistical distance method. The is, the slopes of these plots). In particular,
CPMP notes for guidance (9,10) do not ex- the following nonparametric procedure based
plicitly recommend using the multivariable upon the ratio of release rates is proposed.
statistical distance method. For release testing, an apparatus with six
In the context of dissolution profile test- cells must be used, with alternating applica-
ing, the term model-dependent methods is tion of test (‘t’) and reference (‘r’) in each
used for methods that are based upon para- run. In each run, it is recommended to deter-
metric modeling of the whole dissolution mine release data for every test unit at multi-
curves. The application of a model-depen- ple (≥5) sampling times. In the first stage,
dent procedure is recommended as an alter- two runs of the six cells are performed, yield-
native to the f2 method in FDA (4). However, ing six slopes for ‘r’ and six for ‘t’ each.
there are no clear directions provided for the Based upon this, a nonparametric 90% confi-
choice between the two approaches. For de- dence interval for the ratio of median in vitro
ciding on a specific parametric model, it is release rates ‘t/r’ (in percentage) is con-
suggested “to select the most appropriate structed. To this end, all possible 36 (= 6 ×
model for the dissolution profiles from the 6) individual ‘t/r’ ratios are calculated, and
reference batches,” but without specifying the 8th and the 29th largest of them are used
the criteria for this selection. A model with as the lower and upper confidence bounds cl
no more than three parameters is recom- and cu, respectively. If (cl, cu) is contained in
mended. The commonly used models for de- the interval (75%, 133.33%), then no further
scribing dissolution curves can be found, for testing is considered necessary. If not, there
example, in Tsong & Hammerstrom (14), or should be a second stage with 4 additional
in Tsong et al. (15). Examples suggested in runs, leading to 12 additional (ie, 18 in all)
the guideline are the linear, quadratic, logis- slopes for each product. Then the 90% confi-
tic, probit, and Weibull models. The compari- dence interval for the ratio of median in vitro
son of two drug products is performed in release rates ‘t/r’ (in percentage) based upon
terms of the model parameters. The similari- all 2 × 18 slopes is given by the 110th and the
ty region must be “set based on the varia- 215th of the 324 possible individual ratios.
tion of the parameters of the fitted model for Again, this must be in (75%, 133.33%) in
test units . . . from the standard approved order to conclude similarity. It is stated that
batches.” For the actual comparison of test this procedure “does not take into account
and reference batches, the multivariate statis- the block structure of the test, since there is
tical distance in model parameters between no evidence of an important run-to-run ef-
test and reference batches and a 90% confi- fect, and since both products are included in
dence region for the true difference must be each run, if a run-to-run-effect should occur.”
calculated. If the confidence region is within The FDA draft guidance (7) focuses on
the limits of the similarity region, the test BA/BE studies and related in vitro release
batch is considered to have a similar disso- testing of topical dermatological drug prod-
lution profile to the reference batch. This ucts. Here, in vitro release approaches for
870 Gudrun Freitag

the comparison of lower strength(s) of a ref- proposed by Amidon et al. (17). Here oral
erence and a test product are considered drug products are classified with respect to
when higher strengths of the products have their solubility and permeability characteris-
previously been shown to be bioequivalent tics in the following way:
in a suitable BA/BE study. Again, it is recom-
mended to use the release rates, that is, a • Class 1: High Solubility-High Permeability
linear model, for the analysis. For the investi- Drugs,
gation of a lower strength, in vitro release • Class 2: Low Solubility-High Permeability
rates must be obtained both for the higher and Drugs,
the lower strength of the reference product • Class 3: High Solubility-Low Permeability
(these rates shall be called rh and rl, respec- Drugs, and
tively), and analogously for the test product • Class 4: Low Solubility-Low Permeability
(th and tl). Then the ratio of the release rates Drugs.
of the two strengths of the test product should
be about the same as the ratio of the release The guidance states that this classification
rates of the reference product, that is, “can provide a basis for predicting the likeli-
hood of achieving a successful IVIVC.” In
rh ! th rh ⴢ t l ! particular, “for . . . BCS classes 1 and 3 IR
⬇ ⇔ ⬇ 1.
rl tl rl ⴢ t h products using currently available excipients
and manufacturing technology, an IVIVC
For the right hand side, it is suggested that may not be possible. For poorly water soluble
“using appropriate statistical methods, the products, BCS class 2, an IVIVC may be
standard BE interval (80, 120) for a lower possible.” Furthermore, it is suggested that
strength comparison of test and reference rapidly dissolving BCS class drugs “should
products should be used.” However, no de- not have any bioavailability problems,”
tails regarding the appropriate statistical whereas Class 4 drugs “present significant
methods are given. problems for oral drug delivery.” It is pro-
FDA (5,6) and CPMP (9,10) provide fur- posed that to achieve an in vitro/in vivo cor-
ther guidelines mentioning model-dependent relation, at least three batches that differ in
methods. The latter two suggest using the the in vivo as well as the in vitro perfor-
linear or Weibull model, but there is no mances should be available.
detailed description of the procedure to be The FDA guidance (6) focuses on in vitro/
used. in vivo correlations for extended release dos-
age forms, for which an in vitro/in vivo cor-
IN VITRO/IN VIVO CORRELATION relation is especially important. The guid-
The importance of dissolution testing mainly ance presents a classification of in vitro/in
depends upon the strength of the relationship vivo correlations into several levels, which
between the in vitro dissolution characteris- have been used since 1988. Most important
tics of a drug product and the rate and extent (and recommended, if possible) is the so-
of its in vivo bioavailability. Therefore, it is called Level A correlation, which is defined
essential to evaluate in vitro/in vivo correla- via the relationship between the whole in
tions (IVIVC). The main applications of an vitro dissolution curve and the plasma con-
in vitro/in vivo correlation are the setting of centration-time curve of a drug product. Rec-
dissolution specifications for new drug prod- ommendations are provided for the develop-
ucts and the possibility of granting biowaiv- ment of a Level A in vitro/in vivo correlation
ers for changes in the manufacturing of a (see, for example, 18,19,20), as well as for
drug product (see, for example, the next sec- the evaluation of its internal predictability
tion). (based upon the initial data) and of its exter-
The FDA guidance (4) refers to the Bio- nal predictability (with the help of additional
pharmaceutics Classification System (BCS) test data). The CPMP note for guidance (10)
Guidelines on Dissolution Profile Comparison 871

principally makes the same recommenda- profile comparison, and do not use an in
tions. vitro/in vivo model. This refers to the bio-
waivers defined in the FDA SUPAC-MR
guidance (2) “that do not necessitate either
BIOWAIVERS
BE testing or an IVIVC.” Furthermore, in
The FDA SUPAC-IR guidance (2) mentions situations where the SUPAC-MR guidance
two potential cases for achieving biowaivers. recommends a biostudy, the possibility of
The first is the situation of Level 2 compo- biowaviers for lower strengths of a drug
nents and composition changes in BCS Class product is stated, if “BE has been demon-
1 drugs with dissolution of 85% in 15 min- strated on the highest strength (comparing
utes. The second is given in cases of the changed and unchanged drug product)” and
similarity of certain multipoint dissolution if several additional conditions are met. The
profiles after Level 2 or 3 components and three other categories of biowaivers are based
composition or manufacturing process changes, upon using an established in vitro/in vivo
where an acceptable in vitro/in vivo correla- correlation model. Here the plasma concen-
tion has been verified. trations for test and reference product, which
The FDA guidance (3) briefly discusses are predicted from the model on the basis of
the evidence available at that time about the dissolution data, must be used for assessing
value of in vitro release testing for nonsterile the similarity in BA of the two drug products.
semisolid preparations, concluding in partic- More specifically, the differences in pre-
ular that “in vitro release testing, alone, is dicted means of Cmax and AUC must be within
not a surrogate test for in vivo BA or BE.” specified limits, depending on the particular
In the FDA SUPAC-IR guidance (2), the situation at hand. Again, this refers to the
possibility of waiving BE requirements for possible biowaivers defined in FDA (5). In
lower strengths of a dosage form is con- addition to those there are potential biowaiv-
sidered. It is suggested that “for multiple ers for lower strengths described.
strengths of IR products with linear kinetics, For oral immediate release forms with
the BE study may be performed at the highest systemic action, the CPMP (draft) note for
strength and waivers of in vivo studies may guidance (9) provides an example for a case
be granted on lower strengths, based on an where in vitro data alone would be accept-
adequate dissolution test.” Similar conditions able. Here all of the following criteria must
are given in the CPMP (draft) note for guid- be fulfilled: the drug has no narrow therapeu-
ance (9). Refer also to the remarks in the tic range, the first pass metabolism is <70%,
FDA guidance (8) with respect to biowaivers the drug has linear pharmacokinetics within
for lower strengths, based upon dissolution the therapeutic range, it is highly water solu-
similarity via the f2 statistic. ble, rapidly dissolved, and highly permeable
The FDA SUPAC-MR guidance (2) states in the intestine (the extent of absorption is
the possibility of achieving biowaivers for greater than 80%), and the excipients of the
several situations. For most Level 3 changes medicinal product are well established (and
and some Level 2 changes, the conduct of no interaction with the pharmacokinetics of
a BE study is required in addition to the the active substance is expected). Then a BE
comparison of dissolution profiles. However, study may be waived based upon “no case
in these cases it is stated that “the BE study history of BA problems and similarity of dis-
may be waived in the presence of an estab- solution profiles which are based on discrim-
lished IVIVC,” referring to FDA (6) for fur- inatory testing.” The similarity should be jus-
ther details. tified by dissolution profiles covering at least
The FDA guidance (6) presents four cate- three time points, and attained at three differ-
gories of biowaivers for extended release oral ent buffers.
dosage forms. The first category comprises In the FDA draft guidance (11), similar
biowaivers that are based only on dissolution conditions are set up for BCS Class 1 drugs.
872 Gudrun Freitag

It is stated that to request a waiver of in vivo is no rationale given for the choice of (75,
BA/BE studies, the drug should be rapidly 133) as the equivalence interval.
dissolving, highly soluble, and highly perme- As indicated above, the f2 method has been
able, it should show a dissolution >85% in 30 extensively investigated recently. Simula-
minutes in three recommended dissolution tions on the f2 method can be found, for ex-
media, have a nonnarrow therapeutic index, ample, in O’Hara et al. (21) and Ju & Liaw
the stability of active substance in medium (22). Some points of criticism with respect
of the gastrointestinal tract should be assured to the use of the f2 method are listed below:
as >95%/3 hours, the excipients should be
well established and unproblematic, and the • The f2 method is highly liberal in deciding
similarity of dissolution profiles for test and for similarity (see, for example, 23,24),
reference products should be shown using • The formulation of a precise statistical hy-
the f2 metric. pothesis is impossible due to the fact that
f2 itself is a sample statistic and its expected
DISCUSSION value is not known; hence, it is not possible
to evaluate the false positive and false nega-
The guidelines usually contain detailed re- tive rates (see, for example, 22,23,25),
quirements concerning the testing conditions • The f2 statistic does not take account of the
for dissolution testing. On the other hand, variability or the correlation between time
the recommendations with respect to the use points in the dissolution data (see, for ex-
of statistical methods for analyzing the disso- ample, 21,26), and
lution data are often not very precise. In the • The value of f2 is very sensitive to which
following, we focus only on the issue of com- time points are chosen for dissolution mea-
paring dissolution profiles. surements, especially after the plateau has
Almost all guidelines on dissolution pro- been reached (see, for example, 24,27).
file comparison strongly recommend using
the f2 statistic, in spite of all the disadvantages A possible improvement of the f2 method
of this method that have been discussed in is presented in Shah at al. (26). There, a
the methodological literature since its intro- population measure corresponding to f2 is in-
duction in the FDA guidance (2). This cir- troduced, which we denote by f 02,
cumstance is probably based upon the sim-

冉 冋 册冊
plicity of the method. An advantage for its p 1
1 −
practical use is certainly the fixed similarity
limit of 50 that was established in recent
f 20 := 50 log10 100 1 +
p
∑ (µ
k=1
Xk − µYk)2 2

冉 冊
years. For the multivariate statistical differ-
1
ence method and the model-dependent proce-
dure suggested by FDA (4), there are only
= 100 − 25 log10 1 +
p
∑ (µ Xk − µYk)2 .

vague recommendations concerning the

choice of the equivalence limits. In contrast Note that here the weights are chosen as wk =
to guidelines on statistical methods for show- 1, k = 1, . . . , p. It is shown that the f2 statistic
ing BE, the similarity limits for the above (with weights equal to 1) is a biased estimate
methods for dissolution profile comparison of f 20, which can be seen from the approxima-
are primarily related to absolute changes in tion
percentages, rather than relative changes. An

冉
exception is given by the methods using re- p
1
lease rates in the FDA guidances (3,7). In E(f2) ⬇ 100 − 25 log10 1 +
p
∑ (µ Xk − µYk)2
this respect, is should be noted that the FDA k=1

冊
guidance (7) erroneously states the “standard p
1
BE interval” as (80,120), instead of (80,125).
For the method proposed by FDA (3), there
+
p
∑ (σ
k=1
2
Xk + σYk
2
)/n ,
Guidelines on Dissolution Profile Comparison 873

for n1 = n2 =: n ( f2 is asymptotically unbi- use of the multivariate statistical difference

ased, for n → ∞) (see, for example, 23,25). method is not appropriate. However, the
Shah et al. (26) propose the calculation of a guidelines proposing their use do not provide
90% confidence interval for E( f2) based upon clear directions as to when they are to be
the bootstrap method and the comparison of applied instead of the f2 method. A (minor)
its lower limit with a prespecified similarity advantage of the model-dependent methods
limit, for example, the established value of is that they allow for unequal time points in
50. This is seen to be a conservative test the different units tested. The main problem
procedure for the hypotheses H0 : f 20 ≤ 50 here is the choice of the right model. Also,
versus H1 : f 20 > 50. In the following, we will it might be that a model suitable for the refer-
refer to this method as the f 20 method. The f 20 ence product does not well fit to the data
method is examined in a simulation study in of the test product. However, there are no
Ma et al. (28). It is seen that for n = 12 dosage recommendations on model selection to be
units in each group it is only mildly conserva- found in the guidelines. For applications or
tive and provides adequate power when the discussions of model-dependent methods
two profiles are, in fact, similar. Overall, it see, for example, Tsong et al. (13), or Polli
is concluded that the f 20 method is adequate et al. (27). For using the procedure recom-
for the assessment of similarity of dissolution mended by the FDA (4), the assumption of
profiles. It remains to be seen whether this normality with equal variance-covariance
bootstrap-based method will replace the cur- matrices must be made for the estimators of
rent f2 method in future guidelines on disso- the parameter vectors for each sample. Since
lution profile comparison. the comparison is based upon the multivari-
The use of the multivariate statistical dif- ate statistical differences, it will again be
ference method is restricted to the assump- more likely to conclude for similarity in cases
tion of normality and equal variance-covari- of large variations in these estimators.
ance matrices. The number of sampling time
points must be small (see, for example, 13),
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