# A new principal component analysis-based approach for testing "similarity" of drug dissolution profiles.

**ABSTRACT** A new approach for testing batch "similarity" through comparison of drug dissolution profiles, based on principal component analysis with the establishment of a confidence region (PCA-CR), is presented. The dissolution curves corresponding to three brands each of Furosemide and Acetaminophen tablets, taken as model drugs, were prepared by dissolution measurements at multiple pre-specified time points. Reference and test data were simultaneously subjected to PCA and pairwise comparisons between the dissolution characteristics of lots of the same and different brands were carried out. The comparisons involved plotting the weighed scores of the first two principal components of reference and test lots, while decision about "similarity" was made by checking for inclusion of more than 80% of the tablets of the test lot in the 95% confidence ellipse of the reference samples. Two published datasets were also analyzed in the same fashion and all the results were compared with information provided by the difference (f1) and similarity (f2) factor tests. Unlike the f2 criterion, the proposed method reflects variability within the individual dissolution curves, being also highly sensitive to profile (shape and size) variations. Comparison between the area enclosed by the confidence ellipses of the weighed scores plot and the region obtained from the bootstrap-calculated acceptable values of the corresponding f2 tests suggested that PCA-CR represents, in general, a more discriminating standard.

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- Hai-yan Li, Xiang-yong Cui, Feng Gao, Peter York, Qun Shao, Xian-zhen Yin, Tao Guo, Zhen Guo, Jing-kai Gu, Ji-wen Zhang[Show abstract] [Hide abstract]

**ABSTRACT:**It is essential to develop effective methods for the quality control of the traditional medicine with multiple components. However, few researches on the quality control have been conducted to interpret the holistic characteristics of the traditional medicine in terms of dissolution/release. In this study, the multi-component release kinetics of Traditional Chinese Medicine (TCM) dosage forms was characterized and mapped by multivariate analysis techniques in the field of “-omics”. The Liuweidihuang pill was used as a model formulation. The multi-component release kinetics of the concentrated and water-honeyed Liuweidihuang pills at rotation speeds of 50 and 100 rpm were analyzed by chemomic release kinetic theory and modified LC/MS/MS method. Mass features of 103 (concentrated pills) and 101 (water-honeyed pills) were selected with a linear correlation coefficient ≥0.99 between mass responses and concentrations. To compose the chemomic standard spectrum, the relative abundance of both mass features was no less than 1% as compared with an internal standard. The correlation coefficients between six samples of various solutions were in line with analytical requirements of precision (r≥0.985). The score plots of principal component analysis showed that the concentrated Liuweidihuang pills presented better chemomic release reproducibility than the water-honeyed pills. Conversely, the impact of rotation speed on the chemomic release was less obvious. The heat maps of hierarchical clustering analysis did not show significant changes in individual clusters of mass features along different time intervals, reflecting the release integrity of the mass features. Therefore, both multivariate analysis methods, the principal component analysis and the hierarchical clustering analysis, seemed to be effective techniques to demonstrate the multiple component release performance of TCM. The research provided the basis of a new strategy for the quality control procedures of the dissolution/release for the traditional medicine and multi-component natural products to address increasing regulatory requirements and scrutiny across the world.Acta Pharmaceutica Sinica B. 08/2011; 1(2):106–114. - SourceAvailable from: tifnet.com.br[Show abstract] [Hide abstract]

**ABSTRACT:**This paper presents the use of experimental design, optimization and multivariate techniques to investigate root-cause of tablet dissolution shift (slow-down) upon stability and develop control strategies for a drug product during formulation and process development. The effectiveness and usefulness of these methodologies were demonstrated through two application examples. In both applications, dissolution slow-down was observed during a 4-week accelerated stability test under 51°C/75%RH storage condition. In Application I, an experimental design was carried out to evaluate the interactions and effects of the design factors on critical quality attribute (CQA) of dissolution upon stability. The design space was studied by design of experiment (DOE) and multivariate analysis to ensure desired dissolution profile and minimal dissolution shift upon stability. Multivariate techniques, such as multi-way principal component analysis (MPCA) of the entire dissolution profiles upon stability, were performed to reveal batch relationships and to evaluate the impact of design factors on dissolution. In Application II, an experiment was conducted to study the impact of varying tablet breaking force on dissolution upon stability utilizing MPCA. It was demonstrated that the use of multivariate methods, defined as Quality by Design (QbD) principles and tools in ICH-Q8 guidance, provides an effective means to achieve a greater understanding of tablet dissolution upon stability.European journal of pharmaceutics and biopharmaceutics: official journal of Arbeitsgemeinschaft fur Pharmazeutische Verfahrenstechnik e.V 12/2010; 78(1):141-50. · 3.15 Impact Factor - SourceAvailable from: Teodoro S Kaufman[Show abstract] [Hide abstract]

**ABSTRACT:**A simple chemometric approach to differentiate among the three crystalline polymorphs of the model drug Furosemide (FUR) in a pharmaceutical dosage form is presented. The proposed method is based on the principal component analysis with confidence regions (PCA-CR) comparison of the dissolution profiles of the test pharmaceutical formulation, and formulations containing the different polymorphs, employed as the corresponding references. For the elaboration of the references, FUR polymorphs I, II and III were prepared, characterized and compounded with the excipients found in the test commercial formulation. The dissolutions were carried out in a discriminating HCl-KCl dissolution medium (pH 2.2), and the corresponding profiles were constructed from the absorbances (274 nm) of the dissolution samples. PCA-CR was able to differentiate among the three crystalline polymorphs of FUR and to confirm the presence of polymorph I in the test sample, with 99% statistical confidence. The PCA-CR results were compared with those obtained by a bootstrap-mediated implementation of Moore and Flanner's difference factor (f(2)). The same conclusion was reached employing an f(2)-based comparison, despite its inability to differentiate between polymorphs II and III. Therefore, PCA-CR may be considered a complementary and useful tool for probing the polymorphic form present in a pharmaceutical formulation.International Journal of Pharmaceutics 06/2009; 378(1-2):187-93. · 3.99 Impact Factor

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/ejps

A new principal component analysis-based approach for

testing “similarity” of drug dissolution profiles

Rub´ en M. Maggioa,∗, Patricia M. Castellanoa, Teodoro S. Kaufmana,b,∗∗

aSchool of Biochemical and Pharmaceutical Sciences, National University of Rosario, Suipacha 531, S2002LRK Rosario, Argentina

bInstitute of Chemistry of Rosario (IQUIR, CONICET-UNR), Suipacha 531, S2002LRK Rosario, Argentina

a r t i c l e i n f o

Article history:

Received 19 December 2007

Received in revised form

14 February 2008

Accepted 20 February 2008

Published on line 4 March 2008

Keywords:

Principal component analysis

Dissolution profiles

Similarity test

Acetaminophen

Furosemide

Multivariate method

a b s t r a c t

A new approach for testing batch “similarity” through comparison of drug dissolution

profiles, based on principal component analysis with the establishment of a confidence

region (PCA-CR), is presented. The dissolution curves corresponding to three brands each

of Furosemide and Acetaminophen tablets, taken as model drugs, were prepared by disso-

lution measurements at multiple pre-specified time points. Reference and test data were

simultaneouslysubjectedtoPCAandpairwisecomparisonsbetweenthedissolutioncharac-

teristics of lots of the same and different brands were carried out. The comparisons involved

plotting the weighed scores of the first two principal components of reference and test lots,

while decision about “similarity” was made by checking for inclusion of more than 80% of

the tablets of the test lot in the 95% confidence ellipse of the reference samples. Two pub-

lished datasets were also analyzed in the same fashion and all the results were compared

with information provided by the difference (f1) and similarity (f2) factor tests. Unlike the f2

criterion, the proposed method reflects variability within the individual dissolution curves,

being also highly sensitive to profile (shape and size) variations. Comparison between the

area enclosed by the confidence ellipses of the weighed scores plot and the region obtained

from the bootstrap-calculated acceptable values of the corresponding f2tests suggested that

PCA-CR represents, in general, a more discriminating standard.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

In vitro dissolution testing is an economic and useful quality

control tool to effectively assure acceptable product quality

during different stages of the development and production of

tablets, capsules and other solid dosage forms (Dressman and

Kramer, 2005). The test enables detection of the influence of

key manufacturing factors including excipients, binder and

mixing effects, as well as granulation procedure and coating

parameters,providingbettercontroloftheproductionprocess

and assuring consistent batch to batch quality of the product.

∗Corresponding author.

∗∗Corresponding author at: School of Biochemical and Pharmaceutical Sciences, National University of Rosario, Suipacha 531, S2002LRK

Rosario, Argentina.

E-mail address: kaufman@iquios.gov.ar (T.S. Kaufman).

0928-0987/$ – see front matter © 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.ejps.2008.02.009

The dissolution has also been employed in product develop-

ment and during dosage form optimization to assist in proper

formulation selection. In addition, it has served as a means

to compare different formulations (Naylor et al., 1993) and

determine final dissolution specifications for pharmaceutical

dosage forms (Elkoshi, 1999).

The dissolution test has also been used during stability

studies, helping establish shelf life, and it has been recognized

asanimportantinvitroparameteroftablets’qualitybecauseof

its correlation with drug bioavailability (Williams et al., 1991;

Fassihi and Ritschel, 1993; Munday and Fassihi, 1995; Grundy

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

67

et al., 1997). As a result, under certain strictly defined condi-

tions, the test can also be employed as a surrogate of in vivo

studies for the assessment of product bioequivalence, helping

to reduce costs by circumventing the need to perform human

volunteer experiments (Leeson, 1995; Yu et al., 1996).

Because it is essential to investigate the drug release

characteristics of pharmaceutical preparations, dissolution

has become highly significant and one of the primary phar-

macopoeial tests that is performed to ensure that tablets,

capsulesandotherdrugproductscomplywithpre-established

quality standards.

For a drug product, the curve of the mean dissolution rate

over time is referred to as its dissolution profile. There are

several circumstances under which comparison of the disso-

lution profiles of two solid oral dosage forms is important.

Among them, when an approved formulation is subjected to

a post-approval change due to modifications of some criti-

cal parameters, including manufacturing site, composition,

manufacturing process and batch size. In these cases, FDA

guidances for scale-up and post-approval changes for solid

oral dosage forms (FDA, 1995) require that the dissolution pro-

files of the pre-change and post-change products must be

“similar”.

Another paradigmatic scenario is in the development of

generic preparations. Here, a proprietary product, which has

been available in the market for some time and has a clinically

established efficacy, is selected as a reference against which

to compare the new formulation. Because of the “similarity”

requirement, the generic preparation should be formulated

with its dissolution profile as closely similar as possible to that

of the proprietary product.

In response to the need of assessing “similarity”, numer-

ous strategies have been proposed for comparing dissolution

profiles. These, which are divided in ANOVA-based, model-

dependent and model-independent approaches, have been

extensively reviewed (Polli et al., 1996, 1997; O’Hara et al.,

1998;CostaandSousaLobo,2001).TheANOVA-basedmethods

(Mauger et al., 1986; Yuksel et al., 2000) assume the existence

of underlying models, but do not require fitting of a curve.

They test statistical differences of the dissolution profiles in

terms of “shape” and “size” of the curves, providing proba-

bility values related more to statistical equivalence than to

pharmaceutical similarity.

Model-dependent methods rely on curve-fitting proce-

dures, which facilitate data analysis and interpretation

because they describe the dissolution profiles as functions of

a few model parameters that can be determined and statis-

tically compared. In general, however, these are rather rigid

representations, there is no universal model to fit all dissolu-

tion profiles and there are no established criteria to select the

proper mathematical model.

Model-independent methods do not require a precon-

ceived or fitted model. The difference (f1) and similarity (f2)

factors introduced by Moore and Flanner (1996) as mathemat-

icalindicestocomparedissolutionprofilesconstitutethemost

widely known examples of the model-independent approach.

This procedure, where the dissolution behaviour of a num-

ber of samples (n) of reference (R) and test (T) products are

compared at t time points (Eqs. (1) and (2)), is being recom-

mended by the FDA Guidance for Industry (FDA, 1995), and

has been accepted by European agencies and other regulatory

bodies (Human Medicines Evaluation Unit, 1999). For testing

purposes, a discriminatory medium can be identified by vary-

ing stirring rate and parameters of the dissolution medium,

including pH, ionic strength, volume, etc.

f1= 100

⎛

⎜

⎜

⎝

⎜

⎜

n

?

t=1

|Rt− Tt|

n

?

??

t=1

Rt

⎞

⎟

⎟

⎠

⎟

⎟

(1)

f2= 50 log

⎧

⎩

⎨

1 +

?1

n

?

n

?

t=1

(Rt− Tt)2

??−0.5

× 100

⎫

⎭

⎬

(2)

Since drug release depends on many variables, such as the

physicochemical properties of the drug, the excipients and

the structural properties of the tablet matrix, an understand-

ing of the complex causalities between different variables and

responses becomes difficult. Therefore, for decision taking, it

isusefultocollapsethiscomplexinformationintoaminimum

identifiablenumberofparameters.Asavariablesimplification

approach, in many cases two batches are compared through

thedeterminationoftheirpercentageofdissolvedactivecom-

ponent at a certain time point. However, this provides less

meaningful conclusions than the independent comparison of

specifications at each of multiple time points or the analysis

of the entire dissolution profile. For such problems, multivari-

ate data analysis is the tool of choice. Multivariate methods

such as principal component analysis (PCA) have been sug-

gested for the evaluation of dissolution profiles (Tsong et al.,

1997; Adams et al., 2001, 2002), while other approaches includ-

ing artificial neural networks with similarity factor (Peh et al.,

2000; Goh et al., 2002, 2003) and Gaussian mixture models (Lim

et al., 2005) as well as partial least squares (Korhonen et al.,

2005), have been proposed as multivariate strategies for the

prediction of dissolution profiles.

Here, we propose the application of PCA with confidence

regions (PCA-CR) as a new and alternative method to com-

pare solid dosage forms dissolution behaviour and decide

about their “similarity”. The usefulness of the suggested strat-

egy was demonstrated by comparing different brands and

lots of tablet preparations containing either Furosemide or

Acetaminophen, as models, and also two selected literature

datasets. For assessing the scope and limitations of the pro-

posed approach, the PCA-CR results were confronted in each

case with the conclusions provided by the corresponding f1

and f2factors, taken as reference.

2. Materials and methods

2.1.Equipment, software and reagents

Dissolution tests were performed with a Hanson SR8-Plus

dissolution test station configured as USP-apparatus II (pad-

dle). The amounts of drug dissolved were determined in 1-cm

quartz cells, employing a Shimadzu UV-1601PC spectropho-

tometer interfaced to a computer running UV-Probe software

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

v. 2.00. Determinations were carried out against a blank of

dissolution medium, on filtered samples suitably diluted with

dissolution medium, by comparison with standard solutions

containing known concentrations of the corresponding ana-

lytes. All the reagents employed were of analytical grade;

double distilled water was employed as solvent. All the com-

putations were performed in Matlab v. 5.3 (Natwick, MA); the

Matlab scripts are freely available from the authors.

2.2.Tablet preparations and dissolution conditions

All the brands and lots of Furosemide and Acetaminophen

drug products used met the pharmacopoeial specifications for

weight variation, content uniformity and assay.

2.2.1.

Eight lots corresponding to three different brands of tablet

products (40mg) were studied. Each product was randomly

labelled with a specific letter for identification, designating

with A1the reference lot of the innovator product. The release

characteristics were determined at 37±0.5◦C, using the pro-

cedure of the “Dissolution Test 1” of USP 30 (USP Convention,

2007). The medium was 900ml of Phosphate buffer (0.05M, pH

5.8) and the stirring rate was 50rpm. One tablet was used in

each vessel, and each test comprised two runs of six tablets

yielding a total of 12 tablets per lot (FDA, 1995). During each

experiment, aliquots of 3ml were removed at 2, 3, 4, 5, 6, 7,

8, 9, 10, 12, 14, 16, 18, 20, 22, 26 and 30min, filtered and suit-

ably diluted with medium. The amount of drug dissolved was

determined from the absorbances of the samples at 274nm.

Each dissolution curve contained a total of 17 time points.

Furosemide

2.2.2.

Threedifferentbrandsoftabletproducts(500mg)werestudied

and brand A was used as the reference product (innovator).

The other brands were each randomly designated with letters

BandCforidentification.Thedissolutionsweredeterminedat

37±0.5◦C in 900ml of Phosphate buffer (0.05M, pH 5.8), using

a slight modification (stirring rate was 30rpm) of the USP 30

procedure in order to increase selectivity. One tablet was used

in each vessel, and each test comprised two runs of six tablets

yielding a total of 12 tablets per lot (FDA, 1995). Aliquots of

3ml were removed at 2, 6, 10, 14, 18, 22, 26, 30, 45 and 60min,

filteredandsuitablydilutedwithmedium.Theamountofdrug

dissolved was determined at 243nm. Each dissolution curve

contained 10 time points.

Acetaminophen

2.2.3.

Data taken from the following sources were employed: (a)

Tsong and Hammerstrom (1994): dissolution curves of three

approved batches and a new test batch (12 tablets each, deter-

mined at 7 time points). (b) Shah et al. (1998) and Ma et al.

(2000): data of a pre-change lot and five post-change lots (12

tablets each, determined at 4 time points).

Literature data

2.2.4.

and the PCA algorithm

2.2.4.1. Factors f1and f2as estimators of difference and sim-

ilarity. Eqs. (1) and (2) correspond to the difference (f1) and

similarity (f2) factors, respectively (Moore and Flanner, 1996).

Theoretical background of the f1and f2estimators

The f1 index computes the absolute cumulative differences

between drug release in reference and test samples, relative

to the drug dissolved in the reference sample. Therefore, the

value of this parameter, which is proportional to the average

difference between both profiles, depends on which sample is

taken as reference. Acceptable values of f1are 0≤f1≤15.

On the other hand, f2is a logarithmic function of the recip-

rocalofthemeansquare-roottransformofthesumofsquared

errors at all points, and is a measure of the degree of similar-

ity in the percent rate of drug release between two dissolution

profiles. The f2values are independent from the sample taken

as reference, and they range between 0 and 100, with a higher

number indicating better similarity between profiles. Accept-

able values are 50≤f2≤100, which is considered equivalent

to a difference in approximately 10% between the dissolution

profiles being compared (Shah et al., 1998).

2.2.4.2. Principal component analysis. The principles underly-

ing PCA have been extensively discussed elsewhere (Wold et

al., 1987); the following is a brief description of this multivari-

ate method.

Given matrix X(p×t), where each row contains t different

pieces of information gathered from p objects, the column

mean centred data matrix Xc can be obtained by subtract-

ing the row vector containing the mean values of its columns

(Xm), from each row of the original matrix (X).

In turn, Xc can be decomposed into the product of an

orthogonal matrix U, a diagonal matrix S and another orthog-

onal matrix V (Eq. (3)), where U S VTrepresents the singular

value decomposition (SVD) of Xc (Manly, 1986).

Xc(p×t)= U(p×t)S(t×t)VT

(t×t)(p > t) (3)

ThescorematrixU(p×t)istheunweighed(normalized)score

matrix and represents the projections of the data on the PCs;

therefore, similar samples are represented by similar scores.

On the other side, the diagonal matrix S(t×t)contains the

singular values, which are the square roots of the eigenval-

ues associated to the corresponding PCs (eigenvectors). These

diagonal terms reflect the dynamics of the dissolution; there-

fore, the largest eigenvalues correspond to the dimensions

that explain larger amounts of variance of the dataset. Matrix

T(t×t)known as the weighed (unnormalized) score matrix, is

the product between U and S (T=U·S). Finally, the loadings

matrix V(t×t)contains in its columns the weights contributed

by the original variables (eigenvectors) to the PCs.

2.2.5.

Outlier detection was performed by means of Hotelling’s test

(Jackson, 1991). For that purpose, the test was implemented

for each dataset, according to Eq. (4), where ?xis the mean

of the data and S−1

matrix SXX(Eq. (5)). The required Mahalanobis distance was

calculated according to Eq. (6), where q is the number of dis-

solution curves in the reference and test lots (Section 2.2.9),

and was compared with the corresponding Chi square value

at a 99% confidence level and t (number of data points per

Detection of outliers

XXis the inverse of the data covariance

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

69

curve) degrees of freedom.

P[y = (x − ?x)TS−1

XX(x − ?x) < yp] = 1 − ˛

(4)

SXX= (t − 1)−1· XcXcT

(5)

q(x − ?x)TS−1

XX(x − ?x) < ?2

0.99,t

(6)

2.2.6.

components

As the principal components (PCs) are weighed in decreas-

ing order of variance coverage, the variation of the dataset

can be conveniently expressed in terms of a small number of

significant variables, while the remaining variables (residual),

contain mostly noise. Thus, the reconstructed data matrix X*c

can be obtained (Eq. (7)) by employing a reduced number (r<t)

of PCs.

Selection of the optimum number of principal

X∗c(p×t)= U∗

[r ≤ p − 1(p ≤ t)andr ≤ t(p > t)]

(p×r)S∗

(r×r)V∗T

(r×t)= T∗

(p×r)V∗T

(r×t),

(7)

The number of significant PCs to be retained (r) can be

obtained by different means, including cross-validation, set-

ting a threshold to the minimum variance explained, or

evaluating the residuals between Xc and X*c. Observation of

the shape of the PCs also constitutes a useful hint. In this

work, X*c was reconstructed from matrices U*, S*and V*

with an increasing number of PCs, until the optimum num-

ber of factors, yielding the error matrix E (Eq. (8)) similar to

instrumental error, was obtained. Two PCs were found to sat-

isfactorily reconstruct the original dataset in the four studied

cases.

E(p×t)= Xc(p×t)− X∗c(p×t)

(8)

2.2.7.

In order to test the hypothesis of similarity, the 95% a confi-

dence region (˛=0.05) was drawn for each pair of lots being

compared, taking into account the variability of the weighed

scores data of the reference lot. This confidence ellipse was

obtained from Hotelling’s test (Eq. (6)) and plotted according

to Eq. (9), where d1and d2are eigenvalues of SXX, while w1

and w2are elements of matrix w = B(x − ?x); the rows of B are

eigenvectors of SXX. w1and w2provide information related to

the orientation of the ellipse, which axes’ lengths are defined

by (d1?21−?, r)0.5and (d2?21−?, r)0.5, respectively. The degrees of

freedom (r) of the ?2equal the number of the selected PCs

(Section 2.2.6).

Confidence regions

P

??

w2

1

d1?2

1−˛,r

?

+

?

w2

2

d2?2

1−˛,r

?

< 1

?

= 1 − ˛

(9)

2.2.8.

region

The mean vector of data a(1×t)(dissolution profile) of the refer-

ence lot was successively transformed into a new vector d(1×t)

by replacing some of its items with artificial data containing

deviations able to originate f2values around 50. This proce-

dure was repeated a number of times, and in each case the

Bootstrapping procedure for finding the f2≤50

values of f2and the PCs of the artificial dissolution curve were

calculated (Efron and Tibshirani, 1986, 1993; Shah et al., 1998;

Adams et al., 2001). Plots of the f2=50 ellipses (enclosing the

f2≤50 region) are shown in the graphics.

2.2.9.

Given the data matrices A(q×t)and B(q×t), containing the dis-

solution curves of q tablets each corresponding to the lots of

dosage forms to be compared, taken at the same t time points,

the following five steps are proposed to be sequentially carried

out:

Procedure for the comparison of dissolution profiles

(a) Detect outliers in the individual datasets, employing

Hotelling’s test (Section 2.2.5).

(b) Construct the matrix X(2q×t), which contains the data of A

and B (2q=p, see Section 2.2.4.2); mean-center (column-

wise) this matrix and carry out the SVD operation on the

resulting matrix Xc(2q×t)(obtain matrices U, S and V).

(c) Select the number of PCs to be retained (Section 2.2.6) and

compute matrix T∗

(d) Draw the 95% confidence region (Section 2.2.7), in order to

test the hypothesis of similarity.

(e) Decide about “similarity”, based on the inclusion of the

test data (>80%) in the confidence ellipse of the reference.

(p×r).

3.Results and discussion

3.1.

approach

Characteristic features of the proposed PCA-CR

The proposed approach for the assessment of “similarity”

through the PCA-CR analysis of dissolution curves entails five

steps, including (a) detection of outliers in reference and test

data matrices; (b) construction and column mean centering

of a single data matrix containing both data of reference and

test samples, which is submitted to a SVD operation; (c) selec-

tion of the number of PCs to be retained; (d) plotting of the

weighed scores of reference and test lots, and drawing of the

95% confidence region based on scores plot of the reference

lot; (e) “similarity” decision making based on the percentage

of test samples included in the above confidence region.

These sequential steps constitute the appropriate means

for pre-processing, analyzing and visualizing the data, also

establishing a convenient approach for final decision taking.

Hotelling’s test represents a useful strategy for outlier detec-

tion, helping to avoid inclusion of dissolution curves with

exceptionally high variability. On the other hand, PCA is a

mathematical procedure that allows the representation of a

complex set of multivariate data with a reduced number of

new and uncorrelated variables (PCs), which are linear combi-

nations of the original data. In the proposed method, joining

reference and test datasets and carrying out the SVD on a

single matrix allows the optimization of system parameters

leading to an improved projection of the test data in the

reference–test joint data space; therefore, misadjustements

resultingformfittingtestdataintoapre-establishedreference

model, are avoided.

By discarding feature elements with low variability, PCA

allows data visualization and the discovery of hidden trends

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

in fewer dimensions. The PCs are ordered according to their

ability to explain data variability, and in the selected examples

discussed below, plot of the weighed scores of the first two PCs

is proposed, as these allow satisfactory reconstruction of the

original data matrix. This approach is much simpler than that

proposed by Tsong et al. (1997), which employs all the PCs for

comparison.

After some trial and error experiments, and taking into

account that “similarity” is a property of the lot and not of

the individual tablets, for decision taking, the following cri-

terion was adopted “test lots are considered to be ‘similar’ if

they contain more than (the arbitrarily chosen value of) 80%

of their tablets (Chen and Tsong, 1997) inside of the 95% con-

fidence region of the reference lot”. The “>80%” requirement

takes into account test data variability, while the 95% confi-

dence ellipse considers variability of the weighed scores in

the reference lot.

In order to assess the usefulness of the proposed method,

the dissolution curves of Acetaminophen and Furosemide

tablets, and two datasets selected from the literature, were

individually analyzed by the PCA-CR methodology and com-

pared with the information provided by the f1/f2 criteria.

Results for each set of data are presented below and discussed

separately.

3.2. Dissolution of Furosemide tablets

Eight lots of Furosemide tablets, corresponding to three differ-

ent brands, A (lots A1, A2and A3), B (lots B1, B2and B3) and C

(lots C1and C2), were studied, with brand A being the inno-

vator. The mean percentages of drug released over a 30-min

period are depicted in Fig. 1.

The individual profiles of the eight lots complied with the

FDA requirements for the evaluation of similarity and differ-

Fig. 1 – Dissolution profiles of eight lots of Furosemide

tablets, corresponding to three different brands (A, B and C);

for the sake of clarity, error bars (<20% for the first time

points; <10% at time points above 6min) were omitted.

ence; i.e., the tablets dissolved less than 85% of their active

principle in the first 15min, the data coefficient of variation

(CV%) was less than 20% for the first time points, being less

than 10% for the remaining time points (≥6min) and the

overall CV% was less than 15%. The corresponding f1and f2

values were calculated, employing data acquired at 2, 7, 12,

18 and 26min, taking care that no more than one time point

(26min) corresponded to more than 85% of dissolved drug.

For the sake of the analysis, all of the possible pairwise lot

comparisons were carried out, with the results consigned in

Table 1.

From the data of Table 1, it follows that when compared

against A1, both additional lots of tablets of brand A (A2and

Table 1 – Results of the pairwise comparison of eight lots of Furosemide tablets, employing the difference (f1) and

similarity (f2) criteriaa

Lot

f-CriterionA1

A2

A3

B1

B2

B3

C1

C2

A1

f1

f2

2.7

78.0

2.8

78.4

4.0

77.0

3.7

70.7

6.5

63.5

11.3

53.7

8.9

59.2

A2

f1

f2

2.8

78.0

1.0

94.5

5.0

67.4

6.6

64.6

9.4

58.2

8.8

57.7

6.4

64.6

A3

f1

f2

2.9

78.4

1.0

94.5

4.3

68.5

5.9

67.1

8.7

60.1

9.4

55.8

7.0

61.9

B1

f1

f2

4.0

77.0

4.8

67.4

4.2

68.5

4.8

74.1

6.1

67.4

11.6

51.3

9.2

56.2

B2

f1

f2

3.6

70.7

6.2

64.6

5.6

67.1

4.7

74.1

2.6

84.1

14.5

46.9

12.1

51.1

B3

f1

f2

6.1

63.5

8.6

58.2

8.0

60.1

5.7

67.4

2.6

84.1

16.7

43.9

14.4

47.4

C1

f1

f2

12.7

53.7

9.7

57.7

10.4

55.8

13.1

51.3

16.9

46.9

20.0

43.9

2.7

81.1

C2

f1

f2

9.7

59.2

6.8

64.6

7.5

61.9

10.1

56.2

13.8

51.1

16.8

47.4

2.6

81.1

aLetters designate different brands; numbers differentiate between different lots of the same brand. Non-complying figures are shown in

italics.

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

71

Fig. 2 – Weighed scores plot for the PCA-based pairwise comparison between dissolution data of reference (?) and test (?)

lots of Furosemide. (a) A1–A2; (b) A1–B1; (c) A1–B2; (d) A1–C1; (e) A1–C2; (f) C1–C2; (g) B2–C1; (h) B3–C1; (i) B3–C2. The 95%

confidence region (—), as well as the f2=50 ellipse (–+–) and the means of the PC scores of the reference (?) and test (?) lots

are also shown.

A3) exhibited acceptable difference (2.7 and 2.8) and similar-

ity (78.0 and 78.4) results; analogously, the parameters for the

three lots of brand B (f1=3.7–6.5 and f2=63.5–77.0) indicated

thattheyshouldbeconsideredsimilartoA1.Thef1/f2-testalso

suggested that tablets of brand B were similar among them

and with brand A. On the other hand, although complying

with the requirements for similarity when compared against

the tablets of brand A, brand C exhibited a different range of

f1/f2values(f1=6.4–11.3andf2=53.7–64.6),whichshiftedmore

towards non-compliance when analyzed against the data of

lot B1 (f1=9.2–11.2 and f2=51.3–56.2). This trend was more

clearly evidenced when they were tested against lots B2and

B3, furnishing in some cases non-complying values. Interest-

ingly, both lots of brand C demonstrated to be similar to each

other (f1=2.6, 2.7 and f2=81.1). Among the tested lots, both

f-factors allowed to arrive at the same conclusion, except in

the case of the B2–C1comparison, where the f1estimator sug-

gested “similarity”, while its f2counterpart indicated that the

lots were not similar.

To evaluate the performance of the PCA-CR method,

Hotelling’s test was run and, since no outliers were detected,

the weighed scores of the first two PCs of pairs of Furosemide

lots were plotted, with selected results shown in Fig. 2. Each

plotdisplaysthecorresponding95%confidenceellipseandthe

coordinates of the mean values of the weighed scores of the

referenceandtestlots.Theregionswheremostofthesamples

would exhibit f2=50, calculated employing the bootstrapping

technique, are also included (Shah et al., 1998).

The images clearly show that lots A2, B1and B2can be con-

sideredsimilartoA1(Fig.2a–c),despitethatoneofthesamples

of lot B2falls out of the 95% confidence region (Fig. 2c). On the

other hand, and contradicting f1/f2predictions, non-similarity

between A1 and both batches of brand C tablets is evident,

despite of the fact that C1and C2exhibit similarity to each

other (Fig. 2f). However, since in the A1–C1comparison only

four tablets of the test lot fall outside of the 95% confidence

ellipse, should a multiple stage acceptance rule be in practice

(Tsong et al., 1995; USP Convention, 2007), lot C1could per-

haps be considered for a second stage. This instance, while

representing a less demanding standard than the single stage

PCA-CR method, may still be more discriminant than the f1/f2-

criteria. As expected, comparison between lots B and C clearly

evidenced non-similarity despite that some of the observed f2

values (>45) were relatively close to the lower acceptable limit.

The similarity and difference factors appear to be simple

and easy to be calculated; perhaps this is the key for their

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

adoption by the industry, despite that they impose restric-

tions to the quality of the data to be used (not more than one

point above 85% dissolution and specific limits to the CV% at

different points of the dissolution profile), and their outcome

exhibit some dependence upon the number and position of

time points employed (Polli et al., 1997). The similarity func-

tion f2has been severely criticized by several authors (Eaton

et al., 2003) arguing that it also lacks statistical justification

(Tsong et al., 1996; Shah et al., 1998; Ma et al., 1999; Chow and

Shao, 2002), and performs unnecessary use of the logarithmic

reciprocal square root transformation, which makes its statis-

tical distribution very complicated and almost intractable (Liu

et al., 1997).

Contrarily, the proposed PCA-CR method offers a sim-

ple graphical and analytical way to decide about similarity,

employing sound mathematical and statistically based proce-

dures. In addition, it is able to make use of all the available

data points, regardless the amount of drug dissolved and data

variability.Thisishighlyadvantageous,sinceitprovidesabet-

ter appreciation of the dissolution behaviour of the lots being

compared.

The PCA-CR results for lots A and B showed good agree-

ment with the outcome of the corresponding determinations

of f1and f2; however, both methods provided different conclu-

sions for the comparison between lots A and C. In the f-test,

brand C exhibited compliance but f1(>6.0) and f2values (<60)

were observed to fall in a different range than those of brands

A and B. This borderline compliance of both lots of brand C

in the f2-test and non-compliance with the PCA-CR method

reflects the fact that the latter method represents a slightly

rigorous standard than the f-based approach, being perhaps

anticipating non-similarity, as detected when brands B and C

were compared.

Both the f-based and the PCA-CR methods revealed a closer

likelihood of brand C towards brand A than with regards to

brand B. In fact, the f-based A–C comparison suggested “sim-

ilarity”, while the B–C comparison indicated “non-similarity”

in the B1/B2–C1/C2cases; analogously, in the case of the PCA-

CR counterpart, while concluding for “non-similarity” in every

case,fewerpointsremainedoutsidethe95%confidenceregion

in the A–C comparisons (Fig. 2c and d) than in the B–C com-

parisons (Fig. 2g–i). On the other hand, as in the f-based

comparison, both lots C – of analogous shape and size – were

considered similar to each other, despite not being able to

achieve “similarity” with the A1reference lot.

Interestingly, significant correlations were obtained when

the number of data points left out of the confidence ellipses

wereplottedagainstf1orf2values.However,despitebeingcor-

related to the f-factors, the PCA-CR represents a more rigorous

standard, being devoid of some of their major drawbacks.

3.3.Dissolution of Acetaminophen tablets

Fig. 3a displays the dissolution profiles of three different

brands of Acetaminophen tablets, and Table 2 contains the

f1/f2values of all possible brand-to-brand comparisons, pre-

pared with data taken at 6, 10, 14, 30 and 45min.

According to the f-criteria, only brands A and B should be

considered “similar”. After running the outlier detection test

and demonstrating the suitability of all the dissolution curves,

Fig. 3 – (a) Dissolution profiles of three different brands of

Acetaminophen tablets. (b) Dissolution profiles of three

standard lots (A1–3) and a new lot (B). Data were taken from

Tsong and Hammerstrom (1994). For the sake of clarity,

error bars (<10% at all the time points) were omitted.

it was observed that this result was in perfect agreement with

the conclusions emerging from application of the proposed

PCA-CR method (Fig. 4a).

Regarding brand C, it exhibited non-complying f1 and f2

values, with the data suggesting a possible borderline situa-

tion for the B vs. C comparisons (f1=15.2 and 17.7; f2=47.4).

Although the latter seemed amenable for a second stage test-

ing, in case of employing a multiple stage acceptance rule

(Tsongetal.,1995;USPConvention,2007),thePCA-CRweighed

scores plot demonstrated beyond doubt that brand C was

unable to achieve the “similarity” requirements at this stage

(Fig. 4c), not qualifying for further “similarity” testing. The

same “non-similarity” conclusion was obtained after compar-

ing brands A and C (Fig. 4b). For the sake of discussion, the B–A

comparisonisalsoshown(Fig.4d);despitethattheconclusion

about “similarity” agrees with the f-based prediction, owing

to different data variability within the reference brand (B), the

test brand (A) exhibits two borderline dissolution curves.

Interestingly, areas of the 95% confidence ellipses not

always were smaller in size than areas enclosed by the

f2=50 ellipses, calculated under bootstrap assistance. This is

because, unlike the f2procedure, the size of the confidence

ellipses is related to the variability of the data in the reference

samples as well as to size and shape of the dissolution curves.

Table 2 – Results of the pairwise f1/f2comparison of

three lots of Acetaminophen tabletsa

Brand

f-CriterionABC

A

f1

f2

7.4

65.8

20.0

43.2

B

f1

f2

7.9

65.8

15.2

47.4

C

f1

f2

25.0

43.2

17.7

47.4

aNon-complying figures are shown in italics.

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73

Fig. 4 – Scores plot for PCA-based pairwise comparison between dissolution data of reference (?) and test (?) brands of

Acetaminophen tablets. (a) A–B; (b) A–C; (c) B–C; (d) B–A. The 95% confidence ellipses (—), the region enclosing acceptable f2

(≤50) values (–+–) and the means of the PC scores of the reference (?) and test (?) brands, are also shown.

3.4.Dissolution data of Tsong and Hammerstrom

Thesedissolutiondata(Fig.3b)havebeenpreviouslyemployed

in different cases for dissolution profile comparisons (Chen

and Tsong, 1997; Tsong et al., 1997). All of the f1/f2possible

pairwise comparisons between the three standard lots (A1–A3)

and a fourth lot (B) are consigned in Table 3. The results indi-

cate that the lots have “similar” dissolution characteristics,

whichever of them is taken as reference. Noticeably, however,

the f2values for test lot B against the lots A are in a markedly

differentrange(63.5–64.7)fromthoseofthelotsA,whentested

against each other (90.3–94.6).

No outlier curves were found in the dataset. Plots of the

weighed scores of the first and second PCs of the three pre-

approved batches (A1, A2and A3) and test batch B are depicted

Table 3 – Results of the pairwise comparison of standard

lots A1, A2and A3, and a new lot (B), employing the f1

and f2criteria

Lot

f-CriterionA1

A2

A3

B

A1

f1

f2

1.6

90.3

1.2

91.2

1.5

63.8

A2

f1

f2

1.6

90.3

0.4

94.6

3.1

63.5

A3

f1

f2

1.2

91.2

0.4

94.6

2.7

64.7

B

f1

f2

1.5

63.8

3.0

63.5

2.7

64.7

in Fig. 5. Here, all the PCA-based comparisons of the former

demonstrated their similarity, despite that the A1–A2compar-

ison plot exhibited two tablets of the test lot out of the 95%

confidence ellipse and those of A2–A3and A1–A3showed one

tablet each, out of the confidence region.

On the other hand, pairwise comparison of batches A1

and A2 with test batch B, revealed that the latter could

not be considered “similar” to any of the former two, sur-

prisingly complying with similarity requirements only with

batch A3, mainly due to its particular data variability. Despite

that the f1/f2 criteria suggest similarity between all of the

dissolution profiles, this is somehow in agreement with con-

clusions reached by Tsong and co-workers on the grounds

of Mahalanobis distance-based multivariate region specifi-

cation criteria (Chen and Tsong, 1997), and on the basis of

confidence intervals of the characteristic parameters (˛ and

ˇ) of a Weibull curve fit (Tsong et al., 1997). The bootstrap-

calculated acceptable values of the corresponding f2 test

showninFig.5revealsthat,beingofamorepermissivenature,

the f2factor estimation also supports the conclusion of lot

similarity.

The graphical result of the A1–A2comparison (and those

of A2–A3 and A1–A3 to a minor extent) can be attributed

to higher tablet data variability within the latter lot, com-

pared with the reference. Since the lengths of the axes of

the ellipse are related to the eigenvalues of the covariance

matrix, the confidence region is sensitive to variability of

the reference data; therefore, it should be made possible for

some samples of the test lot to remain outside the confidence

region due to their own (and sometimes higher) variability,

as proposed.

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

Fig. 5 – PCA-based comparisons [reference (?) and test (?)] between standard batches A1, A2and A3, as well as with a new

test batch (B). Data were taken from Tsong and Hammerstrom (1994). (a) A1–A2; (b) A2–A3; (c) A1–A3; (d) A1–B; (e) A2–B; (f)

A3–B. Confidence ellipse of 95% (—), the f2=50 ellipse (–+–), and the means of the PCs of the reference (?) and test (?) lots are

also shown.

To take into account data variability is another important

feature of the PCA-CR method, in sharp contrast with the f2

criterion, which is a function of mean differences, and has

been criticized for not computing variability within the test

and reference data. Not without reason, authors have recom-

mendedcarefulinterpretationoff2resultswhenthevariances

of the individual profiles are very different (Saranadasa and

Krishnamoorthy, 2005).

Considering that the confidence region in the proposed

method represents a tighter standard than the f1/f2indicators,

the allowance of up to 20% of the samples to fall outside of the

95% confidence ellipse represents a compromise which trans-

forms the proposed PCA-CR method into a less restrictive tool

and a test procedure with pharmaceutical significance, still

remaining diagnostic of “similarity”.

3.5.

al. (1998)

Pre- and post-change dissolution data of Shah et

The dissolution data of one pre-change and five post-change

batches are shown in Fig. 6a, with the f1/f2results of the post-

change batches against the pre-change sample consigned in

Table 4. Many results (three out of five for f1and four out of

five for f2) seem to be borderline (f1>13 or f2<60). However,

despite the differences among the curves and according to

the f-criteria, all of the post-change batches comply with the

requirements for “similarity”.

In their study of this dataset employing bootstrap tech-

niques, Ma et al. concluded that, depending on the estimators

employed, only batch B or batches B and E could be consid-

ered “similar” to the pre-change batch A (Ma et al., 2000). The

PCA-CR analysis of the data was run after assuring absence of

outliers. Interestingly, however, this revealed that even batch

B does not met the “similarity” requirements, displaying five

out of its 12 data points out of the confidence ellipse.

Closer inspection of the dissolution curves of batches A

and B indicated that the CV% of the curves of batch B at

the different time points (10.6, 9.9, 5.7 and 1.6%) were differ-

ent from those of the reference batch, being data dispersion

of the latter comparatively smaller (6.7, 4.8, 3.8 and 2.9%).

Tentatively, this can provide an explanation to the PCA-CR

Table 4 – Comparison of the dissolution profiles of

pre-change batch A with five post-change lots, according

to the f1/f2criteria

f-Criterion/lotBCDEF

f1

f2

8.8

67.1

13.3

58.4

13.6

58.7

7.4

57.5

13.8

55.4

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75

Fig. 6 – (a) Dissolution profiles of (A) pre-change batch; (B) post-change batch 1; (C) post-change batch 2; (D) post-change

batch 3; (E) post-change batch 4; (F) post-change batch 5. Data were taken from Shah et al. (1998). (b–f) PCA-based

comparisons [reference (?) and test (?)] between pre-change batch A and post-change batches 1–5, respectively. The 95%

confidence ellipses (—), the f2=50 ellipses (–+–), and the means of the PCs of the reference (?) and test (?) lots are also shown.

non-similarity result, on account of the sensitivity of the

method to data variability, particularly in the reference lot.

Indeed, the multivariate test allows to conclude that despite

the seemingly analogous shapes of the reference and test pro-

files, the individual dissolution curves in both batches being

compared behave different, hence, “similarity” criteria could

not be reached.

When dissolution profiles of pre-change batch A and post-

change batch E were compared, it was evident that except for

the first time point (where batch E also exhibits considerably

less drug dissolved than batch A), both have similar CV% (15.0,

4.8, 3.8 and 2.8% for batch E); however, since PCA-CR is sensi-

tive to shape and size of the dissolution curves (Adams et al.,

2001), batch E was also correctly interpreted by the multivari-

ate method as possessing a “non-similar” profile.

3.6.Method flexibility

The need for counting at least 80% of the test tablets (Chen

and Tsong, 1997) inside of the 95% confidence ellipse of the

reference lot constitute arbitrary criteria for assessing “simi-

larity”, which relate to the strictness of the proposed method

with regards to decision taking. In this sense, PCA-CR repre-

sents a more rigorous standard than the f-based comparison.

However, the proposed approach is flexible enough, so these

proposed specifications do not rule out alternative combina-

tions of confidence levels for the ellipses and number of test

tablets allowed to remain outside of the confidence region,

which might be set according to the experience or specific

needs. Boostrap studies are suitable means to provide evi-

dence for this fine-tuning of the method.

4.Conclusions

In summary, the use of the weighed scores plot of the rele-

vant principal components of the dissolution curves with 95%

confidence regions (PCA-CR) has been proposed as a new and

alternative strategy for the comparison of in vitro dissolution

profiles of tablet preparations. The results observed with this

multivariate approach exhibited good qualitative correlation

with the f1and f2values computed from the dissolution pro-

files; however, conclusions regarding profile similarity were

not always coincident.

This was mainly due to the facts that the proposed method

is more discriminating, taking into account data variabil-

ity within the reference lot in order to build the confidence

ellipses. Variations within the test lot, as well as shape and

size of the dissolution curves have also influence on the final

result.

Unlike the f1/f2 methods, based on comparison of data

means, the use of confidence ellipses built upon PC values

of the individual tablet dissolution curves of the reference set

allows a simple and rapid graphic assessment of data distri-

bution. In addition, the proposed approach does not impose

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european journal of pharmaceutical sciences 3 4 ( 2 0 0 8 ) 66–77

restrictions to useful data in terms of their variability and

number of allowed time points above a given degree of disso-

lution; making use of the all the available information, avoids

data-dependent outcomes, a characteristic feature of the f-

based methods.

Compared to previously reported PCA-based methodolo-

gies, the SVD operation carried out on a single matrix

containing test and reference data allows the optimization of

system parameters in such a way that an improved projec-

tion of the test data in the joint reference–test data space is

achieved.

The use of boostraping techniques for the representation

of the f2=50 frontiers in the PCA scores’ space, and their

comparison with the region enclosed by the 95% confidence

ellipses clearly demonstrated the relationship between the

official and the proposed methodologies, revealing the poten-

tial of PCA-CR under the proposed conditions, as a stricter but

still useful tool for providing pharmaceutically sound results

in the assessment of “similarity” between different batches of

the same product, or products of different brands containing

the same active ingredient.

The proposed approach is dependable, it can be eas-

ily implemented and profile comparison results are quickly

obtained; with minor modifications, it could also be adapted

to a multiple stage acceptance rule, as given in the USP.

Acknowledgements

The authors gratefully acknowledge CONICET, ANPCyT and

UNR. R.M.M. is also thankful to CONICET for his fellowship.

ProvisionofkeyliteraturereferencesbyDr.Y.Tsong(FDA,USA)

is also acknowledged.

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