3
Experimental design application
and interpretation in
pharmaceutical technology
Jelena Djuris, Svetlana Ibric, and Zorica Djuric,
Department of Pharmaceutical Technology
and Cosmetology, Faculty of Pharmacy,
University of Belgrade
Abstract: This chapter provides a basic theoretical background on
experimental design application and interpretation. Techniques
described include screening designs, full and fractional factorial
designs, Plackett–Burman design, D-optimal designs, response surface
methodology, central composite designs, Box–Behnken design, and
mixture designs, etc. The reader will be introduced to the experimental
domains covered by specifi c design, making it easier to select the one
appropriate for the problem. After theoretical introduction, a number
of illustrative examples of design of experiments application in the
fi eld of pharmaceutical technology are presented.
Key words: design of experiments, screening designs, full and
fractional factorial designs, response surface methodology, mixture
designs.
3.1 Introduction
Experimental design is a concept used to organize, conduct, and interpret
results of experiments in an effi cient way, making sure that as much
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useful information as possible is obtained by performing a small number
of trials. Instead of using the trial-and-error approach, where independent
variables (ingredients of a formulation, processing parameters, etc.) are
varied by chance, pharmaceutical scientists are nowadays urged to apply
experimental design in their product/process development to demonstrate
their knowledge of it. This knowledge of product/process is defi ned by
so-called d esign space, a multidimensional combination and interaction
of input variables (e.g. material attributes) and process parameters, which
have been demonstrated to provide assurance of quality (ICH Q8R2,
2009). Defi nition of a design space is done by applying concepts of
experimental design (design of experiments, DoE). DoE was fi rst used as
a tool mainly by academic researchers, whereas development of
pharmaceuticals in the industry was done mostly on an empirical basis or
by relying on previous experience. With the introduction of user-friendly
software tools, and encouraged by regulatory guidelines and advices,
DoE is surely fi nding its way to becoming an everyday tool in the
pharmaceutical industry.
Proper organization of experiments is a foundation of every thoughtful
research. The number of experiments conducted is not always a
direct measurement of the amount of information gained about the
problem being studied. If multiple independent factors are being varied
in an unorganized manner, then it is impossible to determine
what affected the outcome. If factors are varied in an unreasonable
range, optimization strategies can become diffi cult to manage. These,
among others, are some of problems that can easily be anticipated
by DoE.
There are many purposes of DoE application: screening studies to
determine the most infl uential factors affecting the product/process being
studied; full or fractional designs to quantify factorial effects; in-depth
response surface studies particularly useful for optimization; mixture
designs, etc. The selection of a particular experimental design depends
upon the nature of the problem being studied and the desired level of
information to be gained.
It is proposed that, in the case of pharmaceutical product development,
screening designs are used at the beginning of the experimental
procedure for investigation of a large numbers of factors, with the aim
of revealing the most important ones. Optimization is used for fi nding
a factor combination corresponding to an optimal response profi le,
and robustness testing is used as a last test before the release of a
product, to ensure that it stays within the specifi cations (Eriksson
et al., 1998).
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Experimental design application and interpretation
3.2 Theory
The main goal of any experimental study is to fi nd the relationships
between independent variables (factors) and dependent variables (results,
outcomes) within the experimental framework. Even though it sounds
easy to accomplish, this task can be cumbersome when it is not organized
correctly. In the fi eld of pharmaceutical technology, independent variables
are usually formulation factors (ingredients amount, materials attributes,
etc.) or processing parameters, whereas dependent variables are product
properties or parameters indicating process performance. Experimental
design is, in general, used to simultaneously study the effects of multiple
independent variables (factors) on response variable(s); therefore, it is a
multivariate analysis technique. DoE requires defi nition of levels (values)
of analyzed factors and often this phase uses knowledge from previous
experience about the problem being studied.
In the simplest screening experimental design, a relatively large number
of factors can be studied in a small number of experiments. In this way,
the most infl uencial factors are identifi ed and further examined in more
detail using full factorial or response surface designs. The screening
design usually varies the factors on two levels and only a few of all
possible combinations of different factors on different levels are used.
Response surface design enables optimization of the most infl uential
factors. In this design, factors are varied on at least three levels, and many
more combinations of factors on different levels are used (in comparison
to screening designs). A mixture design is used for studies where examined
factors are mixture related, such as in the amounts of formulation
ingredients. There is a constraint that the total sum of ingredient masses
must remain the same and the factors represent a fraction of the given
ingredients in the formulation.
The reader is advised to consult relevant textbooks in the fi eld of
pharmaceutical experimental design for further explanations of
experimental design concepts (Montgomery, 1997; Lewis et al., 1999;
Armstrong, 2006).
3.2.1 Screening designs
Screening designs are used to identify the most infl uential factors from
those that potentially have an effect on studied responses. A huge number
of factors, f , can be screened by varying them on two levels in a relatively
small number of experiments N ≥ f + 1. Typical two-level screening
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designs are fractional factorial or Plackett–Burman designs (Montgomery,
1997; Lewis et al., 1999). When the number of factors, f , is small, then
full factorial design can also be used for screening purposes (Dejaegher
and Heyden, 2011). Screening designs allow simultaneous investigation
of both qualitative (discrete) and quantitative (continuous) factors, which
makes them extremely useful for preliminary formulation development.
When f factors are varied on two levels, all possible combinations of
these variations make up the two-level full factorial design. The number
of experiments, N , in this design is L f = 2 f . Note that designs are usually
denoted as e f , meaning that in a 2 3 design, 3 factors (f) are varied on
2 levels (e) (as represented in T able 3.1 ). Note that factor levels are in
coded values, which enables them to be compared. The lower factor level
is denoted as −1, and 1 stands for the upper factor level.
When the experiments are organized and conducted according to an
experimental design, the results are used to calculate factor effects, which
demonstrate to what extent certain factors infl uence the output (i.e.
studied dependent variable).
Factor effects are used to build the regression model:
[3.1]
where y is the response (dependent variable), β 0 the intercept, and β i the
regression coeffi cients (regression coeffi cients stand for factor effects).
Full factorial designs allow identifi cation of factor interactions.
Independent variables, that is, factors can interact meaning that the
Table 3.1 23 full factorial design
Factors
Experiment
A B C
1 − 1 −1 −1
2 1 −1 −1
3 − 1 1 −1
4 1 1 −1
5 − 1 −1 1
6 1 −1 1
7 − 1 1 1
8 1 1 1
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Experimental design application and interpretation
infl uence of one factor on the response is different at different levels of
another factor(s). Interactions are calculated from the columns of contrast
coeffi cients ( Table 3.2 ).
Fractional factorial designs are denoted as 2 f -v , where 2 − v (1/2 v ) represents
the fraction of experiments from the full factorial designs that are omitted
( v = 1, 2, 3 . . .). An example of fractional factorial design for 4 factors,
24 -1 design, is represented in T able 3.3. By fractioning the combinations of
factors levels, some of the information is lost.
Table 3.2 Determination of factor interactions
Contrast coeffi cients
Experiment
AB AC BC ABC
1 1 1 1 − 1
2 − 1 −1 1 1
3 − 1 1 − 1 1
4 1 −1 − 1 − 1
5 1 −1 − 1 1
6 − 1 1 − 1 − 1
7 − 1 −1 1 − 1
8 1 1 1 1
Table 3.3 2 4-1 fractional factorial design
Factors
Experiment
A B C D
1 − 1 −1 − 1 − 1
2 1 −1 − 1 1
3 − 1 1 − 1 1
4 1 1 − 1 − 1
5 − 1 −1 1 1
6 1 −1 1 − 1
7 − 1 1 1 − 1
8 1 1 1 1
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Table 3.4 Plackett–Burman design for seven factors
Factors
Experiment
A B C D E F G
1 1 1 1 −1 1 −1 −1
2 −1 1 1 1 −1 1 −1
3 −1 − 1 1 1 1 −1 1
4 1 −1 − 1 1 1 1 −1
5 −1 1 − 1 −1 1 1 1
6 1 −1 1 −1 −1 1 1
7 1 1 − 1 1 −1 − 1 1
8 −1 − 1 − 1 −1 −1 − 1 −1
Fractional factorial design does not indicate potential factor interactions
and if it is highly fractioned, some factors effects are estimated together
(factors are confounded).
A special type of screening design, the Plackett–Burman design (1946),
allows estimation of factor effects for f = N – 1 factors, where N is the
number of experiments with a multiple of 4. These designs are especially
useful for preliminary investigations of huge numbers of potentially
infl uential factors, as represented in Table 3.4 for a 27 -4 design.
Other special kinds of screening designs are asymmetrical,
supersaturated, or mixed-level designs. D-optimal design can also be
adapted for screening purposes (Dejaegher and Heyden, 2011).
When fractional factorial designs are applied, there is always a
possibility that a signifi cant factor effect is not detected, due to all possible
factor level combinations not being investigated.
3.2.2 Response surface designs
Response surface designs are used to analyze effects of the most signifi cant
factors that are recognized by screening studies (or are known from the
previous experience), where the number of these factors is usually 2 or 3.
Factors are varied on at least three levels. The main goal of response
surface designs is usually optimization. Note that qualitative (discrete)
factors cannot be used in these designs. Response surface designs are
accompanied by visual representation of the factors’ infl uence on the
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Experimental design application and interpretation
studied response. Therefore, it is possible to display the infl uence of the
two factors on the studied response in a graphically comprehensible
manner. For more than two factors, only fractions of the entire response
surface are visualized (Dejaegher and Heyden, 2011).
Response surface designs can be symmetrical or asymmetrical
(Montgomery, 1997). Symmetrical designs cover the symmetrical
experimental domain (Dejaegher and Heyden, 2011). Some of the most
often used symmetrical designs are three-level full factorial, central
composite, Box–Behnken design (BBD), etc. Three-level full factorial
design for three factors is represented in Figure 3.1 .
In order to determine the experimental error, the central point is often
replicated several (3–5) times.
Central composite design (CCD) is composed of a two-level full
factorial design (2 f experiments), a star design (2f experiments), and a
center point, therefore requiring N = 2 f + 2f + 1 experiments to examine
the f factors (Montgomery, 1997) (T able 3.5) . The points of the full
factorial design are situated at factor levels −1 and +1, those of the star
design at the factor levels 0, − α and + α , and the center point at factor
level 0. Depending on the value of α , two types of designs exist, a
face-centered CCD (FCCD) with | α | = 1, and a circumscribed CCD
(CCCD) with | α | > 1. Therefore, in the case of FCCD and CCCD, factors
are varied on three or fi ve levels, respectively.
Three-level full factorial design for 3 factors, 33
Figure 3.1 design
with 27 experiments
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Table 3.5 CCD for three factors
Factors
Experiment
A B C
1 −1 −1 −1
2 1 −1 −1
3 −1 1 −1
4 1 1 −1
5 −1 −1 1
6 1 −1 1
7 −1 1 1
8 1 1 1
9 − α 0 0
10 + α 0 0
11 0 − α 0
12 0 + α 0
13 0 0 −α
14 0 0 +α
15 (+ replicates) 0 0 0
A BBD is described for a minimum of three factors and contains N =
(2 f ( f − 1)) + c0 experiments, of which c 0 is the number of center points
(Box and Behnken, 1960). The BBD is the most common alternative to
the CCD (Vining and Kowalski, 2010). BBDs are second-order designs
based on three-level incomplete factorial designs (Ferreira et al., 2007). It
can be seen, from Table 3.6, that the fi rst 4 experiments (i.e. the fi rst
experimental block) is a full 22 design for factors A and B, whereas factor
C is constantly at the level0 . The second experimental block is a full 22
design for factors A and C (factor B is at level 0), whereas the third
experimental block is a full 22 design for factors B and C (factor A is
at level 0). Therefore, BBD can be presented in a simplifi ed manner
( Table 3.7) . When there are 5 or more factors, Box and Behnken
recommended using all possible 2 3 designs, holding the other factors
constant (Vining and Kowalski, 2010). One of the main advantages of
BBD is that it does not contain combinations for which all factors are
simultaneously at their highest or lowest levels, meaning that experiments
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Experimental design application and interpretation
Table 3.6 BBD for three factors (center point is replicated
three times)
Factors
Experiment
A B C
1 − 1 −1 0
2 1 −1 0
3 − 1 1 0
4 1 1 0
5 − 1 0 −1
6 1 0 −1
7 − 1 0 1
8 1 0 1
9 0 −1 −1
10 0 1 −1
11 0 −1 1
12 0 1 1
13 0 0 0
14 0 0 0
15 0 0 0
Table 3.7 BBD for three factors (simplifi ed)
Factors
Experiment
A B C
1–4 ±1 ± 1 0
5–8 ±1 0 ±1
9–12 0 ±1 ±1
replicates 0 0 0
performed under extreme conditions (for which unsatisfactory results
might occur) are avoided (Ferreira et al., 2007).
A Doehlert (uniform shell) design has equal distances between all
neighboring experiments (Doehlert, 1970). In this design, factors are
varied at different numbers of levels, in the same design. This enables the
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researcher to select the number of levels for each factor, depending on its
nature and desired experimental domain. The Doehlert design describes a
spherical experimental domain and stresses uniformity in space fi lling. For
two variables, the design consists of one central point and six points
forming a regular hexagon, and therefore is situated on a circle (Ferreira
et al., 2004) (T able 3.8) . Doehlert designs are effi cient in the mapping of
experimental domains: adjoining hexagons can fi ll a space completely and
effi ciently, since the hexagons fi ll space without overlapping (Massart
et al., 2003). In this design, one variable is varied on fi ve levels, whereas
the other is varied on three levels (T able 3.8) . Generally, it is preferable to
choose the variable with the stronger effect as the factor with fi ve levels, in
order to obtain most information from the system (Ferreira et al., 2004).
A comparison between the BBD and other response surface designs
(central composite, Doehlert matrix, and three-level full factorial design)
has demonstrated that the BBD and Doehlert matrix are slightly more
effi cient than the CCD, but much more effi cient than the three-level full
factorial designs, where the effi ciency of one experimental design is
defi ned as the number of coeffi cients in the estimated model divided by
the number of experiments (Ferreira et al., 2007).
Asymmetrical designs are used for investigation in the asymmetrical
experimental domain. Typical examples are D-optimal designs. These
(asymmetrical) designs can also be adapted for investigation of the
symmetrical experimental domain, which is not the case for application of
symmetrical designs for the asymmetrical domain. D-optimal designs are
computer-generated designs tailor-made for each problem, allowing great
fl exibility in the specifi cations of each problem and are particularly useful
Table 3.8 Doehlert matrix for two variables
Factors
Experiment
A B
1 0 0
2 1 0
3 0 .5 0 .866
4 −1 0
5 −0.5 − 0.866
6 0.5 − 0.866
7 −0.5 0 .866
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Experimental design application and interpretation
Table 3.9 Doehlert matrix for three variables
Factors
Experiment
A B C
1 0 0 0
2 1 0 0
3 0 .5 0 .866 0
4 0 .5 0 .289 0.817
5 − 1 0 0
6 − 0.5 −0.866 0
7 − 0.5 −0.289 −0.817
8 0 .5 − 0.866 0
9 0 .5 − 0.289 −0.817
10 − 0.5 0.866 0
11 0 0 .577 −0.817
12 − 0.5 0.289 0.817
13 0 − 0.577 0.817
when it is necessary to constrain a region and no classical design exists.
D-optimal design is an effi cient tool in experimental design, making it
possible to detect the best subset of experiments from a set of candidate
points. Starting from an initial set, several subsets with different type and
number of experiments are selected. When analyzing the quality criteria
(i.e. determinant of the information matrix, infl ation factors) of each
subset of different size, it is possible to fi nd a good compromise between
the quality of information obtained and the number of experiments to be
performed (Frank and Todeschini, 1994). D-optimal designs are used for
irregular experimental regions, multi-level qualitative factors in screening,
optimization designs with qualitative factors, when the desired number of
runs is smaller then required by a classical design, model updating,
inclusions of already performed experiments, combined designs with
process, and mixture factors in the same experimental plan (Eriksson et al.,
2008). In D-optimal designs, N experiments forming the D-optimal design
are selected from the candidate points, forming a grid over the asymmetrical
domain. These experiments are the b est subset of experiments selected
from a candidate set (Eriksson et al., 2008). The term ‘best’ refers to the
selection of experimental runs according to a given criterion. The criterion
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most often used is that the selected design should maximize the determinant
of the matrix X ’X for a given regression model. This is the reason why
these designs are referred to as D (from ‘D’ in determinant) (Eriksson et al.,
2008). More detailed information on the construction of D-optimal
designs is provided in Lewis et al. (1999) and Eriksson et al. (2008).
In all of the above described response surface designs, the regression
model is defi ned as:
[3.2]
where y is the response, β 0 the intercept, β i the main coeffi cients, β ij the two-
factor interaction coeffi cients, and β ii the quadratic coeffi cients. Usually,
higher-order interactions (higher then two-factor interactions) are ignored
and non-signifi cant model terms are eliminated after statistical analysis.
More details on regression analysis are provided in the following sections.
3.2.3 Mixture designs
Mixture designs are used to study mixture variables such as excipients in
a formulation. All mixture components are examined in one design. The
characteristic feature of a mixture is that the sum of all its components
adds up to 100%, meaning that the mixture factors (components) cannot
be manipulated completely independently of one another (Eriksson et al.,
1998). In comparison to other (unconstrained) experimental designs,
mixture designs cannot be viewed as squares, cubes, or hypercubes.
Furthermore, data analysis is more complicated, since mixture factors are
correlated. In the case of a three-component mixture, available designs
are represented in Table 3.10 and Figure 3.2 .
Simplex lattice mixture designs can be defi ned with three (experiments
1–3 in T able 3.10) or six experiments (experiments 1–6 in T able 3.10) . If
experiment 7 is included, then it is a simplex lattice-centroid design and
if all ten experiments are considered, then it is an augmented simplex
lattice–centroid mixture design.
The three most commonly used mixture designs support linear,
quadratic, and special cubic models (F igure 3.3) . The linear design is
taken from the axial designs, whereas quadratic and special cubic designs
are derived from simplex centroid designs. The design supporting a linear
model is useful when the experimental objective is screening or robustness
testing, whereas the designs supporting quadratic or special cubic models
are relevant for optimization purposes (Eriksson et al., 1998).
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Experimental design application and interpretation
Table 3.10 Factor levels in mixture designs
Factors
Experiment
A B C
1 1 0 0
2 0 1 0
3 0 0 1
4 0 .5 0.5 0
5 0 .5 0 0.5
6 0 0.5 0.5
7 0 .333 0.333 0 .333
8 0 .670 0.165 0 .165
9 0 .165 0.670 0 .165
10 0 .165 0.165 0 .670
Figure 3.2 Experimental points for the mixture design
Generally, mixture designs are of K – 1 dimensionality, where K is the
number of factors (mixture components). The mixture regions of two-,
three-, and four-component mixtures are line, triangle, and tetrahedron,
respectively.
Previously described mixture designs are regular, since there are no
bounds on the proportion of mixture components (other than the total
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Three most commonly used mixture designs for
Figure 3.3
three-component mixtures supporting linear (left),
quadratic (center), and special cubic (right) models.
Solid dots represent compulsory experiments, whereas
open circles are optional and useful extra experiments.
The three open circles positioned at the overall
centroid correspond to replicated experiments
(adapted from Eriksson et al., 1998)
sum of 100%). However, there are often certain limitations to mixture
components, making it necessary to defi ne some constraints. When
constraints are defi ned (e.g. all three mixture components must be
present, and weight ratio of one of the components should not exceed a
certain percentage, etc.), experimental points are not part of the triangle
represented in Figure 3.2 (in the case of a three-component mixture).
Domains of different shape within the triangle (tetrahedron, etc.) are
then selected. In this case, regular mixture designs no longer apply, and
irregularity in experimental design is best handled with D-optimal design
(Eriksson et al., 1998). D-optimal design maps the largest possible
experimental design for selected model (linear, quadratic, or special
cubic). It is therefore necessary to carefully defi ne the purpose of
experimental study (screening, optimization, or robustness testing) prior
to selection of adequate mixture design.
Once D-optimal search algorithms for dealing with very constrained
mixtures were improved (DuMouchel and Jones, 1994), it was possible
to create effi cient statistical experimental designs handling both mixture
and process factors simultaneously (Eriksson et al., 1998).
3.2.4 Data analysis
There are different ways to determine the effects of different factors
investigated in an experimental design. In the case of a simple regression
model of screening design:
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Experimental design application and interpretation
[3.3]
regression coeffi cients β i can be determined by solving a system of
equations. It is therefore necessary that the number of experiments
performed is equal to or exceeds the number of factors being investigated.
The regression model can also be written in the form of vector components:
y = X β + ε [3.4]
where response vector y is an N × 1 matrix, model X is an N × t matrix
( t is the number of terms included in the model), β is the t × 1 vector of
regression coeffi cients, and ε is the N × 1 error vector. Regression
coeffi cient b is usually calculated using least squares regression:
b = ( X T X ) −1 X T y [3.5]
where X T is the transposed matrix of X .
Also, the effect of each factor x on each response y is estimated as:
[3.6]
where Σ y (+1) and Σ y (−1) represent the sums of the responses, where
factor x is at the (+1) and (−1) levels, respectively, and N is the number of
design experiments.
Because effects estimate the change in response when changing the
factor levels from −1 to +1, and coeffi cients between levels 0 and +1, both
are related as follows:
E x = 2 b x [3.7]
In order to determine the signifi cance of the calculated factor effect,
graphical methods and statistical interpretations are used. Graphically,
normal probability or half-normal probability plots are drawn
(Montgomery, 1997). On these plots, the unimportant effects are found on
a straight line through zero, while the important effects deviate from this
line (Dejaegher and Heyden, 2011). Statistical interpretations are usually
based on t -test statistics, where the obtained t value or the effect E x value
is compared to critical limit values t c ritical and E x critical . All effects greater
than these critical values (in absolute terms) are then considered signifi cant:
[3.8]
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where (SE)e is the standard error of an effect. The critical t value, t c ritical ,
depends on the number of degrees of freedom associated with (SE) e and
on the signifi cance level, usually α = 0.05. The standard error of an effect
is usually estimated from the variance of replicated experiments, but
there are also other methods (Dejaegher and Heyden, 2011).
In the case of response surface designs, the relationship between factors
and responses is modeled by a polynomial model, usually second-order
polynomial. Interpretation of the model effects is similar to previously
described screening design interpretation. Graphically, the model is
visualized by two-dimensional contour plots or three-dimensional
response surface plots. These plots become more complicated when the
number of factors exceeds two. The fi t of the model to the data can be
evaluated statistically applying either Analysis of Variance (ANOVA), a
residual analysis, or an external validation using a test set (Montgomery,
1997). Also, the previously described procedure for determination of
signifi cant factor effects can be applied and non-signifi cant factors are
then eliminated from the model.
Interpretation of mixture design models is similar to response surface
designs. But, since mixture factors (components) are dependent on each
other (the main constraint that the sum of all components is 100% is
always present), application of multiple regression models requires data
parameterization in order to alleviate the impact of the mixture constraint.
Chemometric techniques, such as partial least squares regression (PLS),
described in more detail in Chapter 4 ) do not assume mathematically
independent factors and are, therefore, directly applicable to mixture
data analysis (Kettaneh-Wold, 1992).
3.3 Examples
In the 1980s, the use of experimental design, especially the factorial
design, was generalized in the development of solid dosage forms, and
appropriate statistical analysis allowed determination of critical process
parameters (CPP), the comparison between materials and improvement,
or optimization of formulations. In 1999, Lewis suggested mathematical
modeling and pointed out the statistical background needed by
pharmaceutical scientists. The recent regulations from the key federal
agencies, to apply quality-by-design (QbD), have pursued researchers in
the pharmaceutical industry to employ experimental design during drug
product development.
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Experimental design application and interpretation
The following examples present several case studies (among many of
them), presented in the pharmaceutical literature, from screening studies,
through analysis of factor effects, to the optimization of formulation and/
or pharmaceutical processes.
Example 1
DoE was applied to evaluate infl uence of the granulation processing
parameters on the granule properties and dissolution characteristics
of a modifi ed release drug (Ring et al., 2011). This work accentuated
that understanding the relationship between high shear wet
granulation processing parameters and the characteristics of
intermediate and fi nal products is crucial in the ability to apply QbD
and process analytical technologies (PAT) to secondary
pharmaceutical processes. The objective of the work was to map
the knowledge domain for a high shear granulation/tableting
process, by analyzing the relationship between critical granulation
processing parameters and critical quality attributes (CQA) of the
intermediate and fi nal products. The following critical controlled
parameters (CCP) were investigated: impeller speed, wetting rate,
granulation time, and jacket temperature, with additional control of
granule particle size by two different milling techniques. A Taguchi
L-9 orthogonal design methodology was chosen for the study, and
in addition to determining the dissolution of the resulting tablets
after 2 and 4 h, a comprehensive range of granule and tablet
characteristics were monitored. Four factors were varied on 3
levels in 36 experiments, which were further split into 2 separate
18 experimental runs by using 2 different milling techniques. The
three-level Taguchi designs require relatively few data points and
assume that all two-way interactions are negligible. The
consequence is that some of the unexplained variance can be due
to the effect of interactions that are not negligible, thus increasing
the possible sources of error. The overall data analysis was
performed by the ANOVA test and p -values were used to relate CQA
of the system to CPP. It was demonstrated that with respect to
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granule properties, granulation time followed by wetting rate and
jacket temperature have an important infl uence on the product/
intermediate quality. Statistically signifi cant CPPs were identifi ed
for granule hardness, granule density, and granule particle size.
These granule properties were also identifi ed as contributing to the
dissolution release characteristics. Dissolution modeling and
prediction was achieved within the DoE structure.
Example 2
Asymmetrical factorial design was used for screening of high shear
mixer melt granulation process variables using an asymmetrical
factorial design (Voinovich et al., 1999). The factors under
investigation were binder grade, mixer load, presence of the
defl ector (all analyzed at 2 levels), binder concentration, impeller
speed, massing time, type of impeller blades (these 4 at 3 levels),
and jacket temperature (considered at 4 levels). Two granule
characteristics were analyzed: the geometric mean diameter and
the percentage of particles fi ner than 315 μ m. The factorial
arrangement 23 3 4 4 1 //25 was used, where 25 represents the
number of runs. Asymmetrical factorial design allowed reduction in
the number of runs from 2592 to 25. In addition, this technique
permitted the selection of the factor levels, which have the major
‘weight’ on the 2 granule characteristics under study. Two additional
trials were performed to attest the screening validity. The weight of
each factor level was estimated by means of the least squares
method.
Example 3
The Plackett–Burman design was used to study the effects of 11
different factors on stabilization of multicomponent protective
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Experimental design application and interpretation
liposomal formulations (Loukas, 2001). These formulations
contain ribofl avin in either free form or complexed with cyclodextrin
as a model drug, sensitive to photochemical degradation, as well
as various light absorbers and antioxidants incorporated into the
lipid bilayer and/or the aqueous phase of liposomes. The following
factors were varied on 2 levels: ribofl avin complexation (free
vitamin or γ -cyclodextrin complex), presence or absence of light
absorbers oil red O, oxybenzone, dioxybenzone, sulisobenzone, and
the antioxidant β -carotene. The multilamelar liposomes were
prepared either by the dehydration–rehydration technique or by the
disruption of lipid fi lm method containing cholesterol in low or high
concentrations, 1,2-distearoyl- sn -glycero-3-phosphocholine (DSPC)
as an alternative lipid, and sonicated through a bath or probe
sonication for a low or higher period of time. All these variations
comprise the 11 factors that directly affect the physical stability of
liposomes, as well as the chemical stability of the entrapped
vitamin. To perform a full factorial design for the examination of
11 factors, at 2 levels for each, it would be necessary to prepare
21 1 = 2048 liposomal formulations. The Plackett–Burman design
allows reduction in the number of experiments from 2048 to 12,
for 11 factors studied, where each is at its 2 levels. As described
in the introduction, the Plackett–Burman design is a 2-level
fractional factorial design. The effect of each factor in the presented
study can be determined as:
Effect = 1/6 [ Σ ( y at + level) − Σ ( y at − level)] [3.9]
The authors have highlighted that the Plackett–Burman design is
especially useful for a multivariate system with many factors that
are potentially infl uential on system properties. Once these
infl uential factors are recognized (by Plackett–Burman design) and
their number signifi cantly reduced, other forms of experimental
design, such as full or fractional factorial design, are used.
Plackett–Burman designs cannot be used for detection of factors
interactions. It was found that the presence of light absorber oil
red O demonstrates the most signifi cant effect on liposome
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Computer-aided applications in pharmaceutical technology
stabilization, followed by the complexation with the γ -cyclodextrin
form of the vitamin, the preparation method (dried reconstituted
vesicles – DRV or multilamellar vesicle – MLV), sonication type,
and molar ratio of cholesterol as signifi cant factors.
Example 4
The Plackett–Burman design was used to model the effect of
Polyox–Carbopol blends on drug release (El-Malah and Nazzal,
2006). The aim of the study was to screen the effect of 7
factors – Polyox molecular weight and amount, Carbopol, lactose,
sodium chloride, citric acid, and compression force on
theophylline release from hydrophilic matrices. A Plackett–Burman
experimental design of 12 experiments was performed to
investigate the effects of 7 factors. A polynomial model was
generated for the response, cumulative amount of theophylline
released after 12 h, and validates using ANOVA and residual
analysis. Results showed that only the amounts of Polyox and
Carbopol polymers have signifi cant effects on theophylline release.
Regular Plackett–Burman design for 7 factors requires 8
experiments. In the presented study, 12 experimental runs were
performed, where additional runs allow derivation of regression
equations, since some of information from experiments can be
used for error estimation. Note that if there are 8 experiments,
there are 8 degrees of freedom – one for each of the factors and
one for the intercept of the equation.
Example 5
Experimental design was used to optimize drug release from a
silicone elastomer matrix and to investigate transdermal drug
delivery (Snorradóttir et al., 2011). Diclofenac was the model drug
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Experimental design application and interpretation
selected to study release properties from medical silicone
elastomer matrix, including a combination of 4 permeation
enhancers as additives and allowing for constraints in the properties
of the material. The D-optimal design included 6 factors and 5
responses describing material properties and release of the drug.
Limitations were set for enhancer and drug concentrations, based
on previous knowledge, in order to retain elastometric properties of
matrix formulations. The total concentration of the excipient and
drug was limited to 15% (w/w ratio) of the silicone matrix; the
maximum drug content was set to 5% and the minimal drug content
to 0.5%, as drug release was one of the most important responses
of the system. With these constraints, the region of experimental
investigation becomes an irregular polyhedron and the D-optimal
design was therefore used. The fi rst experimental object was
screening, in order to investigate the main and interaction effects,
based on 29 experiments. All excipients were found to have
signifi cant effects on diclofenac release and were therefore
included in the optimization, which also allowed the possible
contribution of quadratic terms to the model and was based on 38
experiments. Generally, the enhancers reduced tensile strength
and increased drug release, thus it was necessary to optimize
these 2 responses. Screening and optimization of release and
material properties resulted in the production of 2 optimized
silicone membranes, which were tested for transdermal delivery.
The results confi rmed the validity of the model for the optimized
membranes that were used for further testing for transdermal drug
delivery through heat-separated human skin.
Example 6
Statistical experimental design was applied to evaluate the
infl uence of some process and formulation variables and possible
interactions among such variables, on didanosine release from
directly-compressed matrix tablets based on blends of 2 insoluble
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Computer-aided applications in pharmaceutical technology
polymers, Eudragit RS-PM and Ethocel 100, with the fi nal goal of
drug release optimization (Sánchez-Lafuente et al., 2002). Four
independent variables were considered: compression force used
for tableting, ratio between the polymers, their particle size, and
drug content. The considered responses were the percentage of
drug released at 3 predetermined times, the dissolution effi ciency
at 6 h, and the time to dissolve 10% of the drug. These responses
were selected, since the percentage of drug released after certain
time points is considered the key parameter for any in vitro/in vivo
correlation process. The preliminary screening step, carried out by
means of a 12-run asymmetric screening matrix according to a
D-optimal design strategy, allowed evaluation of the effects of
different levels of each variable. Different levels of each
independent variable on the considered responses were studied:
compression force and granulometric fractions of polymers were
varied on 2 levels, drug content was varied on 3 levels, and the
ratio between the polymers was varied on 5 levels. Starting from
an asymmetric screening design 2 2 3 1 5 1 //18, D-optimal design
strategy was applied and a 12-run asymmetric design was
generated. The drug content and the polymers ratio had the most
important effect on drug release, which, moreover, was favored by
greater polymers particle size; to the contrary, the compression
force did not have a signifi cant effect. The Doehlert design was
then applied for a response-surface study, in order to study in-depth
the effects of the most important variables. In general, the
Doehlert design requires k 2 + k + n experiments, where k is the
number of factors and n the number of central points. Replicates
at the central level of the variables are performed in order to
validate the model by means of an estimate of the experimental
variance. In this study, drug content was varied on 3 levels and the
polymer ratio was varied on 5 levels. Response surfaces were
generated and factors interactions were investigated. The
desirability function was used to simultaneously optimize the 5
considered responses, each having a different target. This
procedure allowed selection, in the studied experimental domain,
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Experimental design application and interpretation
of the best formulation conditions to optimize drug release rate.
The experimental values obtained from the optimized formulation
highly agreed with the predicted values.
Example 7
A modifi ed co-acervation or ionotropic gelation method was used to
produce gatifl oxacin-loaded submicroscopic nanoreservoir systems
(Motwani et al., 2008). It was optimized using DoE by employing a
3-factor, 3-level Box–Behnken statistical design. Independent
variables studied were the amount of the bioadhesive polymers:
chitosan, sodium alginate, and the amount of drug in the
formulation. The dependent variables were the particle size, zeta
potential, encapsulation effi ciency, and burst release. Response
surface plots were drawn, statistical validity of the polynomials
was established, and optimized formulations were selected by
feasibility and grid search. An example of the response surface
plot, showing effect of chitosan and sodium alginate concentration
on encapsulation effi ciency, is displayed in Figure 3.4 .
Objective function for the presented study was selected as
maximizing the percentage encapsulation effi ciency, while
minimizing the particle size and percentage burst release. BBD
was used to statistically optimize the formulation parameters and
evaluate the main effects, interaction effects, and quadratic
effects of the formulation ingredients on the percentage
encapsulation effi ciency of mucoadhesive nano-reservoir systems.
A 3-factor, 3-level design was used to explore the quadratic
response surfaces and for constructing second-order polynomial
models. This cubic design is characterized by a set of experimental
points (runs) lying at the midpoint of each edge of a multidimensional
cube and center point replicates (n = 3), whereas the ‘missing
corners’ help the experimenter to avoid the combined factor
extremes. A design matrix comprising of 15 experimental runs was
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Computer-aided applications in pharmaceutical technology
Figure 3.4 Response surface plot showing effect of
chitosan and sodium alginate concentration
on encapsulation effi ciency (reprinted from
Motwani et al., 2008; with permission
of Elsevier)
constructed and used for generation of regression equation
accounting for linear and quadratic factor effects, as well as for
factor interactions. The Box–Behnken experimental design
facilitated the optimization of a muco-adhesive nano-particulate
carrier systems for prolonged ocular delivery of the drug.
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