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

Published by Woodhead Publishing Limited, 2013

31

Computer-aided applications in pharmaceutical technology

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).

Published by Woodhead Publishing Limited, 2013

32

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

Published by Woodhead Publishing Limited, 2013

33

Computer-aided applications in pharmaceutical technology

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

Published by Woodhead Publishing Limited, 2013

34

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

Published by Woodhead Publishing Limited, 2013

35

Computer-aided applications in pharmaceutical technology

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

Published by Woodhead Publishing Limited, 2013

36

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

Published by Woodhead Publishing Limited, 2013

37

Computer-aided applications in pharmaceutical technology

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

Published by Woodhead Publishing Limited, 2013

38

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

Published by Woodhead Publishing Limited, 2013

39

Computer-aided applications in pharmaceutical technology

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

Published by Woodhead Publishing Limited, 2013

40

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

Published by Woodhead Publishing Limited, 2013

41

Computer-aided applications in pharmaceutical technology

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).

Published by Woodhead Publishing Limited, 2013

42

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

Published by Woodhead Publishing Limited, 2013

43

Computer-aided applications in pharmaceutical technology

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:

Published by Woodhead Publishing Limited, 2013

44

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]

Published by Woodhead Publishing Limited, 2013

45

Computer-aided applications in pharmaceutical technology

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.

Published by Woodhead Publishing Limited, 2013

46

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

Published by Woodhead Publishing Limited, 2013

47

Computer-aided applications in pharmaceutical technology

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

Published by Woodhead Publishing Limited, 2013

48

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

Published by Woodhead Publishing Limited, 2013

49

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

Published by Woodhead Publishing Limited, 2013

50

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

Published by Woodhead Publishing Limited, 2013

51

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,

Published by Woodhead Publishing Limited, 2013

52

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

Published by Woodhead Publishing Limited, 2013

53

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.

3.4 References

Armstrong , A.N. (2 006 ) P harmaceutical Experimental Design and Interpretation ,

2nd edition. Boca Raton, FL : CRC Press, Taylor & Francis Group .

Box , G.E.P. and B ehnken , D.W. ( 1960 ) ‘S implex sum designs: a class of second

order rotatable designs derivable from those of fi rst order’ , Ann. Math.

Stat. , 31 : 838 – 64 .

Published by Woodhead Publishing Limited, 2013

54

Experimental design application and interpretation

Dejaegher , B . and H eyden , Y .V. (2 011 ) ‘ Experimental designs and their recent

advances in set up, data interpretation, and analytical applications ’,

J. Pharmaceut. Biomed. , 56 ( 2 ): 141 – 58 .

Doehlert , D.H. ( 1970 ) ‘ Uniform shell designs ’, Appl. Stat. , 19 : 231 – 9 .

DuMouchel , W. and Jones, B. ( 1994 ) ‘ A simple Bayesian modifi cation of

D-optimal designs to reduce dependence on an assumed model ’,

Technometrics , 36 ( 1 ): 37 – 47 .

El-Malah , Y. and Nazzal , S. ( 2006 ) ‘H ydrophilic matrices: application of Placket–

Burman screening design to model the effect of POLYOX–carbopol blends

on drug release ’, Int. J. Pharm. , 309 : 163 – 70 .

Eriksson , L . , J ohansson , E . , and W ikström, C . (1 998 ) ‘M ixture design – Design

generation, PLS analysis, and model usage ’, C hemometr. Intell. Lab. ,

43 : 1 – 24 .

Eriksson , L. , Johansson , E. , Kettaneh-Wold , N. , Wikström, C. , and Wold, S.

( 2008 ) Design of Experiments: Principles and Applications, 3rd edition.

Umeå, Sweden : MKS Umetrics AB .

Ferreira , S.L.C. , dos Santos, W.N.L. , Quintella , C.M. , Neto, B.B. , and B osque-

Sendra , J.M. ( 2004 ) ‘D oehlert matrix: a chemometric tool for analytical

chemistry – Review ’, Talanta , 63 ( 4 ): 1061 – 7 .

Ferreira , S.L.C. , Bruns , R.E. , Ferreira, H.S. , Matos , G.D., David, J.M., e t al.

( 2007 ) ‘ Box–Behnken design: an alternative for the optimization of

analytical methods ’, Anal. Chim. Acta , 597 ( 2 ): 179 – 86 .

Frank , I.E. and Todeschini , R. ( 1994 ) The Data Analysis Handbook. Amsterdam,

The Netherlands : Elsevier .

ICH Q8 R2 (2 009 ) I CH Harmonised Tripartite Guideline: Pharmaceutical

Development .

Kettaneh-Wold , N. (1 992 ) ‘A nalysis of mixture data with partial least squares ’,

Chemometr. Intell. Lab. , 14 : 57 – 69 .

Lewis , G.A. , Mathieu , D. , and Luu , P.T. ( 1999 ) Pharmaceutical Experimental

Design . New York : Marcel Dekker .

Loukas , Y.L. ( 2001 ) ‘ A Plackett–Burman screening design directs the effi cient

formulation of multicomponent DRV liposomes’ , J. Pharmaceut. Biomed. ,

26 : 255 – 63 .

Massart , D .L. , V andeginste , B .G.M. , B uydens , L .M.C., d e Jong, S. , L ewi, P .J. ,

and S meyers-Verbeke, J . (2 003 ) H andbook of Chemometrics and

Qualimetrics , Part A. Amsterdam, The Netherlands : Elsevier .

Montgomery , D .C. (1 997 ) D esign and Analysis of Experiments, 4 th edition.

New York : John Wiley & Sons, Inc .

Motwani , S.K. , Chopra , S. , Talegaonkar , S. , Kohli, K. , Ahmad, F.J., and Khar , R.

(2 008 ) ‘C hitosan–sodium alginate nanoparticles as submicroscopic

reservoirs for ocular delivery: formulation, optimization and in vitro

characterization ’, Eur. J. Pharm. Biopharm., 68 : 513 – 25 .

Plackett , R .L. and B urman , J .P. (1 946 ) ‘ The design of optimum multifactorial

experiments ’, Biometrika , 33 : 302 – 25 .

Ring , D.T. , Oliveira , J.C.O. , and C rean , A. ( 2011 ) E valuation of the infl uence of

granulation processing parameters on the granule properties and dissolution

characteristics of a modifi ed release drug’ , A dv. Powder Technol. , 22 ( 2 ):

245 – 52 .

Published by Woodhead Publishing Limited, 2013

55

Computer-aided applications in pharmaceutical technology

Sánchez-Lafuente , C. , Furlanetto , S. , Fernández-Arévalo, M. , Alvarez-Fuentes, J. ,

Rabasco , A .M. , et al . (2 002 ) ‘ Didanosine extended-release matrix tablets:

optimization of formulation variables using statistical experimental design’ ,

Int. J. Pharm. , 237 : 107 – 18 .

Snorradóttir , B.S. , Gudnason , P.I. , Thorsteinsson , F ., and M ásson , M . (2 011 )

‘ Experimental design for optimizing drug release from silicone elastomer

matrix and investigation of transdermal drug delivery ’, E ur. J. Pharm. Sci. ,

42 : 559 – 67 .

Vining , G. and Kowalski , S. ( 2010 ) Statistical Methods for Engineers. Boston

MA : Cengage Learning .

Voinovich , D . , Campisi , B. , Moneghini , M. , V incenzi , C. , and Phan-Tan-Lu , R.

( 1999 ) ‘S creening of high shear mixer melt granulation process variables

using an asymmetrical factorial design ’, Int. J. Pharm. , 190 : 73 – 81 .

Published by Woodhead Publishing Limited, 2013

56