Experimental design application and interpretation in pharmaceutical technology - Computer-Aided Applications in Pharmaceutical Technology - page 46

where (SE) e is the standard error of an effect. The critical t value, t critical ,
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).

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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.