unit- 5 Biostatistics and Research Methodology.pdf

BIOSTATICS & RESEARCH METHODOLOGY
UNIT-5

CONTENTS
Design and Analysis of Experiments:
Factorial Design: Definition, 2, 2, 2' design. Advantage of factorial design
Response Surface methodology: Central composite design, Historical design,
Optimization Techniques

FACTORIAL DESIGN
The factorial designs are commonly used in the different types of experiments where it
is important to explain the effects of various factors, experimental results, or conditions.
The practical implementation of factorial designs can be seen in those experiments
which are carried out to find out the effect of pressures and lubricant on the tablet
formulation hardness, to find out the effect of disintegrant and lubricant concentration
on the dissolution of tablet, or to find out the effectiveness of a number of two active
elements in an over the counter cough medicine.
Factorial designs can be seen as the designs presented for the selection of
simultaneous determination of the impact of the number of interactions and elements.

The various definitions of factorial design can be given below:
Factor: A factor can be seen as an assigned variable like concentration, temperature,
lubricating agent, drug treatment, or diet. The experimental objectives will
decide the selection of the factors that are to be incorporated in the experiment
and it will be decided by the experimenter. This factor can be either qualitative or
quantitative in nature. In the case of the quantitative factor, there will be a numerical
value for the factor. For example, l %, 2%, or 3% values can be assigned with the
concentration factors. Treatment, diets, batches of material, laboratories, analysts,
and tablet diluent will be example of qualitative factors.

Levels: The values or designations that are associated with the factor are termed as the
level of the factor. For example, the temperature can be represented as 30° and 50°, concentration
can be represented as O.l molar and 0.3 molars and for drug treatment and we can use the
“drug” and “placebo”. There may be a number of different levels of various factors in the runs
or trails that includes factorial experiments
When we use the term “Low” and “high” it indicates the low and high concentrations that
are selected before for the lubricant and drugs. The standard notions for the
combination of the different factors are given as (l), a, b, ab. In case of the low levels of
both the factors, the combination will be represented as (l). The a.b combination is used
when a high level is associated with factor A while the low level is related to factor B that
will reflect the high-level value of only factor B and in order to represent the high-level
values of both factors A and B, we will use ab.

Effects: The change in the responses resulted due to the variation of the factor
level is called the effect of a factor. The main effect can be seen as the effect of a factor that
is been averaged in the different levels of various factors. For example, in an
experiment having two factors with two levels each of lubricant and drug, the
main effect resulting from the drug can be seen as the variation between the
average response during the high-level values of a drug (runs b and ab) and the
average response with the high-level drug (runs b and ab) and the average response in
case of low-level drug (runs (1) and a].

22 Factorial Design
22 factorial experiments describe that there are two factors, all at two levels.
The simplest 2k design is the 22 design. Thus, two-factor factional design deals
with two levels of factors, A and B. Since 22 designs have only 4 runs, multiple (n)
replicates are taken.
In particular, we use the notations a, b, ab, and (1) to show the sum of responses
for all replicates at every corresponding levels of A and B :
1) In case the lowercase letters visible,then such factorisations higher (+1) level.
2) In case, the lower case letter does not visible, then such factor is at its lower (-1)

unit- 5 Biostatistics and Research Methodology.pdf

Advantages of Factorial Design
There are several benefits associated with the factorial design: -
1. If there is no interaction, maximum efficiency can be obtained from the factorial designs in predicting the main
effects.
2. In case there is an interaction, it will be important to have factorial designs to indicate and recognize the interaction
3. It is possible to have the conclusion related to the comprehensive range of the conditions as the factor’s effects are
determined with the help of varying levels of various factors
4. Use of data is maximized as the calculation of the different main effects and interactions is done from the different
data.
5. Factorial designs are orthogonal in nature; there is no dependency of different estimated effects and interactions on
effects of different factors. Independence can be seen when we predict the main effect, for example, the outcomes
obtained are mainly because of the main effect of interest and no other factor in the experiment can affect it in the
experiment. When it comes to non-orthogonal designs, there is a dependency on effects. The absence of independence
will result in confounding.

Disadvantages of Factorial Design
1. When there is an increase in the number of factors, it will also increase in
experiment size
2. When there are a large number of treatments, it will not be easy to ensure the
homogeneity of the experimental units.
3. It is not easy to define the factorial experiment size, particularly when there is an
interaction between the factors.

RESPONSE SURFACE DESIGNS
Response surface methodology (RSM) is a method that contains a large number of mathematical and
statistical methods that are used for the development of an empirical model. Response surface
methodology (RSM) is the combination of various statistical and mathematical methods that are quite
relevant for the optimization and approximation of stochastic models.
Response surface methodology (RSM) can also be defined as the group of statistical and mathematical
methods that can be used for the following objectives:
1. Several designs or experiments can be set up to estimate response y,
2. In order to find the hypothesized or empirical model to the data that has been received from the
selected design
3. Finding out the optimum situation related to the input or control variables of the model that can facilitate
minimum or maximum response within the area of interest

Objectives of Response Surface Methodology (RSM)
The various important objectives are stated below:
1. For modeling and analysis of any activity where the interested response is influenced by the number of
variables, the use of response surface methodology (RSM) is done quite comprehensively and the main
goal of this method is to have the response optimisation.
2. This method is commonly used for surface placement. Thus, the main objective of response surface
methodology (RSM) study is to have a better insight into the topography of the response surface that
involves the local maximum, local minimum, and ridgelines and to look for the area which can provide
the most suitable response.
3. The suitable approximation relationship between the input and output variables is analyzed with the
help of RSM and it also looks for the optimal operating conditions for the system that has to be analyzed or
the area of the factor fields that can fulfill the operating conditions.

QUESTIONS
❖ Explain the application of Factorial Designs in Pharmaceutical Designs in
pharmaceutical product development.
❖ Write a note on factorial design.
❖ Write a note of Response surface methodology.

unit- 5 Biostatistics and Research Methodology.pdf

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