The document discusses various statistical design techniques, including statistical design of experiments, response surface methods, factorial designs, and contour designs, highlighting their application in pharmaceutical formulation. It emphasizes the importance of understanding the relationship between independent and dependent variables when optimizing formulations and explains how these methods help in achieving desired outcomes in drug development. Additionally, it provides examples of factorial and contour designs to illustrate their utility in optimizing factors like drug release rates and formulation stability.

1. S TA TIS TICA L DES IGN,
RS M , F A CTORIA L DES IGNS , CONTOUR
DES IGN & A P P LICA TION IN
FORMULA TION
PRESENTEDBY:
Syed Faizan
M.Pharm (Pharmaceutics)
Vidya Bharati College of Pharmacy, Amravati

2. Contents
❖ Statistical design
❖ Terms used
❖ Example of variable
❖ Response surface method
❖ Factorial design
❖ Types of factorial design
❖ Contour design
❖ Application in formulation
❖ Reference

3. STA TI STI CAL DESI GN
❑ Statistical DOE refers to the process of planning the experiment in such a way
that appropriate data can be collected and analyzed statistically.
❑ Techniques used divided in to two types.
Experimentation continues as optimization proceeds. It is represented by
evolutionary operations(EVOP), simplex methods.
❑ Experimentation is completed before optimization takes place. It is
represented by classic mathematical & search methods.
❑ In later one it is necessary that the relation between any dependent variable
and one or more independent variable is known.

4. ❑ In There are two possible approaches for this :
➢ Theoretical approach : If theoretical equation is known , no
experimentation is necessary.
➢ Empirical or experimental approach : With single independent
variable formulator experiments at several levels.
❑ Optimization may be helpful in shortening the experimenting time.
❑ The design of experiments is determined the relationship between the
factors affecting a process and the output of that process.

5. TERMS USED:
❑Factor: It is a assigned variables such as concentration, temperature etc.
• Quantitative: Numerical factor is assigned to it.
Example: concentration - 1%,2%,3% etc..,
• Qualitative: Numerical factor is not assigned to it.
Example: Polymer grade, humidity condition etc.
❑Levels: Levels of a factor are the values or designations assigned to the factor.
FACTOR
Temperature
Concentration
LEVELS
30°C, 50 °C
1%, 2%

6. ❑ Variable : The development procedure of the pharmaceutical formulation
involve several variables mathematically these variables are divided into two
groups.
➢ Independent Variable
➢ Dependent Variable
❑ The independent variables are under the control of the formulator. These
might include Ingredients, compression force or the die cavity filling or the
mixing time.
❑ The dependent variables are the response or the characteristics that are
developed due to the independent variables. The more the variables that are
present in the system the more the complications that are involved in the
optimization.

7. EXAMPLES OF DEPENDENT & INDEPENDENT VARIABLES
Independent Variable Dependent Variable
X1 Diluent ratio Y1 Disintegration time
X2 Compressional force Y2 Hardness
X3 Disintegration level Y3 Dissolution
X4 Binder level Y4 Friability
X5 Lubricant level Y5 Weight uniformity

8. RESPON SE S URFACE METHOD
❑ Response Surface Method (RSM) is a powerful Design of Experiment (DoE)
tool widely used in pharmaceutical formulation to design, develop, and optimize
processes.
❑ In formulation development, where multiple input variables (e.g.,
concentration of excipients, temperature, pH) affect output measures (e.g., drug
release rate, particle size, stability), RSM identifies the optimal combination of
these variables to achieve desired outcomes.
❑ For example, in the optimization of tablet formulations, RSM can be used to
study the effects of binder concentration and compression force on hardness and
disintegration time.

9. ❑ The response surface plot, often a three-dimensional graphical representation,
visually illustrates these relationships, showing how changes in input variables
influence responses.
❑ By following the path of steepest ascent, RSM helps researchers efficiently
navigate toward optimal conditions, making it an invaluable tool in achieving
high-quality pharmaceutical products.

10. ❑ Factorial design is a powerful experimental strategy used in scientific
research to study the effects of two or more factors.
❑ These are the designs of choice for simultaneous determination of the
effects of several factors & their interactions.
❑ Factorial designs are optimal to determined the effect of pressure &
lubricant on the hardness of a tablet.
❑ Effect of disintegrant & lubricant conc .on tablet dissolution.
FACTORIAL DESIGN

11. ❑ It identifies the chance variation (present in the process due to accident)
and the assignable variations (which are due to specific cause.)
❑ Factorial design are helpfull to deduce IVIVC.

12. FULL FACTORIAL DESIGN
❑ Includes all possible combinations of factor levels, giving a complete
picture of main effects and interactions.
EXAMPLE :
➢ For two factors (A and B), each at 2 levels (low and high), the design will
have 2^2 = 4 combinations:
1. (A Low, B Low),
2. (A Low, B High),
3. (A High, B Low),
4. (A High, B High).

13. TWO-LEVEL FACTORIAL DESIGN
EXAMPLE :
➢ Each factor has two levels (e.g., high and low), making it ideal for
screening studies.
➢ For three factors (A, B, C), the design will have 2^3=8 combinations.
1. A low, B low, C low.
2. A low, B low, C high.
3. A low, B high, C low.
4. A low, B high, C high.
5. A high, B low, C low.
6. A high, B low, C high.
7. A high, B high, C low.
8. A high, B high, C high.

14. THREE-LEVEL FACTORIAL
❑It is written as 3k factorial design.
❑ It means that k factors are considered each at 3 levels.
❑ These are usually referred to as low, medium & high values.
❑ These values are usually expressed as 0, 1 & 2.
❑For two factors (A, B), each with three levels, the design will have
3^2=9 combinations.

15. Factor
Low Level
(mg)
High Level
(mg)
A : Stearate 0.5 1.5
B : Drug 60.0 120.0
C : Starch 30.0 50.0
EX AMPLES OF FA CTO RS IN FACTOR IAL DESI GN

16. CONTOUR DESIGN
❑ Contour design is a graphical technique used to visualize data by plotting
lines connecting points of equal value.
❑ Contour designs are employed to identify the optimal combinations of
different formulation variables that yield the desired drug delivery
outcomes.
❑ These designs are particularly useful in multi-variable systems, where
multiple independent variables influence the formulation’s properties, such
as drug release rate, stability, bioavailability, and therapeutic effect.

17. EXAMPLE :
➢ A pharmaceutical company wants to develop a controlled-release tablet for
a drug like Diclofenac sodium.
➢ The main challenge is to balance polymer concentration and compression
force to get the desired release profile.
➢Independent Variables (Factors):
• Polymer Concentration (X1) :- (HPMC), which controls the drug's
release.
• Compression Force (X2) :- The force used to compress the tablet, which
influences tablet hardness and porosity.

18. ❑ Dependent Variable (Response):
• Drug Release Rate (Y) : The rate at which the drug is released from the
tablet over time, particularly at the 12-hour mark.

19. APPLICATION IN FORMULATION
➢ RSM is used to optimize the composition of pharmaceutical formulations, such
as tablet formulations, liquid solutions, and creams.
➢ RSM can be used to optimize parameters affecting the solubility and
dissolution rate of poorly soluble drugs, which directly impacts their
bioavailability.
➢ RSM is a core tool in the Quality by Design (QbD) approach, which aims to
design pharmaceutical products and processes with built-in quality.
➢ Factorial design is used in Bioavailability and Bioequivalence Studies

20. ➢ Researchers use contour designs to optimize the excipient concentrations
(e.g., binders, disintegrants, lubricants) in tablet formulations.
➢ Researchers can use contour design to used to optimize the ratio of oil
phase (such as emollients) and water phase (such as humectants) to achieve a
desired viscosity and stability in the cream.

21. REFERENCE:
❑Modern pharmaceutics-by Gilbert S. Banker, Christopher Rhodes, 4th
edition, chapter-20, Page-803-828,
❑Textbook of industrial pharmacy by sobha rani R. Hiremath., 1st edition,
page-214-218, 111-117.
❑Dr. Vinod Kumar; Dr. Sanjay Sharma; Dr. Deepak Kumar, Biostatistics and
research methodology, Pee Vee Publisher, page- 227- 252.