DOE in Pharmaceutical and Analytical QbD.

QbD is “a systematic approach to pharmaceutical development that begins with predefined objectives and emphasizes product and process understanding and process control, based on sound science and quality risk management”
Goals Of Pharmaceutical QbD:
To achieve meaningful product quality specifications
To increase process capability and reduce product variability
To increase pharmaceutical development and manufacturing efficiencies and
To enhance cause-effect analysis and regulatory flexibility
Acoording to ICH Q8 Quality should be built into the product.
Design of Experiments (DoE) generate knowledge about a product or process and established a Mathamatical relationship of dependent variables and independent variables.
The most common screening designs, such as two-level full factorial, fractionate factorial, and Plackett- Burman designs.
optimization designs, such as three-level full factorial, central composite designs (CCD), and Box-Behnken designs.
Analysis of variance (ANOVA) used in multiple regression analysis to evaluate regression significance, residual error, and lack-of-fit adjustment.
determination coefficients (R2, R2 -adj, and R2 -pred) is also evaluated.

1. 1 CONTENT Abstract Introduction Steps of QbD Experimental designs Conclusion References

2. ABSTRACT According to ICH Q8 Quality should be built into the product. Design of Experiments (DoE) generate knowledge about a product or process and established a Mathematical relationship of dependent variables and independent variables. The most common screening designs, such as two-level full factorial, fractionate factorial, and Plackett - Burman designs. Optimization designs, such as three-level full factorial, central composite designs (CCD), and Box-Behnken designs. Analysis of variance (ANOVA) used in multiple regression analysis to evaluate regression significance, residual error, and lack-of-fit adjustment. Determination coefficients (R 2 , R 2 -adj, and R 2 -pred) is also evaluated. 2

3. INTRODUCTION Quality By Design: QbD is “a systematic approach to pharmaceutical development that begins with predefined objectives and emphasizes product and process understanding and process control, based on sound science and quality risk management” Goals Of Pharmaceutical QbD : To achieve meaningful product quality specifications To increase process capability and reduce product variability To increase pharmaceutical development and manufacturing efficiencies and To enhance cause-effect analysis and regulatory flexibility 3

4. STEPS OF PHARMACEUTICAL QUALITY BY DESIGN AND ANALYTICAL QUALITY BY DESIGN Pharmaceutical QbD Analytical QbD Establishing Quality Target Product Profile Identifying Of CQA Risk Assessment DOE (Defining Design Space) Implementing Control strategy and continuous Improvement Establishing Analytical Target profile Analytical Method Performance Characteristics Risk Assessment DoE(Method Operable Design Region) Implementing Control strategy and continuous Improvement 4

5. Establishing of Quality Target Product Profile (QTPP) / Analytical Target Profile (ATP): Quality Target Product Profile (QTPP) is a summary of quality characteristics of pharmaceutical product. Main goals of a new product or method should be defined before its development. 5

6. Identifying of Critical Quality Attributes (CQA)/Analytical Method Performance Characteristics (AMPC): CQA is chemical, physical, biological or microbiological properties or characteristics of pharmaceutical product (in-process or finished) that must be within appropriated specifications to ensure quality. CQA may include Identity Assay Content uniformity Degradation Drug release or dissolution Moisture content, microbial limits, and physical properties such as color, shape, size, and friability. Potential CQA derived from QTPP are used to guide product and process development. 6

7. Risk assessment: Risk assessment is a systematic process of organizing knowledge information to support decision. There are three essential elements in risk assessment: Risk identification: systematical use of information to identify potential sources of hazard. Risk analysis: the estimation of risk associated with the identified hazards. Risk evaluation: comparison of the estimated risks using quantitative or qualitative scale to determine their significance. 7

8. DESIGN OF EXPERIMENTS (DoE): DoE is a structured and organized method for determining the relationships between input factors (xi – independent variables) affecting one or more output responses (y – dependent variables), through the establishment of mathematical models y = f(xi) Terms And Concepts: Factors : It is an Independent variable that may affect the response and of which different levels are used in an experiment. Factors are also known as Explanatory variables, predictor variable, or input variable. Levels: It is the Setting or adjustment of factor at a specific level during an experiment. High = {+} Optimum = {0} Low = {-} 8

9. Response variable: It is an output Variable that shows the observed results or values of an experimental treatment. These are one that we want to optimize. It is also called as Dependant variable or ‘Y’ variable. Effect: It is a relationship between a factor and a response variable. It includes- 1. Main Effect 2. Dispersion Effect 3. Interaction effect Design Space: It is multidimensional region of possible treatment combinations formed by the selected factors and their levels. 9

10. Why use Design of Experiments? To Identify important design variables (screening). Statistical Methodology for systematically investigating a systems input-output relationship. To Optimize product or process Design. To Achieve robust performance. Key technology in product and process design. Reduce time to develop/design new process and product. To improve performance of product. 10

11. The Nine Step DoE Process: Define problem to be solved/objective using DoE. Determine Responses and their measurements. Determine factors and their Levels Determine Suitable experimental Design Determine experimental Runs based on selected design Conduct experiment and conduct data Analyse data and feed into DoE Software Interpret the results in light of set objectives Verify the results and conduct additional experiments as required . 11

12. Selection of experimental design: Selections of best experimental design should consider several aspects, such as Defined objectives. Number of input factors and interactions to be studied. Statistical validity. Effectiveness of each design. Experimental Design Divided Into Two Types: Screening Design. Optimization Design. 12

13. Screening design: Screening designs are often used in the first step to DoE. In order to select the most important input factors and discard the insignificant ones. Evaluation of large number of input factors with a reduced number of experiments require. These experimental designs allow one to study a wide number of input factors with reduced numbers of experiments. Screening designs are useful in the early stages: Two-level full factorial design Fractionate Factorial design Placket-Burman design 13

14. Two-level full factorial designs: Allow to estimate main effects of input factors and their interactions on output responses. The number of experiments = 2 k Where, k is the number of input factors to be studied. Run X1 X2 1 -1 -1 2 -1 +1 3 +1 -1 4 +1 +1 14 2 LEVEL 2 FACTORIAL DESIGN

15. RUN X1 X2 X3 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 RUN X1 X2 X3 X3 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 9 +1 -1 -1 -1 10 +1 -1 -1 +1 11 +1 -1 +1 -1 12 +1 -1 +1 +1 13 +1 +1 -1 -1 14 +1 +1 -1 +1 15 +1 +1 +1 -1 16 +1 +1 +1 +1 2 Level 4 Factorial Design 15 2 Level 3 factorial design

16. Fractional Factorial Designs: No. Of Runs = 2 k-p P=1 indicates a half fraction (2 4-1 ) P=2 indicates a quarter fractional design (2 4-2 ) Confounding Or Aliased Effect: Attention should be paid to the estimation of main effects and interaction effects using fractionate factorial designs, because some of them are aliased (or confounded). Confounded or Aliased means when main effect is mixed with interaction effect. “Mixing of Effect”. 16

17. 2 3-1   III   =2 2 Fractional factorial design: X1 X2 X3 X1X2 X1X3 X2X3 + - - - - + - - + + - - - + - - + - + + + + + + X3=X1X2 X2=X1X3 X1=X2X3 When Main Effect aliased with two factor interaction –Resolution III 17

18. BCD ACD ABD CD BD AD D Run A B C AB AC BC ABC 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 Main effect aliased with 3-factor interaction-Resolution IV design When using resolution IV designs, main effects are aliased with 3rd order interactions 2nd order interactions are aliased with 2nd order interactions. 18

19. Design Runs Design generator Resolution 2 3-1 4 C= AB III 2 4-1 8 D= ABC IV 2 5-1 16 E= ABCD V 2 5-2 8 D= AD, E= AC III 2 6-1 32 F= ABCDE VI 2 6-2 16 E= ABC, F= ACD IV 2 6-3 8 D= AB III Design generator: For half fraction always alias the highest (additional) factor with the highest order interaction column. Resolution III : (1+2) main effect aliased with second order interaction. Resolution IV : (1+3 or 2+2) main effect aliased with 3-order interaction and 2 factor interaction aliased with 2 nd order interaction. Resolution V : (1+4 or 2+3) main effect are aliased with 4-order interaction and 2 factor interaction are aliased with 3-factor interaction. 19

20. Plackett -Burman designs: Plackett-Burman designs are special types of two-level fractionate factorial designs (resolution III) allow one to study up to N-1 input factors with N experiments. N should be multiple of 4. 4,8,12,16,20……….so we can study 3,7,11,15,19 factors. We can study main effect at 2 levels. Design Generator for placket- Burman design N=8 (+ + + - + - - ) N=12 (+ + - + + + - - - + - ) Only main effects are seen. Dummy variables are there Design the experiment in such a way that any combination of levels of any two factors should repeat for the same no. of time. No. of experiment(N)= no. of factor - 1 20

21. RUN A B C D E F G 1 + - - + - + + 2 + + - - + - + 3 + + + - - + - 4 - + + + - - + 5 + - + + + - - 6 - + - + + + - 7 - - + - + + + 8 - - - - - - - Plackett - Burman Design Matrix to study 7 input factors (A-G) with 8 experiments 21

22. Pareto Chart: To select the most important input factors and discard the insignificant ones. Because they allow to put the input factors (and their interactions) in order of importance. Pareto chart representation of main effects (X1,X2 And X3) Pareto chart representation of main effects (X1 and X2) and interaction effect (X1*X2) of input factors. 22

23. Main Effects and Interaction Plots: Pareto charts does not provide information of how the output responses are affect by varying input factor level. Main effects (a) and interaction (b) plots of input factors X1 and X2. 23

24. Optimization designs: Central Composite design matrix: For fitting quadratic response surface. Incorporates five levels(coded –alpha, -1, 0, +1, +alpha). Shares screening runs . Run X1 X2 X3 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 -1.68 10 +1.68 11 -1.68 12 +1.68 13 -1.68 14 +1.68 15 16 17 18 19 20 24

25. Box-Behnken Design: A Box- Behnken design is specially designed for  response surface methodology . In the Box- Behnken design the Levels of the factors are at the midpoints of the edges (Red dots) and in the center. the  Center point  (Blue dot). For each factor 3 levels required. 25

26. Box-Behnken Matrix Run X1 X2 X3 1 -1 -1 2 -1 +1 3 +1 -1 4 +1 +1 5 6 -1 -1 7 -1 +1 8 +1 -1 9 +1 [phone] +1 13 +1 -1 14 +1 +1 15 Box-Behnken design are special types of three-level fractionate factorial designs. Which allows modeling 1st and 2nd order response surfaces. These designs are more cost-effective than three-level full factorial designs, particularly for large number of input factors. TRICK: X1 X2 X3 EXP ± ± 4 ± ± 4 ± ± 4 3 26

27. 27 linear response surface linear + interaction function linear + quadratic function linear + interaction + quadratic

28. Analysis of Variance (ANOVA) 28

29. Determination coefficients (R 2 , R 2 -adj, and R 2 -pred): Determination coefficient (R 2 ) is the proportion of the variance in the output response that is predicted from the input factors. In other words, how much of output response (Y) is explained by the input factors ( Xs ). R 2 will always increase by adding new terms to the regression model. To overcome this we use adj.R 2 . The R 2 -adj increases only if the new term improves the regression model. On the other hand, it decreases when the term does not improve the regression model. 29

30. Predictive R 2 ( R 2 - pred): Indicates how well a regression model predicts output responses for new observations. R 2 -pred is calculated by systematically removing each observation from the data set, estimating the regression equation. And determining how well the model predicts the removed observation. R 2 -adj and R 2 -pred are always lower than R 2 . 30

31. Defining Design Space (DS) / Method Operable Design Region (MODR): Design Space (DS) is a multidimensional combination and interaction of input factors (usually CMA and CPP) that have been proofed to provide assurance of quality, and consequently, safety and efficacy. Ensure regulatory flexibility. Design space region may be obtained by graphical optimization from overlaid counter plots of output responses (Ys) as functions of input factors ( Xs ). 31

32. The desirability approach is a popular method that assigns a "score" to a set of responses and chooses factor settings that maximize that score. optimization of multiple response processes. For each response  Y i ( x ) , a desirability function  d i ( Y i )  assigns numbers between 0 and 1 to the possible values of  Y i , with  d i ( Y i ) = 0  representing a completely undesirable value of  Y i  and  d i ( Y i ) = 1  representing a completely desirable or ideal response value. The individual desirabilities are then combined using the geometric mean, which gives the  overall desirability   D : D =( d 1( Y 1) d 2( Y 2)⋯ dk ( Yk ))1/ k with  k  denoting the number of responses. Notice that if any response  Y i  is completely undesirable  ( d i ( Y i ) = 0) , then the overall desirability is zero. Let  L i ,  U i  and  T i  be the lower, upper, and target values, respectively, that are desired for response  Y i , with  L i  ≤  T i  ≤  U i . ..\Downloads\desirability function.pdf 32

33. Implementing control strategy and Continuous improvement: Control strategy is required to ensure that critical material attributes (CMA) and critical process parameters (CPP) are within the expected limits. Control space should be within the design space. Analytical Process Technology (PAT) is an important tool in control strategy implementation. Once it enables real-time release testing and provides an increased level of quality assurance compared to conventional end product testing. Control strategy is derived from the data collected during method development and validation, which enables to predict the ability of method to meet analytical target profile (ATP). 33

34. Summary of screening and optimization designs characteristics, number of experiments, levels, and factors: Application Experimental design Experiments Levels Factors Screening Two level full factorial 2 k 2 2<k<5 Fractional factorial 2 k-p res 2 K>4 Plackett-Burman N 2 <N-1 Optimization Box-Behnken 2k(k-1)+C 3 3<k<5 Central Composite design 2 k +2k+C 5 2k<5 3 level factorial 3 k 3 2<k<3 34

35. Different Software Used In DOE: 35

36. Conclusion : QbD provide knowledge and scientific understanding to support pharmaceutical development. QbD Comprises elements like QTPP, Identifying CQA, Risk assessment, DoE, defining design space and implementing control strategy. Experimental design divided into two types- A) Screening Design B) Optimization Design Experimental design and optimization play an important role in the procedure carried out when a new analytical method is developed and validated. Screening design consist of placket-Burman, FFD, two level full factorial and Optimization design consist of Box-Behnken, CCD and 3k factorial Design. This can be very useful guide to experimenter how to design and conduct experiments, and how to analyse and interpret data. Mathematical model should be selected based on the application of Analysis of Variance (ANOVA). 36

37. References International Conference on Harmonization (ICH), Tripartite guidelines, 2009 ‘ICH Q8 (R2): Pharmaceutical Development’, London. Fukuda, I. M., Fidelis Pinto, C. F., Santos Moreira­, C. dos, Saviano, A. M., & Lourenço , F. R. (n.d.). SciELO - Brasil - Design of Experiments (DoE) applied to Pharmaceutical and Analytical Quality by Design (QbD) ; dx.doi.org. Retrieved June 27, 2022, from http://dx.doi.org/10.1590/s2175-97902018000001006 Periodicals of Engineering and Natural Sciences (PEN). (n.d.). Periodicals of Engineering and Natural Sciences (PEN); pen.ius.edu.ba. Retrieved June 27, 2022, from http://pen.ius.edu.ba S.R. Schmidt and R.G. Launsby , Understanding Industrial Designed Experiments (4th ed.), Air Academy Press, 1997,page no.102-135. Candioti LV, De Zan MM, Cámara MS, Goichoechea HC. Experimental design and multiple response optimization. Using the desirability function in analytical methods development. Talanta . 2014;124:123-138. Sanford Bolton, pharmaceutical statistics, practical and clinical Applications,Marcel Dekker,INC,New York and Basel, second edition,volume 44,1990,page no.308-334 ;532-563. 37

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