How to Define Design Space

1. How to Define Design Space Lynn Torbeck

2. Overview • Why is a definition important? • Definitions of Design Space. • Deconstructing Q8 Definition. • Basic science, Cause and Effect • SIPOC Process Analysis • Three Levels of Application. • Case Study with Example.

3. Why is this Important? • ICH Q8 is in its final version. • Design Space is defined in Q8. • Many presenters are using the term. • All are repeating the same definition. • Many presenters don’t understand the statistical implications of the issue. • Need for a detailed ‘Operational Definition’

4. Regulatory Impact • “Design space is proposed by the applicant and is subject to regulatory assessment and approval.” • “Working within the design space is not considered a change.” • “Movement out of the design space is considered to be a change and would normally initiate a regulatory post approval change process.” • This is a big deal, it needs to be done correctly ! • The economic impact of this can be huge.

5. Potential Benefits • Real process understanding and knowledge, not just tables of raw data. • Reduced rejects, deviations, discrepancies, lost time, scrap and rework. • Fewer 483 citations and warning letters. • Fewer investigations and CAPA. • Freedom to operate with design space

6. ICH Q8 Definition • “The multidimensional combination and interaction of input variables and process parameters that have been demonstrated to provide assurance of quality.” • This is not universally understood by all parties involved. We need to harmonize several viewpoints, statistical, scientific, engineering and regulatory.

7. Deconstructing the Definition • Need to deconstruct the definition to get to a day to day working Operational Definition that can be implemented. • Need enough detail to write a Standard Operating Procedure or SOP. • Need to see an example of what it looks like.

8. Multidimensional • Also called multivariable or multivariate • More than one variable at a time is considered. • The practice of holding the world constant while only considering one-factor-at-a-time has been shown to be grossly inefficient and ineffective.

9. Interaction • Defined in the PAT guidance • “Interactions essentially are the inability of one factor to produce the same effect on the response at different levels of another factor.” • Interactions are the joint action of two or more factors working together.

10. Example Interaction

11. “Input” Variables • Input Variables: • The “cause” • Independent variable • Factor • Output Variables • The “effect” • Dependent variable • Responses

12. Assurance of Quality • Assurance is a high probability of meeting: • Safety • Strength • Quality • Identity • Purity • For all measured quality characteristics.

13. Basic Science Cause Effect ?

14. Critical Cause and Effect Multiple Causes Effects Dependent Independent Responses Factors

15. Design Space Dependent Response Space Independent Factor Space ?

16. FACTOR SPACE N dimension X’s X1 X2 X3 X4 X5 XN RESPONSE SPACE M dimension Y’s Y1 Y2 Y3 Y4 Y5 YM Design Space

17. Factor Space • “Potential Space” Areas that could be investigated • “Uncertain Space” Insufficient data for a decision. • “Unacceptable Space” Factors and ranges have been shown to not provide assurance of SSQuIP. • “Acceptable Space” Data to demonstrate assurance of SSQuIP. • “Production Space” Factors and ranges that are selected for routine use.

18. Response Space • “Potential space” or “Region of Interest” • “Uncertain Space”, unknown responses • “Unacceptable Space” unacceptable responses • “Region of Operability,” acceptable responses • “Production Space” for manufacturing • Optimal Conditions or Control Space

19. Conceptual Design Space Design Space Opt Region of Interest Region of operability Uncertain space

20. Filler Lactose Mannitol Lubricant Steraric Acid Mag Stearate Disintegrant Maze Starch Microcrystalline Cell Binder PVP Gelatine Intact drug % Content uniformity Impurities Moisture Disintegration Dissolution Weight Hardness Friability Stability Tablet Process Example

21. Catalyst 10-15 lbs Temperature 220-240 degrees Pressure 50-80 lbs Concentration 10-12% Yield Percent converted Impurity pH Color Turbidity Viscosity Stability Chemical Process Example

22. Statistical Design Space • “The mathematically and statistically defined combination of Factor Space and Response Space that results in a system, product or process that consistently meets its quality characteristics, SSQuIP, with a high degree of assurance.” LDT

23. Modeling the World • “All Models are wrong, but some are useful.” G. E. P. Box • Empirical Models: • Simple linear, y = a + bx • Quadric equation, y = a + bx + cx2 • Mechanistic Models: • A physical or chemical equation.

24. Model Prediction • Equations for critical factors and the mechanistic connection with the critical responses allow for the prediction of the quality characteristics in quantitative terms. • Multidimensional in factors and responses.

25. S.I.P.O.C. Model

26. Macro View The Whole New Product Development Cycle Unknown Controllable Factors Controlled Responses Product Process Design Uncontrolled Responses Concomitant Uncontrollable Factors

27. Mid-Level View • Pre-formulation / formulation studies • Pharmacology / toxicology • Animal studies • Product development • Process development • Clinical trials • Validation and process improvement

28. Micro Level View:Design Space Independent Factor Space Dependent Response space

29. Existing Products • Design Space can be inferred by using existing information and historical data . • Retrospective process capability studies. • Annual Product Review analysis • Comparison of historical data to specs • Risk management and assessment, Q9

30. Factor Space • ASTM E1325-2002 • “That portion of the experiment space restricted to the range of levels of the factors to be studied in the experiment …” • AKA, “Design Regions” • The Cambridge Dictionary of Statistics. • B. S. Everitt, Cambridge University Press

31. Quick Dry Example • Five batches of product had been lost to an impurity exceeding the criteria • The criteria for impurity 1 was NMT 1.0% • Four factors studied. • Four responses.

32. FACTOR SPACE Drying time 3-9 mins Drying Temperature 40-100 Excipients Moisture 1.2-5 % %Solvent 1-14 % RESPONSE SPACE Impurity-1 % Impurity-2 % Intact drug % Final moisture % Quick Dry Example

33. Factor Space

34. Design Space Independent Factor Space Dependent Response space f(x)=? Process understanding is cause and effect quantitated. We find a mathematical and statistical formula that describes the relationship between factor space and response space.

35. 2 Factor InteractionEffects to Consider • Time * Temperature • Time * Moisture • Time * Solvent • Temperature * Moisture • Temperature * Solvent • Moisture * Solvent

36. Time*Temp Interaction Plot

37. Time* Moisture Interaction Plot

38. Temp*Moisture Interaction Plot

39. Time*Temp Contour Plot Temp Time

40. Time*Moisture Contour Plot Moisture Time

41. Temp*Moisture Contour Plot Moisture Temp

42. Time*Temp Surface

43. Time*Moisture Surface

44. Temp*Moisture Surface

45. FACTOR SPACE Drying time 3-9 mins Drying Temperature 40-100 Excipients Moisture 1.2-5 % %Solvent 1-14 % RESPONSE SPACE Impurity-1 % Impurity-2 % Intact drug % Final moisture % Quick Dry Example

46. FACTOR SPACE Solvent, no effect Time, decrease Temp, decrease Moisture, decrease RESPONSE SPACE Impurity 1 Less than 1% R2 = 0.95 Conclusions

47. f(Xi) Design Space • Impurity = • +0.6079 • +Time * -0.0057 • +Temperature * -0.0058 • +Moisture * +0.1994 • +Time*Temp * +0.00061 • +Time*Moist * -0.29386 • +Temp*Moist * -0.00502 • +T*T*M * +0.00713

48. Goal • Find a set of levels for Time, Temperature, and Moisture that will predict impurity of less than 1 percent. (Solvent doesn’t matter.) • The combination of levels is the design space for impurity 1.

49. Predictive Equation

50. Predictive Equation