How to Define Design Space Lynn Torbeck 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. 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’ 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. 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 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. 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. 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 onefactor-at-a-time has been shown to be grossly inefficient and ineffective. 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. Example Interaction AB Interaction Effect 70 60 Average Effect 50 40 A Low A High 30 20 10 0 0.5 1 B Low 1.5 2 B High 2.5 “Input” Variables Input Variables:    The “cause” Independent variable Factor Output Variables    The “effect” Dependent variable Responses Assurance of Quality Assurance is a high probability of meeting:      Safety Strength Quality Identity Purity For all measured quality characteristics. Basic Science Cause ? Effect Critical Cause and Effect 1. 3. 5. Multiple Causes Effects R= Independent Factors 2. 4. 6. Dependent Responses Design Space Independent Factor Space ? Dependent Response Space Design Space FACTOR SPACE N dimension X’s X1 X2 X3 X4 X5 XN RESPONSE SPACE M dimension Y’s Y1 Y2 Y3 Y4 Y5 YM 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. 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 Conceptual Design Space Design Space Opt Region of Interest Region of operability Uncertain space Tablet Process Example 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 Chemical Process Example Catalyst  10-15 lbs Temperature  220-240 degrees Pressure  50-80 lbs Concentration  10-12% Yield Percent converted Impurity pH Color Turbidity Viscosity Stability 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 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. 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. S.I.P.O.C. Model Culture Management Supplier Input Supplier Input Supplier Input SPO's Facilities People Process Equipment Systems Regulations Measurement Environment Output Customer Output Customer Output Customer The Whole New Product Development Cycle Unknown Controllable Factors Concomitant Uncontrollable Factors Product Process Design Controlled Responses Uncontrolled Responses Macro View Mid-Level View Pre-formulation / formulation studies Pharmacology / toxicology Animal studies Product development Process development Clinical trials Validation and process improvement Micro Level View: Design Space Independent Factor Space Dependent Response space 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 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 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. Quick Dry Example 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 % Factor Space B B +1 +1 1.90 3.80 5.20 1.30 15.50 -1 0.70 5.20 0.80 A 20.70 -1 1.00 -1 C 1.00 -1 -1 0.80 6.10 -1 0.50 +1 0.60 C Left Cube Is D = LOW q62 +1 Right Cube is D = HIGH A +1 Design Space Independent Factor Space f(x)=? Dependent Response space Process understanding is cause and effect quantitated. We find a mathematical and statistical formula that describes the relationship between factor space and response space. 2 Factor Interaction Effects to Consider Time * Temperature Time * Moisture Time * Solvent Temperature * Moisture Temperature * Solvent Moisture * Solvent Time*Temp Interaction Plot Interaction Graph DESIGN-EXPERT Plot Impurity -1 B: T em perature 20.7 X = A: Time Y = B: Temperature 15.2894 Impurity-1 B- 40.000 B+ 100.000 Actual Factors C: Moisture = 3.10 D: Solv ent = 7.50 9.87889 4.46834 -0.94222 3.00 4.50 6.00 A: T i m e 7.50 9.00 Time* Moisture Interaction Plot Interaction Graph DESIGN-EXPERT Plot Impurity -1 C: M oi sture 20.7 X = A: Time Y = C: Moisture Impurity-1 C- 1.200 15.4312 C+ 5.000 Actual Factors B: Temperature = 70.00 D: Solv ent = 7.50 10.1624 4.89364 -0.37515 3.00 4.50 6.00 A: T i m e 7.50 9.00 Temp*Moisture Interaction Plot Interaction Graph DESIGN-EXPERT Plot Impurity -1 C: M oi sture 20.7 X = B: Temperature Y = C: Moisture C- 1.200 C+ 5.000 Actual Factors A: Time = 6.00 D: Solv ent = 7.50 15.2697 Impurity-1 Design Points 9.8395 4.40925 2 -1.021 40.00 55.00 70.00 85.00 B: T em perature 100.00 Time*Temp Contour Plot Impurity-1 Design-Expert® Sof tware 100.00 Impurity -1 20.7 8 0.1 85.00 Actual Factors C: Moisture = 3.10 D: Solv ent = 7.50 Temp B: Temperature X1 = A: Time X2 = B: Temperature 6 4 70.00 2 55.00 1 40.00 3.00 4.50 Time 6.00 A: T i m e 7.50 9.00 Time*Moisture Contour Plot Impurity-1 Design-Expert® Sof tware 5.00 Impurity -1 20.7 8 0.1 C: Moisture Moisture Actual Factors B: Temperature = 70.00 D: Solv ent = 7.50 6 4.05 X1 = A: Time X2 = C: Moisture 4 3.10 2 2.15 1 1.20 3.00 4.50 6.00 Time A: T i m e 7.50 9.00 Temp*Moisture Contour Plot Impurity-1 Design-Expert® Sof tware 5.00 Impurity -1 Design Points 20.7 8 0.1 Moisture Actual Factors A: Time = 6.00 D: Solv ent = 7.50 6 C: Moisture X1 = B: Temperature X2 = C: Moisture 4.05 3.10 1 3 4 2 2.15 1.20 40.00 55.00 70.00 Temp B: T em perature 85.00 100.00 Time*Temp Surface Design-Expert® Sof tware Impurity -1 20.7 0.1 12 X1 = A: Time X2 = B: Temperature 9 Impurity-1 Actual Factors C: Moisture = 3.10 D: Solv ent = 7.50 6 3 0 100.00 9.00 85.00 7.50 70.00 B: Temperature 6.00 55.00 4.50 40.00 3.00 A: Time Time*Moisture Surface Design-Expert® Sof tware Impurity -1 20.7 0.1 9.1 X1 = A: Time X2 = C: Moisture 7.025 Impurity-1 Actual Factors B: Temperature = 70.00 D: Solv ent = 7.50 4.95 2.875 0.8 5.00 9.00 4.05 7.50 3.10 C: Moisture 6.00 2.15 4.50 1.20 3.00 A: Time Temp*Moisture Surface Design-Expert® Sof tware Impurity -1 20.7 0.1 12 X1 = B: Temperature X2 = C: Moisture 9 Impurity-1 Actual Factors A: Time = 6.00 D: Solv ent = 7.50 6 3 0 5.00 100.00 4.05 85.00 3.10 C: Moisture 70.00 2.15 55.00 1.20 40.00 B: Temperature Quick Dry Example 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 % Conclusions FACTOR SPACE Solvent, no effect Time, decrease Temp, decrease Moisture, decrease RESPONSE SPACE Impurity 1  Less than 1% R2 = 0.95 f(Xi) Design Space Impurity = +0.6079 +Time * +Temperature * +Moisture * +Time*Temp * +Time*Moist * +Temp*Moist * +T*T*M * -0.0057 -0.0058 +0.1994 +0.00061 -0.29386 -0.00502 +0.00713 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. Predictive Equation Factor Intercept A-Time B-Temperature C-Moisture AB AC BC ABC Coefficient Factor Level 0.607940 -0.005702 4 -0.005813 70 0.199410 1 0.000614 280 -0.293860 4 -0.005018 70 0.007127 280 Impurity 1.0 Predictive Equation Factor Intercept A-Time B-Temperature C-Moisture AB AC BC ABC Coefficient Factor Level 0.607940 -0.005702 9 -0.005813 43 0.199410 5 0.000614 387 -0.293860 45 -0.005018 215 0.007127 1935 Impurity 1.0 Design Space Overlay Plot Design-Expert® Sof tware 100.00 Ov erlay Plot Impurity -1 X1 = A: Time X2 = B: Temperature B: Temperature Actual Factors C: Moisture = 5.00 D: Solv ent = 7.50 85.00 70.00 55.00 Impurity-1: 1 40.00 3.00 4.50 6.00 A: T ime 7.50 9.00 Design Space Overlay Plot Design-Expert® Sof tware 100.00 Ov erlay Plot Impurity -1 X1 = A: Time X2 = B: Temperature B: Temperature Actual Factors C: Moisture = 1.20 D: Solv ent = 7.50 85.00 70.00 Impurity-1: 1 55.00 40.00 3.00 4.50 6.00 A: T im e 7.50 9.00 Multidimensional Specifications Specifications should not be set one factor at a time. We need to consider all responses together. We need to do the same analysis for impurity 2, intact drug and final moisture and then overlay the four solutions to find the design space that will meet all of the criteria at the same time. Scale-Up Scale-up may not be linear Assume that the basic equations will apply Assume the design space will be somewhat robust and rugged. Need to do confirmation experiments to confirm assumptions. Or reestablish the design space. Design Space Conclusions ICH Q8 and the FDA are asking for designed experiments and predictive equations for each aspect of a new product. Descriptions need to be mathematical and statistical equations. Empirical equations are the most common, but a few mechanistic equations may be possible. Design Space Conclusions This is a new and perhaps confusing issue for the pharmaceutical industry. To implement this approach will require designed experiments with overlays of multiple responses for each new product. Sometimes retrospective studies of existing products can be done with historical data.