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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?.

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## How to Define Design Space

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**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 one-factor-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.**“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**Multiple Causes Effects Dependent Independent Responses Factors**Design Space**Dependent Response Space Independent Factor 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 Design Space**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**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**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**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.**Macro View**The Whole New Product Development Cycle Unknown Controllable Factors Controlled Responses Product Process Design Uncontrolled Responses Concomitant Uncontrollable Factors**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.**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**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.**2 Factor InteractionEffects to Consider**• Time * Temperature • Time * Moisture • Time * Solvent • Temperature * Moisture • Temperature * Solvent • Moisture * Solvent**Time*Temp Contour Plot**Temp Time**Time*Moisture Contour Plot**Moisture Time**Temp*Moisture Contour Plot**Moisture Temp**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**FACTOR SPACE**Solvent, no effect Time, decrease Temp, decrease Moisture, decrease RESPONSE SPACE Impurity 1 Less than 1% R2 = 0.95 Conclusions**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**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.

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