Disegno Sperimentale (DoE) come strumento per QbD

Transcription

1 Giornata di Studio Disegno Sperimentale (DoE) come strumento per QbD Università degli Studi di Milano Dipartimento di Scienze Farmaceutiche Milano, 22 aprile 2013 Dr. Lorenza Broccardo

2 Introduction Nowadays, product quality cannot be tested into the finished product but it must be designed and built into a product and its manufacturing process The International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use provides a guide for pharmaceuticals process developers that introduce the QbD concept: Quality by Design is systematic approach to development that begins with predefined objectives and emphasizes product and process understanding and process control, based on sound science and quality risk management --ICH Q8 (R), Step 2

3 Tools to achieve QbD: Design by Experiments (DoE) Risk Assessment Multivariate data Analysis (MVA) Design of Experiments (DOE) is an statistical methodology useful to plan a set of experiments in order to obtain the maximum amount of information with the minimum amount of experiments

4 About DoE Which applications? process products When is it useful? development (new process-new product) optimisation (process/product-performance) minimization (cost-discard-pollution) robustness testing (method-instrument) selection of influencing variables understand the relation between responses and variables define the set point define the design space

5 Examples pharmaceutical problems well handled by DoE define factors influencing a reaction yield optimization of a chromatographic separation optimization of a mixture (mixture: blend which components cannot be manipulated independently of one another) production of active substance as powder: define the design space, that is, the experimental conditions assuring a production inside specifications

6 Definitions Factors independent variables, X, controlled by the experimenter Range [X min ; X max ] Experimental domain the numbers of factors and their ranges of variability define the experimental domain Responses dependent variables, Y, measured Objective The experimentation purpose: screening (preliminary information) optimization (detailed information) robustness testing (evaluate the process robustness)

7 Why an experimental planning? To obtain new information about the system, the experimenter causes a controlled variation of factors and measure the corresponding modification of the responses information are located in the factors setting (X matrices): a careful planning of experiments increases the amount of information an appropriate experiments planning allow to connect matrix X and Y by a mathematical equation (model) which enable prediction X MODEL Y factors responses

8 Classical vs DOE approach Classical 1. incomplete sampling of the X space 2. gives different implications with different starting points 3. no quantification of interactions 4. does not lead to the real optimum 5. leads to many experiments and poor information 6. what about: X=3 and Y=2? 10 X X 1 DOE 1. homogeneous sampling of the X space 2. result independent from the starting point 3. quantification of interactions 4. experimental results are interpreted by a regression model - system description by a surface - predictive power - information about the real optimum 5. requires few experiments to obtain al lot of information 6. handles complex systems X X 1

9 DoE make use of design Design: organized distribution of experiments within the experimental domain Full Factorial Composit Box-Behnken x 1 =1 Doehlert x 2 =1 x 3 =1 Simplex

10 The design generates the worksheet

11 Experiments are analyze and interpret by a model The model is a mathematical relation between X (set) and Y (measured) ƒ(x) = b 0 + b 1 x + b 2 x 2 + b n x n + e Three main types of polynomial models linear: y = b 0 + b 1 x 1 + b 2 x e interaction: y = b 0 + b 1 x 1 + b 2 x 2 + b 12 x 1 x e quadratic: y = b 0 + b 1 x 1 + b 2 x 2 + b 11 x b 22 x b 12 x 1 x The model graphical representation It is a m dimensional surface representing Y as a function of all X i (m = i X i + 1) Y = f (X i ) It is used for Y prediction 11

12 Objectives, Design and Model are linked objective design model response surface 2 factors 3 factors > 3 Screening (factors<4) Hyper cube Linear Interactions Screening (factors>4) Rob. testing Balanced fraction of hyper cube Linear Optimization Hyper cube + axial points Quadratic 12

13 QbD steps that achieve benefit from DoE application Identification of influencing input process parameters Early stage of system study (screening) Find out which factors are the dominating ones Many factors are investigated in few runs List of supposed influencing factors is proposed on the bases of: previous knowledge on the system fishbone (cause-and-effect) diagram risk assessment (FMEA) Factors effect is tested by a screening design outcome:

14 Definition of appropriate experimental domain Early stage of system study (screening) Find out which factors ranges include the experimental condition corresponding to the required response(s) value Many factors are investigated in few runs X X

15 Sul Mof Temp Sul*Sul Mof*Mof Temp*Temp Sul*Mof Sul*Temp Mof*Temp % Define the set point conditions As a result of the screening phase, the most important factors and their appropriate range of variability have been defined Optimization: understand the relation between each factor and each response (linear, interaction, quadratic) plot the responses predicted value by the polynomial models predict the best set point conditions Few factors are investigated in many runs Scaled & Centered Coefficients for Yield

16 Robustness testing It is usually carried out before the release of a product or an analytical method as a latest test to assure quality. The objective is to verify the process stability and define the design space Responses specifications must be defined Set point Factor combination which is currently used for running the process Experimental domain small shift around the set point Design Linear (many factors are investigated in few runs) Outcome the process is robust: release the set point factor combination and the factors variability ranges that assure quality the process is not robust: identify factors responsible for the process high sensitivity and define how to reduce their impact

17 PlateN Nature of robustness Are responses inside or outside specifications? Is regression model significant or not? Four limiting cases 1) Inside specification/significant model all the measured values are inside the specification regression model significant apply the model to predict maximum variation the process is robust 2) Inside specification/non-significant model ideal outcome changes in parameters correspond to the experimental error the process is robust Target Min Replicate Index

18 AcN# ph# Temp# OSA# Col(A) Col(B) k2 3) Outside specification/significant model discover which factors causes the outside of specification apply the model to understand how factors ranges should be varied to achieve robustness the process is not robust 3,5 3,0 2,5 1 Max Target ,10-0,00-0,10-0,20-0,30 Scaled & Centered Coefficients for k2 Replicate Index

19 vetific vetific 4) Outside specification/non-significant model Most complex limiting case... replicated center-points have much higher response values (left) o might be possible to resolve by shrinking the design o at minimum an additional design one strong outlier (right) o risk for a process that is unstable and then gives strange results o cause of problem needs to be found and a new design performed Investigation: itdoe_roblimcases Investigation: itdoe_roblimcases Investigation: itdoe_roblimcases Plot of Replications for vetific with Experiment Number labels Replicate Index Plot of Replications for vetific with Experiment Number labels Replicate Index Plot of Replications for vetific with Experiment Number labels Replicate Index MOD DE :58:00 MODDE :59:51 MODDE :01:59

20 Design Space The Design Space correspond to the experimental domain centered on the set point and including only experimental conditions that assure quality according with defined standard (y) and the accepted level of risk of failure (DPMO) To define the Design Space, a robustness test is required The design space is calculated on the bases of: regression model model error Monte Carlo simulation responses specifications DPMO (Defect Per Million Opportunities) level accepted Outcome: experimental domain (design space) assuring that all responses are inside specifications according to the accepted level of failure

21 Monte Carlo simulation The Monte Carlo simulations are: random factor settings according to the selected distribution around their optimum value but within the Low and High limits followed by predictions of the responses predictions are performed DPMO (Defect Per Million Opportunities) shows how many response predictions are outside the response specifications based on one million simulations Indicates the sensitivity of the responses to the external perturbation applied to the factors settings Ideal outcome: DMPO = 0

22 Design Space outcome Identify critical factors (AcN, OSA) and define new range of variability Identify critical responses (k2) Verify that the new factors range assure robustness

23 Design space outcome Probability contour plot

24 Conclusion DoE is a tool to achieve QbD is an organized methodology useful to plan a set of experiments efficiently provides tools to analyze the data and make decision makes available a deep understanding of the process allows to save time and money

25 Acknowledgements Scientific committee Organizing committee All attendees