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Session 9, Thu 29Jul2010 1:30-3:00pm
Method Optimization and Validation in the 21st Century
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ICH GUIDELINE PHARMACEUTICAL DEVELOPMENT Q8(R1)
13November08
2 Key Concepts
• Quality by Design (QbD): • Systematic approach to development • Predefined objectives• Emphasizes … process understanding and … control• Based on sound science and quality risk management
• Design Space (DS): • The range of process variables within which quality is assured• Proposed by the applicant• Within the DS not considered a change• Outside the DS requires post-approval change process.
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ICH GUIDELINE QUALITY RISK MANAGEMENT Q9
Current Step 4 version dated 9 November 2005
I.9 Supporting Statistical Tools Statistical tools … facilitate more reliable decision making… principal statistical tools …
• Control Charts• Design of Experiments (DOE)• Histograms• Pareto Charts• Process Capability Analysis
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FDA CDER/CBER/CVM Guidance for Industry Process Validation: General Principles and Practices
DRAFT GUIDANCE November 2008 cGMP
“Design of Experiment (DOE) studies can help develop process knowledge by revealing relationships, including multi-factorial interactions, between the variable inputs … and the resulting outputs.
Risk analysis tools can be used to screen potential variables for DOEstudies to minimize the total number of experiments conducted while maximizing knowledge gained.
The results of DOE studies can provide justification for establishing ranges of incoming component quality, equipment parameters, and in process material quality attributes.”
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ICH Q8(R1), Q9, & FDA PV Guidance Translation
1. Leverage prior knowledge
2. Recognize what is not known
3. Use statistical design of experiments
4. Model your process
5. Predict performance
6. Capture prediction visually
7. State prediction uncertainty
Knowledge =Ability to predict the future
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“QbD” coined 22 years ago … by an Analytical Chemist!!
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QbD, DoE, Response Surface, Chemometrics, Optimization, etc. in the Analytical Chemistry literatureMethodology Analyte ReferenceHPLC polyribosyl-ribitol
phosphateBelfast et al. (2006) J Chromatog B 832, 208-215
FIA perphenazine Sultan & Walmsley (1998) Talanta 46, 897-906
Extraction Transdermal API Li et al (2005) J Pharm & Biomed Anal 37, 493-498
HT Enzyme L-ascorbic acid Vermeir et al (2008) Analytical Chimica ACTA 618, 94-101
FIA (Extraction)
Tricyclic Anti-Depressants
Acedo-Vaenzuela et al (2005) Talanta 66, 952-960
FIA bromazepam Sultan et al (1999) Talanta 50, 841-849Colorimetric tolmetin Agatonovic-Kustrin et al (1991) J
Pharm&Biomed Anal 9, 919-924Micellar electrokinetic chromatog.
ketorolac tromethamine & impurities
Orlandini et al (2004) J Cromotog A 1032, 253-263
Capillary Electrophoresis
ethambutol Ragonese et al (2002) J Pharm&Biomed Anal 27, 995-1007
GCMS Derivitization
anabolic steroids Hadef et al (2008) J Chromotog A 1190, 278-285
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QbD, DoE, Response Surface, Chemometrics, Optimization, etc. in the Analytical Chemistry literatureMethodology Analyte ReferenceExtraction phenolics Liyana-Pathirana & Shahidi (2005) Food
Chemistry 93, 47-56Extraction polysaccharides Wu et al (2007) Food Chemistry 105, 1599-
1605ion chromotography
niacin Saccani et al (2005) Food Chemistry 92, 373-379
capillary electrophoresis
B6, B12, dexamethasone, lidocaine
Candioti et al (2006) Talanta 69, 140-147
ion-pairing HPLC
atomoxetine Gavin & Olsen (2008) J Pharmaceut&Biomed Anal 46, 431-441 (Nice QbD example)
Colorimetric formaldehyde Bosque-Sendra et al (2001) Fresenius J Anal Chem 369, 715-718
RP-HPLC API and impurities Yan Li et al (2010) “A systematic approach to RP-HPLC … http://americanpharmaceuticalreview.com
ELISA AbbottCell Based IA AbbottPotentiometric (enzyme linked)
Urea Deyhimi & Bajalan (2008) Bioelectrochemistry 74, 176-182
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Plan for this session•Introduce the “ACE” method example•OFAT strategy*•Factorial strategy
•Full•Fractional
•Designing/ Analyzing a screening experiment*•Power/ Sample Size*•Interpreting statistical output
•Augmenting to an RSM design*•Analyzing an RSM experiment*•Including a margin for uncertainty•Identifying a design space*
•Running “confirmatory” trials*•Control strategy•Telling your story•Software•What we left out *Computer activity with PMJMP3.xls
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Applying prior knowledge and risk assessment to factor selection
Caution: EVERYTHING depends on getting this right !!!
Accuracy(*Recovery)Precision(LOD, LOQ, *RSD)Specificity (Resolution)Linearity, Dynamic Range
Extraction
*sonicationshaking
volume
Derivitization
timetemperature
concentration
Chromotography
injection volume*flow rate
*temperature*pH
*%ACNcolumn type
ionic strengthvoltage
pressureramp
surfactantDetection
wavelengthbandpass
Data Reduction
calibration modelintegration algorithm
rounding
Reagents
calibrator levelsnumber of calibrators
enzyme lotantibody lot
plate
Environment
sample matrixsample prep
daysystem
runinjection
lab
Analyst
trainingSOP
assumptions
Start here please.What is the analytical target profile?
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Analytical methods are processes tooACE Method Example
ACE Method:Sample Prep
&HPLC
Flow Rate (30-50)
Column Temp (5-15)
pH (1-4)
%ACN (10-40%)
Sonication (1-2)
Recovery % (>90%)
RSD%(<1.7%)
Factors Responses
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Process Knowledge
What is it?The ability to accurately predict/control process responses.
How do we acquire it?Scientific experimentation and modeling.
How do we communicate it?Tell a compelling scientific story.Give the prior knowledge, theory, assumptions.Show the model.Quantify the risks, and uncertainties. Outline the boundaries of the model.Use pictures.Demonstrate predictability.
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One factor at a time (OFAT) strategyTrial FlowRate Column
TemppH %ACN Sonication Recovery%
1 40 10 2.5 25 1 852 40 10 2.5 25 2 953 40 10 2.5 10 1.5 904 40 10 2.5 40 1.5 70
%ACN
Soni
catio
n
85
95
7090
10 401
2
ε+×+×+= ACNcSonbaRecov
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Try the OFAT Strategy(steps 1-10)
(note the Responses contain trial to trial random noise …. ε)
FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)30-50 5-15 1-4 10-40% 1-2 >90% <1.7% Outcome
Experimental Factors Measured Responses
Step 7
FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)30-50 5-15 1-4 10-40% 1-2 >90% <1.7% Outcome
40 10 2.5 25 1.5
Experimental Factors Measured Responses
F9
FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)30-50 5-15 1-4 10-40% 1-2 >90% <1.7% Outcome
40 10 2.5 25 1.5 89.6 1.4 FAIL
Experimental Factors Measured Responses
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Why we need more than OFAT• Contour plot of response vs. 2 factors:
• Goal: Maximize response• Fix Factor 2 at A.
• Optimize Factor 1 to B.• Fix Factor 1 at B.
• Optimize Factor 2 to C.• Done? True optimum is
Factor 1 = D and Factor 2 = E.
• Also, interactions cannot be evaluated easily -more on this soon!
A
Factor 1
Fact
or 2
B
C
D
E80
6040
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Factorial strategyTrial FlowRate Column
TemppH %ACN Sonication Recovery%
1 40 10 2.5 10 1 802 40 10 2.5 10 2 1003 40 10 2.5 40 1 754 40 10 2.5 40 2 85
%ACN
Soni
catio
n
80
85
75
100
10 401
2
ε+××+×+×+= ACNSondACNcSonbaRecov
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Main and Interaction Effects Defined
ε+××+×+×+= ACNSondACNcSonbaRecov
The prediction equation is obtained through the “magic” of regression.
b is a measure of the “main effect” of Sonication
c is a measure of the “main effect” of %ACN
d is a measure of the “interaction effect” between Sonication and %ACNif d = 0, effects of Sonication and %ACN are additiveif d > 0, effects of Sonication and %ACN are synergisticif d < 0, effects of Sonication and %ACN are antagonistic
ε represents trial to trial random noise
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Recognizing Interactions
%ACN
Soni
catio
n
C
B
D
A
10 401
2
C
B
D A
1 2Sonication
Rec
over
y (%
LC)
%ACN=10
%ACN=40
C
B
DA
1 2Sonication
Rec
over
y (%
LC)
%ACN=10
%ACN=40
Parallel LinesNo interactiond = 0
Non-Parallel Linesinteractiond ≠ 0
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Which factors interact?
Ref: Weiyong Li et al (2005) Sample preparation optimization for assay of active pharmaceutical ingredients in a transdermal drug delivery system using experimental designsJ Pharm&Biomed Anal 37, 493-498
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Taking advantage of interactions
10 40%ACN
Rec
over
y (%
LC)
Sonication = 2
Sonication = 1
90
At which Sonication level will Recovery be more robust to %ACN?
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Importance of replicationTrial FlowRate Column
TemppH %ACN Sonication Recovery%
1 40 10 2.5 10 1 762 40 10 2.5 10 2 983 40 10 2.5 40 1 734 40 10 2.5 40 2 825 40 10 2.5 10 1 846 40 10 2.5 10 2 1027 40 10 2.5 40 1 778 40 10 2.5 40 2 88
%ACN
Soni
catio
n
76,84
88,82
73,77
98,102
10 401
2
Notice fitted model based on averages
rSDSD individual
average =
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Replication vs Repetition
Trial FlowRate ColumnTemp
pH %ACN Sonication Recovery%
1 40 10 2.5 10 1 762 40 10 2.5 10 2 983 40 10 2.5 40 1 734 40 10 2.5 40 2 825 40 10 2.5 10 1 846 40 10 2.5 10 2 1027 40 10 2.5 40 1 778 40 10 2.5 40 2 88
Trial FlowRate ColumnTemp
pH %ACN Sonication Recovery%
1 40 10 2.5 10 1 76, 842 40 10 2.5 10 2 98, 1023 40 10 2.5 40 1 73, 774 40 10 2.5 40 2 82, 88
Replication: 1. Every operation that contributes to variation is redone with each trial.2. Measurements are independent.3. Individual responses are analyzed.
Repetition:1. Some operations that contribute variation are not redone.2. Measurements are correlated.3. The averages of the repeats should be analyzed (usually).
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Full Factorials: 23
A
B
C
-1 +1-1
+1
+1
-1
Main Effects Interaction EffectsTrial I A B C AB AC BC ABC
1 + - - - + + + -2 + + - - - - + +3 + - + - - + - +4 + + + - + - - -5 + - - + + - - +6 + + - + - + - -7 + - + + - - + -8 + + + + + + + +
• 8 coefficients from 8 trials = maximum use of data• Follows the RULES OF GOOD DESIGN:
1. Number of trials ≥ Number of coefficients2. Each column must add to 0 (balance)3. Vector product of any 2 columns must = 0 (orthogonality)4. If 2 columns are identical, the coefficients cannot be
distinguished (confounded).
ε++++++++= hABCgBCfACeABdCcBbAay
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Fractional Factorials: 23-1
A
B
C
-1 +1-1
+1
+1
-1
Main Effects Interaction EffectsTrial I A B C AB AC BC ABC
1 + - - - + + + -2 + + - - - - + +3 + - + - - + - +4 + + + - + - - -5 + - - + + - - +6 + + - + - + - -7 + - + + - - + -8 + + + + + + + +
• 4 coefficients from 4 trials = maximum use of data• Follows the RULES OF GOOD DESIGN:
1. Number of trials ≥ Number of coefficients2. Each desired column adds to 0 (balance)3. Vector product of any 2 desired = 0 (orthogonality)4. Note: I=ABC, A=BC, B=AC, C=AC (confounded)
ε++++= dCcBbAay
What if…• we can’t afford 8 trials, or• we have prior knowledge that interactions are not presentTry a half fraction…
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Design Resolution• “I=ABC” for this 23-1 half fraction is called the “Defining Relation”• Note that “I=ABC” implies that “A=BC”, “B=AC”, and “C=AB”.
We like our screening designs to be at least resolution IV (I=ABCD)
• The number of factors in a defining relation is called the “Resolution”• This 23-1 half fraction has resolution III• We denote this fractional factorial design as 2III
3-1
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Experimental Power
• Fractional factorial designs are generally used for “screening”
• Statistical tests (e.g., t-test) are used to “detect” an effect.
• The power of a statistical test to detect an effect depends on the total number of replicates = (trials/design) x (replicates/trial)
• If our experiment is under powered, we will miss important effects.
• If our experiment is over-powered, we will waste resources.
• Prior to experimenting, we need to assess the need for replication.
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Statistical Tests for Effects
Caution: Unless the model contains only main effect terms, statistical tests should be based on coded factor levels (Most DOE packages recode factor levels during analysis).
( ) t~Effect ObservedStd.Err.
Effect ObservedNoise to Signal =
t0
Conclusion of
Statistical test
Ha Type I error
rate=αok
H0ok
Type II error rate
= βH0 Ha
True State
H0: |effect|=0Ha: |effect|=δ
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Rule of Thumb for Replication22
121
4 ⎟⎠⎞
⎜⎝⎛⎟
⎠⎞⎜
⎝⎛ +≥= −− δ
σβα zzN rial)plicates/tdesign)(re in trials(#
• While not exact, this ROT is easy to apply and useful.
• Commercial software will have more accurate formulas.
α z1-α/2
0.01 2.580.05 1.960.1 1.65
β z1-β
0.05 1.650.1 1.280.2 0.85
σ is the trial to trial SD
δ is the size of effect (high – low) you need to detect.
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Rough Trial Number Calculator(steps 11 – 16)
Prior Standard Deviation of Individual MeasurementsAbsolute Change in Response that must be detected
Desired Type I error rateDesired Type II error rate
After entering the above 4 inputs, press F9 to estimate the…Minimum number of Corner Trials in the design
Prior Standard Deviation of Individual Measurements 1.3Absolute Change in Response that must be detected 2
Desired Type I error rate 0.05Desired Type II error rate 0.2
After entering the above 4 inputs, press F9 to estimate the…Minimum number of Corner Trials in the design 14
Prior information for the ACE Method ProcessRecovery (%LC) RSD(%)
*Prior guess of the measurement Standard Deviation 1.3 0.1**Change in Response considered important to detect 2.0 0.2
*** Desired Type I Error Rate 0.05 0.05****Desired Type II Error Rate 0.2 0.2
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2 Level Designs(steps 17-18)
2 3 4 5 6 7 8 9 10 11 12 13 14 154 Full III6 IV8 Full IV III III III
12 V IV IV III III III III III16 Full V IV IV IV III III III III III III III20 III III III III III24 IV IV IV IV III III III32 Full VI IV IV IV IV IV IV IV IV IV48 V V64 Full VII V IV IV IV IV IV IV IV96 V V V
128 Full VIII VI V V IV IV IV IV
Resolution CodesFull Complete factorial. No confounding.
VIII-VI 2-factor interactions confounded with 4-factor or higher interactionsV Main effects confounded with 4-factor interactions and
2-factor interactions confounded with 3-factor interactionsIV Main effects confounded with 3-factor interactions and
2-factor interactions confounded with each otherIII Main effects confounded with 2-factor interactions
Num
ber
of T
rials
Number of Factors
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Screening Design: 2V5-1
(steps 19 – 21)
Trial Type FlowRate ColumnTemp pH %ACN Sonication1 center 40 10 2.5 25 1.52 factorial 30 5 4 10 13 factorial 30 5 1 40 14 factorial 30 15 1 40 25 factorial 30 15 1 10 16 factorial 50 15 1 40 17 factorial 50 5 4 10 28 factorial 50 15 4 10 19 center 40 10 2.5 25 1.5
10 factorial 50 15 4 40 211 factorial 50 15 1 10 212 factorial 50 5 1 10 113 factorial 30 5 4 40 214 factorial 50 5 4 40 115 factorial 50 5 1 40 216 factorial 30 15 4 10 217 factorial 30 5 1 10 218 factorial 30 15 4 40 119 center 40 10 2.5 25 1.5
Experimental Factors
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Value of Center Points
•Provide additional degrees of freedom for statistical tests
•May be process “target” settings
•Provide statistical tests for presence of curvature (lack of model fit)
•May be used as “controls” in sequential experiments.
•May be spaced out regularly in the trial run order as a check for drift.
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Value of randomizing trial orderComplete Randomization: • Randomization is the cornerstone of statistical analysis• Insures observations are independent • Protects against “lurking variables”• Requires a process (e.g., draw from a hat)• May be costly/ impractical
Restricted Randomization:• “Difficult to change factors (e.g., bath temperature) are “batched”• Often needed when pipetting into 96 well trays• May be fine… just consider possible confounding risk.
Blocking:• Include uncontrolled variable (e.g., day) in design.• Excellent way to reduce variation.• Rule of thumb: “Block when you can. Randomize when you can’t block”.
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Screening Experiment(steps 22 – 26)
Trial FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)1 40 10 2.5 25 1.5 2 30 5 4 10 1 3 30 5 1 40 1 4 30 15 1 40 2 5 30 15 1 10 1 6 50 15 1 40 1 7 50 5 4 10 2 8 50 15 4 10 1 9 40 10 2.5 25 1.5 10 50 15 4 40 2 11 50 15 1 10 2 12 50 5 1 10 1 13 30 5 4 40 2 14 50 5 4 40 1 15 50 5 1 40 2 16 30 15 4 10 2 17 30 5 1 10 2 18 30 15 4 40 1 19 40 10 2.5 25 1.5
Experimental Factors Measured Responses
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Screening Experiment(step 27)
Trial FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)1 40 10 2.5 25 1.5 90.9 1.52 30 5 4 10 1 102.8 2.23 30 5 1 40 1 91.6 2.14 30 15 1 40 2 75.4 1.55 30 15 1 10 1 102.7 2.26 50 15 1 40 1 92.6 2.27 50 5 4 10 2 100.7 1.78 50 15 4 10 1 100.3 2.29 40 10 2.5 25 1.5 90.0 1.410 50 15 4 40 2 76.8 1.711 50 15 1 10 2 99.4 1.512 50 5 1 10 1 101.2 2.213 30 5 4 40 2 75.0 1.614 50 5 4 40 1 91.2 2.115 50 5 1 40 2 77.8 1.216 30 15 4 10 2 101.4 1.517 30 5 1 10 2 100.8 1.718 30 15 4 40 1 93.5 2.319 40 10 2.5 25 1.5 91.3 1.5
Experimental Factors Measured Responses
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Analysis of Screening Design(steps 28 – 32)
Trial Intercept FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)1 12 13 14 15 16 17 18 19 110 111 112 113 114 115 116 117 118 119 1
# Trials 19# Parameters 6
RMSE #VALUE!Rsquare #VALUE!Adj-Rsquare #VALUE!
FlowRate ColumnTemp pH %ACN SonicationCoefficients #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Standard Err #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!t value #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!P-value #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
Recovery (%LC)
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Analysis of Screening Design(step 33)
RMSE 4.307Rsquare 0.857Adj-Rsquare 0.801
FlowRate ColumnTemp pH %ACN SonicationCoefficients 119.982 -0.020 0.015 0.006 -0.564 -8.571Standard Err 0.108 0.215 0.718 0.072 2.154t value -0.184 0.068 0.009 -7.858 -3.980P-value 0.857 0.946 0.993 0.000 0.002
RMSE 0.207Rsquare 0.753Adj-Rsquare 0.658
FlowRate ColumnTemp pH %ACN SonicationCoefficients 2.792 -0.002 0.003 0.033 -0.002 -0.640Standard Err 0.005 0.010 0.035 0.003 0.104t value -0.470 0.313 0.949 -0.583 -6.170P-value 0.646 0.759 0.360 0.570 0.000
Recovery (%LC)
RSD(%)
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Statistical output from a screening DOE(Objective: Identify the presence of main effects)
Statistic InterpretationRMSE Root Mean Squared Error. Estimates trial to trial standard
deviation ( s ).Rsquare The proportion of variability in the data explained by the
model.Adj-Rsquare A conservative version of Rsquare that includes a penalty
when the number of model coefficients is close to N Coefficient* The a,b,c,d,… in the prediction equationStandard Err*
Standard error of estimate of the coefficient
t-value* ratio of the coefficient to it’s standard errorP-value* The probability of observing a t-value this large by random
chance alone if, in fact, the factor has no effect
* Caution: if the model contains more than main effects, the t-test should be based on coded factor levels.
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Sequential Knowledge Building
Screening Designs• 2 level factorial/ fractional factorial designs • Weed out the less important factors• Skeleton for a follow-up RSM design
RSM Designs• 3+ level designs • Find design space• Explore limits of experimental region
ConfirmatoryDesigns
• Confirm Findings• Characterize Variability
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Sequential Knowledge Building
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Response Surface MethodologyTrial FlowRate Colum
nTemp pH %ACN Sonication Recovery%
1 40 10 2.5 10 1 802 40 10 2.5 10 2 1003 40 10 2.5 40 1 754 40 10 2.5 40 2 855 40 10 2.5 25 1 856 40 10 2.5 25 2 957 40 10 2.5 10 1.5 908 40 10 2.5 40 1.5 709 40 10 2.5 25 1.5 83
ε+×+×+
××+×+×+=
22 ACNfSoneACNSond
ACNcSonbaRecov
%ACN
Soni
catio
n
80
85
75
100
10 401
2
85
95
7090 83
42
Taking advantage of curvature
Reco
very
Sonication
At which Sonication level will Recovery be most consistent?
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The Box-Behnken RSM Design
Analytical Method examples of this design:1. Bosque-Sendra et al (2001) Fresenius J Anal Chem 369, 715-7182. Saccani et al (2005) Food Chemistry 92, 373-3793. Ragonese et al (2002) J Pharm&Biomed Anal 27, 995-1007
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The Central Composite RSM Design• “Cube Oriented”• 3 or 5 levels for each factor
In 3 factors
Factorial orFractional Factorial
Central Composite Design
+ +
=
Axial PointsCenter Points
Analytical Method examples of this design:1. Belfast et al. (2006) J Chromatog B 832, 208-2152. Sultan & Walmsley (1998) Talanta 46, 897-9063. Acedo-Vaenzuela et al (2005) Talanta 66, 952-960
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Augment Design (Steps 34 – 38)Trial Type FlowRate ColumnTemp pH %ACN Sonication
1 center 40 10 2.5 25 1.52 factorial 30 5 4 10 13 factorial 30 5 1 40 14 factorial 30 15 1 40 25 factorial 30 15 1 10 16 factorial 50 15 1 40 17 factorial 50 5 4 10 28 factorial 50 15 4 10 19 center 40 10 2.5 25 1.510 factorial 50 15 4 40 211 factorial 50 15 1 10 212 factorial 50 5 1 10 113 factorial 30 5 4 40 214 factorial 50 5 4 40 115 factorial 50 5 1 40 216 factorial 30 15 4 10 217 factorial 30 5 1 10 218 factorial 30 15 4 40 119 center 40 10 2.5 25 1.520 axial 40 10 2.5 40 1.521 center 40 10 2.5 25 1.522 axial 40 10 2.5 10 1.523 axial 40 10 2.5 25 224 center 40 10 2.5 25 1.525 axial 40 10 2.5 25 1
Face-Centered Central Composite Design in 2 factors (%ACN and Sonication)Axial trials permit estimation of curvature effects
46
RSM Experiment(steps 39 – 42)
Trial FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)20 40 10 2.5 40 1.5 21 40 10 2.5 25 1.5 22 40 10 2.5 10 1.5 23 40 10 2.5 25 2 24 40 10 2.5 25 1.5 25 40 10 2.5 25 1
Experimental Factors Measured Responses
F9
Trial FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)20 40 10 2.5 40 1.5 85.7 1.621 40 10 2.5 25 1.5 89.8 1.322 40 10 2.5 10 1.5 101.1 1.623 40 10 2.5 25 2 87.7 1.224 40 10 2.5 25 1.5 91.9 1.425 40 10 2.5 25 1 96.5 2.0
Experimental Factors Measured Responses
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Analysis of RSM (steps 43 – 59)
Trial Intercept %ACN Sonication %ACN*Sonication %ACN^2 Sonication^2 Recovery (%LC) RSD(%)1 1 25 1.5 37.5 625 2.25 90.9 1.52 1 10 1 10 100 1 102.8 2.23 1 40 1 40 1600 1 91.6 2.14 1 40 2 80 1600 4 75.4 1.55 1 10 1 10 100 1 102.7 2.26 1 40 1 40 1600 1 92.6 2.27 1 10 2 20 100 4 100.7 1.78 1 10 1 10 100 1 100.3 2.29 1 25 1.5 37.5 625 2.25 90.0 1.4
10 1 40 2 80 1600 4 76.8 1.711 1 10 2 20 100 4 99.4 1.512 1 10 1 10 100 1 101.2 2.213 1 40 2 80 1600 4 75.0 1.614 1 40 1 40 1600 1 91.2 2.115 1 40 2 80 1600 4 77.8 1.216 1 10 2 20 100 4 101.4 1.517 1 10 2 20 100 4 100.8 1.718 1 40 1 40 1600 1 93.5 2.319 1 25 1.5 37.5 625 2.25 91.3 1.520 1 40 1.5 60 1600 2.25 84.3 1.421 1 25 1.5 37.5 625 2.25 89.1 1.422 1 10 1.5 15 100 2.25 100.5 1.823 1 25 2 50 625 4 86.5 1.524 1 25 1.5 37.5 625 2.25 91.9 1.625 1 25 1 25 625 1 95.3 1.9
Measured ResponsesExperimental Factors Derived Factors (Interactions and Curvature Factors)
48
Analysis of RSM (step 60)
RMSE 1.015Rsquare 0.990
Adj-Rsquare 0.987Intercept %ACN Sonication %ACN*Sonication %ACN^2 Sonication^2106.572 -0.221 0.405 -0.491 0.008 1.090
Coefficients
Recovery (%LC)
RMSE 0.124Rsquare 0.893
Adj-Rsquare 0.865Intercept %ACN Sonication %ACN*Sonication %ACN^2 Sonication^2
5.1223 -0.0329 -3.6444 -0.0008 0.0006 1.0149
RSD(%)
Coefficients
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What is a Design Space?
50
Contour Plot of Predicted Mean(steps 61 – 69)
+%ACN* +Sonication* +%ACN*Sonication* +%ACN^2* +Sonication^2*106.57 -0.22 0.41 -0.49 0.01 1.09
Recovery (%LC) =
10.00 13.33 16.67 20.00 23.33 26.67 30.00 33.33 36.67 40.001.00
1.11
1.22
1.33
1.44
1.56
1.67
1.78
1.89
2.00
%ACN
Sonication
Predicted Mean Recovery (%LC)
100-11090-10080-9070-80
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The ring of uncertaintyPrediction is Imperfect
Why?1. Noise in data
2. Imperfect model
3. Process drifts
4. Changes in materials
5. “Lurking” variables
6. Test method drifts
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Contour plot with “margin of uncertainty”(step 70)
10.00 13.33 16.67 20.00 23.33 26.67 30.00 33.33 36.67 40.001.00
1.11
1.22
1.33
1.44
1.56
1.67
1.78
1.89
2.00
%ACN
Sonication
95% Confidence Lower Bound for Predicted Mean Recovery (%LC)
100-11090-10080-9070-80
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Observe the margin for uncertiantyPredicted Mean Recovery 95% Confidence Lower Bound
for Predicted Mean Recovery
10.00 13.33 16.67 20.00 23.33 26.67 30.00 33.33 36.67 40.001.00
1.11
1.22
1.33
1.44
1.56
1.67
1.78
1.89
2.00
%ACN
Sonication
Predicted Mean Recovery (%LC)
100-11090-10080-9070-80
10.00 13.33 16.67 20.00 23.33 26.67 30.00 33.33 36.67 40.001.00
1.11
1.22
1.33
1.44
1.56
1.67
1.78
1.89
2.00
%ACN
Sonication
95% Confidence Lower Bound for Predicted Mean Recovery (%LC)
100-11090-10080-9070-80
54
Describing the Design Space
10.00 13.33 16.67 20.00 23.33 26.67 30.00 33.33 36.67 40.001.00
1.11
1.22
1.33
1.44
1.56
1.67
1.78
1.89
2.00
%ACN
Sonication
95% Confidence Upper Bound on Predicted Mean RSD(%)
2.3-2.62-2.31.7-21.4-1.7
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Design Space for Multiple Responses?
Y1: Yield
Y2: Purity
Y3: Viscosity
Extract Polysaccharides from
Seeds
X1: Temperature
X2: pH
X3: Time
X4: Water
Strategy #1: Overlap contour plots
Wu et al, Optimization of extraction process of crude polysaccharides from boat-fruited sterculia seeds by response surface methodologyFood Chemistry 105 (2007) 1599–1605
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Design Space for Multiple Responses?Yield
Viscosity
Purity
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Design Space for Multiple Responses?
Lid-B12 Res (minimize)
B12-B6 Res (minimize)
B6-Dexa Res (target)
Analysis Time (minimize)
Current (range)
Capillary Electrophoretic Resolution of
Lidocaine, B12, B6, and Dexamethazone
Voltage
Buffer Concn
Strategy #2: Global Desirability Metric (D)
Candioti et al, Multiple response optimization applied to the development of a capillary electrophoretic method for pharmaceutical analysis Talanta 69 (2006) 140–147
58
Design Space for Multiple Responses?
Strategy #2: Global Desirability Metric (D)
RR
w
ii
ii
w
ii
ii
w
ii
ii
i
dddD
LowighHTargetPred|
LowighHPred-High
LowighHLowPred
di
i
i
×××=
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
⎟⎟⎠
⎞⎜⎜⎝
⎛−
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
=
L21
|
range withinkeep to is goal if 0 or 1
target meet to is goal if
minimize to is goal if
maximize to is goal if
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Design Space for Multiple Responses?Strategy #3: Use Multivariate Bayesian MethodsReference: John J. Peterson (2008) A Bayesian Approach to the ICH Q8 Definition of Design Space, Journal of Biopharmaceutical Statistics,18:5,959 — 975
The only strategy that can predict the future probability (risk) of one or more responses not being within the design space. However, it requires the support of a statistician trained in Bayesian methods.
We will use Strategy 1 (contour overlap) for our example.
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Describing the Design Space
10.00 13.33 16.67 20.00 23.33 26.67 30.00 33.33 36.67 40.001.00
1.11
1.22
1.33
1.44
1.56
1.67
1.78
1.89
2.00
DrugPS
Lubricant%
Rec
over
y
10.0
0
13.3
3
16.6
7
20.0
0
23.3
3
26.6
7
30.0
0
33.3
3
36.6
7
40.0
0
1.00
1.11
1.22
1.33
1.44
1.56
1.67
1.78
1.89
2.00
DrugPS
Lubricant%
RSD
10 20 30 40 1.00
1.22
1.44
1.67
1.892.00
1.78
1.56
1.33
1.11
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10.0 10. 5 11. 0 11.5 12.0 12. 5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17. 5 18.0 18.5 19. 0 19.5 20.0 20.5 21.0 21.5 22. 0 22.5 23. 0 23.5 24. 0 24.5 25.0 25.51.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28
1.30 1.32 DS DS DS1.34 DS DS DS DS DS DS DS DS DS DS1.36 DS DS DS DS DS DS DS DS DS DS DS DS DS DS1.38 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS1.40 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS1.42 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS1.44 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS1.46 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS1.48 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.50 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.52 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.54 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.56 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.58 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.60 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.62 DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.64 D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.66 D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.68 D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.70 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.72 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.74 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.76 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.78 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.80 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.82 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.84 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.86 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.88 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.90 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.92 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.94 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.96 DS D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 1.98 D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS 2.00 D S DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS DS
Design Space Identifier Table (DS = Acceptable Performance)
Soni
catio
n
%ACN
Describing the Design Space(step 71)
%ACN Sonication
1 14.0 1.66
2 14.0 1.94
3 16.5 1.80
4 19.0 1.66
5 19.0 1.94
3
5
4
2
1
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“Confirmatory” Trials (steps 72 – 76)
FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)Confirmatory Trial Fixed Fixed Fixed 10-40% 2-Jan >90% <1.7% Outcome
1 40 10 2.5 14.0 1.66 2 40 10 2.5 14.0 1.94 3 40 10 2.5 16.5 1.80 4 40 10 2.5 19.0 1.66 5 40 10 2.5 19.0 1.94
Experimental Factors Measured Responses
FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)Confirmatory Trial Fixed Fixed Fixed 10-40% 2-Jan >90% <1.7% Outcome
1 40 10 2.5 14.0 1.66 97.1 1.3 PASS2 40 10 2.5 14.0 1.94 95.8 1.5 PASS3 40 10 2.5 16.5 1.80 96.3 1.6 PASS4 40 10 2.5 19.0 1.66 95.0 1.4 PASS5 40 10 2.5 19.0 1.94 93.2 1.4 PASS
Experimental Factors Measured Responses
F9
FlowRate ColumnTemp pH %ACN Sonication Recovery (%LC) RSD(%)Confirmatory Trial Fixed Fixed Fixed 10-40% 2-Jan >90% <1.7% Outcome
1 40 10 2.5 14.0 1.66 99.3 1.6 PASS2 40 10 2.5 14.0 1.94 98.2 1.6 PASS3 40 10 2.5 16.5 1.80 95.6 1.7 PASS4 40 10 2.5 19.0 1.66 92.6 1.4 PASS5 40 10 2.5 19.0 1.94 89.0 1.3 FAIL
Experimental Factors Measured Responses
F9
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Why do confirmation trials fail?
One possible reason:
• Design space limits may be set to contain the MEAN performance
• But trials include trial to trial “noise”
• ∴ Trials are outside DS due to random noise
• … not because design space is wrong
Possible Solution(s):
1. Use 95% CI for individual result instead of 95% CI for mean to identify the DS (will give smaller DS).
2. Apply DS acceptance limits to MEAN of multiple trials (requires more work).
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Why do Method Transfers Fail?
Galen Radebaugh, Pfizer, 2010, Isreal
What needs to be transferred?• Analytical Target Profile (method requirements)• SOPs• Knowledge (ability to predict)• Skill (ability to use knowledge)• What is not known• Evidence for Equivalence
What is inadvertently transferred?• Assumptions (things taken for granted)• Checklists• Lack of evidence for non-equivalence
What might help?• Include Design Space detail in SOP/ training• Acknowledge the uncertainties and risks• Include tests for equivalence (USP1010) in protocols• Life cycle communication and quality monitoring
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Control Strategy (ICH Q8R1)• Ensure consistent required quality.• Justify how controls contribute to quality.
• Controls based on understanding • Understanding based on comprehensive development approach and
quality risk management (Q9).
• Sources of variability that impact downstream quality identified, understood, and controlled.
• Emphasize upstream control, not end product testing.
• Adaptive compensation for upstream variability• Periodic internal monitoring to ensure the design space model’s
performance (Control Charts).
• New knowledge used to improve/redefine design space (subject to regional requirements).
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Telling the story• Define Critical Quality Attributes
• quantitatively defined• derived from safety and efficacy
• State, quantitatively, what is known (predictable)• Incorporate applicable theory and prior knowledge • Develop a mechanistic understanding• Use DOE • Outline, quantitatively, the design space.
• Admit, quantitatively, what is unknown• Show that no likely risk has been ignored • Convey a quantitative understanding of the risks• State the confidence levels, probabilities • Outline a comprehensive risk mitigation
• Outline a general control strategy (include SPC)• Use upstream QC (eg Control Charts)• Show commitment to continuous improvement
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SoftwareMinitab•General purpose stat package•User friendly•Good learning tool
JMP•General purpose stat package•Excellent for DOE•Very advanced features
•Monte-Carlo simulation of DOE models•Good D-optimal design features
•May need statistical support for some features
Design Expert•Exclusive focus on DOE (may want addnl tools)•I have not used but my impression is very good
MS Excel•Not what you want for DOE •Maybe OK for illustration (you decide)
55
10
15
Hard%RSD
MixTim7 9 11 13 1me(min)
5 7 9
15
20
2.015 17
32.5 W
2 0
3.0
Water(L)
Surface Plot of Hard%RSD
6 11 16
2.0
2.5
3.0
MixTime(min)
Wat
er(L
)
Overlaid Contour Plot of Hardness...Hard%RSD
Hardness
Hard%RSD
19.520.5
07
Lower BoundUpper Bound
White area: feasible region
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Modeling and simulation in JMP
Contour Profilingand overlay for design space identification
Monte-Carlo Simulationof batch failure rate
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Topics not covered
• Robust design & Taguchi designs
• Mixture (e.g.,gasoline blend) and constrained designs
• D-optimal designs and custom augmentation
• Bayesian approaches• multiple correlated responses• incorporation of prior knowledge
• Categorical factors
• Random factors & Gage R&R
• Split-plot experiments
• Blocked designs
• How to design/ analyze DOE in commercial software
• Verifying statistical assumptions
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Why is QbD a win-win?
Benefits to Regulators:
1. Review based on quantitative science
2. Industry resources focused on higher risk
3. Encourages multi-disciplinary decisions
4. Encourages coordination and consistency across review, compliance and inspection
5. More flexibility in decision making
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Why is QbD a win-win?Benefits to Industry
1. Better understanding of how APIs and excipients affect manufacturing
2. Relate manufacturing to clinical during design
3. Fewer manufacturing surprises
4. Reduced manufacturing costs/waste
5. Less Regulatory scrutinyScience based dialog
Quicker approvalspost market changes
new technology/ continuous improvement
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References1. Conformia CMC-IM Working Group (2008) Pharmaceutical Development case study: “ACE
Tablets”. Available from the following web site: http://www.pharmaqbd.com/files/articles/QBD_ACE_Case_History.pdf
2. LeBlond D (2009) Hypothesis testing: examples in pharmaceutical process and analytical development, Journal of GXP Compliance 13(3), 25-37.
3. Montgomery D (2005) Design and analysis of experiments, 6th edition, Wiley.
4. Myers R, Montgomery D, and Anderson-Cook C (2009) Response surface methodology, Wiley.
5. ICH Expert Working Group (2008) GUIDELINE on PHARMACEUTICAL DEVELOPMENT Q8(R1) Step 4 version dated 13 November 2008
6. ICH Expert Working Group (2005) Guideline on QUALITY RISK MANAGEMENT Q9 Step 4 version dated 9 November 2005
7. FDA CDER/CBER/CVM (November 2008) Draft Guidance for Industry Process Validation: General Principles and Practices (CGMP)
8. Diamond W (1981) Practical Experiment Designs, Wadsworth, Belmont CA
Thank You!!
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ObjectivesI. Appreciating the Regulatory Environment• Managing risk with ICH Q9• Knowledge building with ICH Q8• FDA Process/Method Validation Guidance perspective
II. Awareness of the Win-Win Principles Behind Good Experimental Design• Incorporating prior knowledge into the model• Leveraging hidden replication• Sequential knowledge building strategies• Reducing variation with interactions
III. Getting the Most Out of Your Results• Hearing the message in the noise cloud• Incorporating prior knowledge into predictions• Dealing with multiple responses• Finding robustness through performance simulation
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ObjectivesIV. Good Strategies for Communicating Experimental Results• Telling the story• Identifying the ring of ignorance• Describing the inference space and control strategy• Communicating the risk
V. Interactive ExerciseParticipants work individually or in small groups to reinforce the concepts learned. A simulated method development situation and simple spreadsheet tool is provided.