Method Optimization and Validation in the 21st Century

7/19/2010

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Session 9, Thu 29Jul2010 1:30-3:00pm

Method Optimization and Validation in the 21st Century

[email protected]

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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DRAFT GUIDANCE November 2008 cGMP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


40 10 2.5 25 1.5


F9


40 10 2.5 25 1.5 89.6 1.4 FAIL


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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


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


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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23

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


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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


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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


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


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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

52

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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55

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

56

Design Space for Multiple Responses?Yield

Viscosity

Purity

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57


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


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.

60

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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61

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

62

“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



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


F9


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


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).

64

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).

66

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

68

Modeling and simulation in JMP

Contour Profilingand overlay for design space identification

Monte-Carlo Simulationof batch failure rate

67

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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

70

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

72

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

74

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.

Documents

Method Optimization and Validation in the 21st Century