a quality-by-design based methodology for the rapid ... · a quality-by-design based methodology...

A Quality-by-Design Based Methodology for the

Rapid Development of Robust LC Methods

• Richard Verseput, President

• Graham Shelver, Ph.D., V.P. Sales and Marketing

S-Matrix Corporationwww.smatrix.com

2

Quality-by-Design ?

KNOWLEDGE SPACE

–

“The information and knowledge gained from pharmaceutical development

studies

and manufacturing experience provide scientific understanding to support the establishment of the design space, specifications, and manufacturing controls.”[Q8(R1) -

Pharmaceutical Development Revision 1, November 2007]

pH2.0 7.05.5

65

85

Final %Organic

Experimental RegionAm I doing QbD ?

3

Quality-by-Design –

DOE Experimental Approach

1. Define the Experimental Design Region

a) Select study variables

b) Define study ranges or levels

2. Develop the Knowledge Space

a) Conduct a formal experimental design

b) Analyze results –

build equations of variable effects

3. Establish the Design Space

a) Define best conditions (setpoint optimization)

b) Define process robustness (operating space)

4

Column 5

Column 4

Column 3

Column 2

pH

50

100

2.0 7.0

Final %Organic

Column 1

Experimental Design Region:

pHand

Final % Organic



1. Define the Experimental Design Region

a) Select study variables

b) Define study ranges or levels

FORMAL EXPERIMENTAL DESIGN –

“A structured, organized method for determining the relationship between factors

affecting a process and the output of that process. Also known as “Design of Experiments.”[ICH Q8 -

Guidance for Industry, Pharmaceutical Development, May 2006]

5

Rs

= βo

+ β1

(X1

) + β11

(X1

)2

+ β2

(X2

) + β22

(X2

)2

+ β12

(X1

*X2

)

pH

Final% Organic

50

100

2.0 7.0

2. Develop the Knowledge Space

a) Conduct a formal experimental design

b) Analyze results –

build equations of variable effects

KNOWLEDGE SPACE

–

“The information and knowledge gained from pharmaceutical development studies

and manufacturing experience provide scientific understanding to support the establishment of the design space, specifications, and manufacturing controls.”[Q8(R1) -

Pharmaceutical Development Revision 1, November 2007]



6

50

100

2.0 7.0pH

Final %Organic

Knowledge Space

Acceptable MeanPerformance Only

DESIGN SPACE

–

“The multidimensional combination

and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality.”[ICH Q8 -

Guidance for Industry, Pharmaceutical Development, May 2006]

3. Establish the Design Space

a) Define optimum operating conditions (setpoints)

b) Define robust operating ranges (control limits)



DesignSpace

All study factor combinations within the Design Space have:

• Acceptable mean performance

• Acceptable

robustness

7

Phase 1

─

“Easy to Control”

Parameters

= Instrument method editing

•

Solvent Strength (% Strong Solvent)•

Temperature•

Organic Solvent Type (exclusive “or”)

LC Method Development –

Traditional vs. Quality-by-Design

Traditional Trial-and-Error Approach:

Phase 2

─

“Difficult to Control”

Parameters

= Instrument hardware change out

•

pH (online mixing not advised)•

Ion Pairing Agents (not universal, slow column equilibration)•

Column Type (cost, switching required)

8

Conventional LC –

Example of Automation Support

Fusion AE + CDS

CDS

9

Fusion AE + CDS

CDS

Solvent Valve Assembly

4-RelayPanel

LANLAC/E Card

Network

UPLC –

Example of Automation Support

10

Phase 1

─

Column/Solvent Screening

= Major Effectors

•

Gradient Slope (5%-95%, vary gradient time)•

pH (3 or more levels -

automated solvent switching)•

Column Type (6 columns -

automated column switching)•

Solvent Type (can be included, w/wo

blending)

Method Development –

Traditional vs. Quality-by-Design

Automation-supported Formal Experimental Design:

Phase 2

─

Remaining Parameters

= Secondary Effectors

•

Pump Flow Rate•

Gradient Conditions (optimization)•

Column Temperature•

Ion Pairing / Suppressing Agents

11

Knowledge Required to Constitute a QbD Approach

A valid experimental strategy should provide a data set from which all significant parameter effects can be identified and quantified:

●

Linear additive effects.

●

Simple interaction effects.

●

Complex interaction and non-linear effects.

These effects drive analytical method robustness.

12

Examples of Important Effects

● Linear Additive Effect (no slope change)

)()( 22110 xbxbbArea API ++=

13


● Linear Additive Effect (no slope change)

14


● Pairwise

Interaction Effect (slope change)

)()()( 2*11222110 xxbxbxbbRs +++=

15


● Pairwise

Interaction Effect (slope change)

16


)x()x(b)x(b)x(b)x(bbR 22

1112222

111110s

● Complex interaction and and Non-linear Effects

17


● Complex interaction and and Non-linear Effects

18

Method Development Phase 1 –

Column/Solvent Screening

Current Approaches:

One-factor-at-a-time (OFAT)

First Principles Equation

Simplex (Iterative) Studies

Traditional Design of Experiments (DOE)

As we will discuss:

These approaches can lack the experimental design region coverage and quantitation necessary to Quality-by-Design

(QbD) based practice

Risk Factors in Current Practice

19

Standard approach that varies one parameter at a time

and assess the effect of these changes on parameters such as resolution (R).

One Factor at a Time (OFAT)

OFAT in Column Screening:

Step 1:

Multiple columns

are evaluated at constant method conditions(e.g. constant pH and gradient conditions).

Identify “best”

column by evaluating the various chromatograms.

Step 2:

Select a 2nd

parameter, say pH, and vary it across a series ofinjections using the “best”

column.

Step 3:

Select a 3rd

parameter, say Final % Organic, and vary it acrossa series of injections while using the “best”

pH from Step 2.

And so on ...

20

OFAT and

Experimental Design Region

True Experimental Region

defined by typical study ranges of two study factors

50

100

2.0 7.0pH

Final %Organic

Experimental Design Region:

pHand

Final % Organic

21

OFAT Design Region Coverage –

Step 1 Column 5

Column 4

Column 3

Column 2

pH

50

100

2.0 7.0

85

5.5

Column 1

OFATDesign Region

CoverageFinal %Organic

22

Column/Solvent Screening –

Steps 2 and 3

Table and graph show an OFAT study in which pH and Final % Organic*

were investigated sequentially to increase resolution of a critical pair.

*

–

Reflects the slope, since gradient time is held constant at 30 min.

23

Column/Solvent Screening –

Steps 2 and 3

Table and graph show an OFAT study in which pH and Final % Organic*

were investigated sequentially to increase resolution of a critical pair.

OFAT Completely Missed True Optimum Method Conditions

24

Risks in the OFAT Approach

• Extremely Limited Coverage of Design Region

• No Ability to Study Interaction Effects

25

• Percent organic (reversed-phase isocratic)

• Normal-phase conditions (reversed-phase isocratic)

• pH

• Mobile phase blend (isocratic)

• Ionic strength

• Additive/buffer concentration

• Gradient conditions

• Temperature

• Temperature with gradient conditions (reversed-phase)

Sequential Studies for One

of the Following:

First Principles Equation Approach

26

Normalize the Equation Using Tuning Run Data

1.50

1.25

1.00

Rs

65

75

85

Final % Organic

Normalized (data-adjusted)Model Prediction Line

Original First PrinciplesModel Prediction Line

27

Risk Factor 1

–

Disjoint Factor Space

30.0 50.0

15

GradientTime

Temperature

45

Study #1 Study #2

30.0 50.0

15

GradientTime

pH

45

pH with Temperature ?

28

►

Linear Additive Effects Model –

2 Factors.

►

Pure Curvilinear Effects Model –

2 Factors (Pure Quadratic).

)x(b)x(bbR 22110s

222222

2111110 )()()()( xbxbxbxbbRs ++++=

Risk Factor 2

–

No Interaction Effects

No Interaction Term )x*x(b...bR 21120s

29

Risks in the First Principles Equation Approach

• Limited kinds of paired-variable studies

• Limited coverage of design region

• Provides no knowledge of:Interaction Effects

Complex Effects

(5 Columns)*(3 pH levels)*(2 Gradient Runs) = 30 Runs

Lots of experiments –

very little knowledge yield

30

2.0 7.0

85

65

Final %Organic

pH

Simplex Optimization Approach

LastRun

FirstRuns

31

Risks in the Simplex Optimization Approach

• Limited coverage of design region

• Provides no knowledge of variable effects

-

Variables are too highly correlated to accurately identify effects

Lots of experiments –

no real knowledge yield

32

Traditional Design of Experiments (DOE)

Can provide a data set from which all significant parameter effects may be identified and quantified:

●

Linear additive effects.

●

Simple interaction effects.

●

Complex interaction and non-linear effects.

But –

there are risks ...

33

} EffectsEstimationError

ActualMean Effect

Effect will be poorly estimated when study range = experimental error range.

Risk Factor 1

–

Small Study Ranges

34

Use Large Variable Ranges = Good Signal/Noise Ratio.

Risk Factor 1

–

Small Study Ranges

35

Example -

Plackett-Burman

Designs:

• Typically are Resolution III• Main effects aliased with pairwise

interaction effects• Effective for Robustness Confirmation study• Risky for studies where goal is Knowledge

Limitation is often misunderstood –

also often forgotten in the data analysisand interpretation of results.

Trial1234

X1-+-+

X2--++

X3+--+

X1*X3--++

X1*X2+--+

X2*X3-+-+

Not all DOE Design Types contain equal knowledge potential.

Risk Factor 2

–

Wrong Design Selection

36

Generate experiments.

Manual, off-line, usingnon-validated DOEsoftware or “best guess”.

Calculate sampleAmounts.

Manual, off-line, usingnon-validated toolssuch as MS Excel.

Prepare samples

Run experiments manually.

Manual setup and operationof equipment.

Risk Factor 3

–

Transcription Errors

Conducting the Experiment

37

Statistically analyze andInterpret the data.

Manual, off-line, usingnon-validated toolssuch as MS Excel.

Examine need formore experiments.

Using off-line genericDOE software.

Enter data.Write report.

Manual, error-prone.

Risk Factor 3

–

Transcription Errors

Processing the Data and Results

38

• Column screening experiments, even those done by DOE, often have significantinherent data loss in critical results such as resolution.

• The data loss is due to both compound co-elution

and also changes in compoundelution order (peak exchange) between experiment trials.

These changes are due to the major effects that pH and organic solvent type can have on column selectivity.

Inherent Data Loss in Traditional Performance Metrics:

Risk Factor 4

–

Inherent Data Loss

39

Inherent Data Loss –

Co-elution and Peak Exchange

Trial 19

Trial 13Resolution of Impurity C from API 1

Resolution of Impurity C from Impurity G

40

Inherent Data Loss –

Co-elution and Peak Exchange

Integration Traditionally Involves Peak Tracking

41

Run No. Gradient Time pH Column Type Imp E - USPResolution Imp F - USPResolution Imp G - USPResolution1.a.1.a 8.8 2 C18 1.4 2.32.a.1.a 6.3 2 Phenyl 1.783.a.1.a 10 2 C18 1.45 2.364.a.1.a 5 2 C18 1.155.a.1.a 10 2 Phenyl 1.06 2.256.a.1.a 5 2 Phenyl 1.667.a.1.a 10 2 RP8.a.1.a 5 2 RP9.a.1.a 7.5 2 RP 2.9510.a.1.a 7.5 4.5 C18 0.97 1.18 3.811.a.1.a 7.5 4.5 Phenyl 1.24 2.2712.a.1.a 7.5 4.5 RP 2.08 2.1513.a.1.a 5 4.5 RP 0.9814.a.1.a 7.5 4.5 C18 1 2.63 3.8515.a.1.a 7.5 4.5 Phenyl 1.29 2.2616.a.1.a 7.5 4.5 RP 2.0817.a.1.a 5 7 C18 2.3518.a.1.a 10 7 Phenyl 1.45 1.08 2.4519.a.1.a 5 7 Phenyl 2.0320.a.1.a 10 7 RP 3.0521.a.1.a 5 7 RP 1.0222.a.1.a 8.8 7 Phenyl 1.42 2.3423.a.1.a 6.3 7 RP 1.5424.a.1.a 10 7 C18 1.89 2.99 2.8225.a.1.a 10 7 C18 1.87 2.95 2.8126.a.1.a 5 7 C18

Risk Factor 4

–

Inherent Data Loss

42

Inherent Data Loss Can Not Model Chromatography

Table above shows -

data can not be accurately modeled.

Result –

Phase 1 is reduced to a “Pick the Winner”

Strategy.

Solution:

Trend Responses -

independent of peak tracking –i.e. Peak Count Based, Peak Results Based

Compound Name R2-Adj. Value

Impurity F 0.4785

Impurity G 0.9725

Regression ModelStatistics

43

Risks in the Traditional DOE Approach

• Traditional Use of Small Study Variable Ranges-

Low Signal-to-Noise Ratio.

• Traditional Use of Highly Fractionated Factorial Designs-

Variables effects are confounded. Can not identify true effectors.

• Manual experiment design building and results data entry-

Transcription errors can corrupt experiment design and data analysis.

• Limitations in Traditional Performance Metrics-

Too much missing data for accurate effects modeling.

-

Data often do not represent variable effects.

44

1)

User selects the experimental parameters (study factors).

2)

Software generates a statistical experimental design and exports

it to the chromatography data system (automated).

3)

LC system runs the various conditions defined in the experimental design on the instrument (automated).

4)

Software imports results from the CDS (automated).

5)

Software generates and applies mathematical models to predict the optimum method (automated).

Automated DOE is carried out in the following five steps:

QbD-Based Design of Experiments –

A Case Study

The following slides present a case study of an Automated DOE experiment carried at a major Pharma company.

45

Case Study –

Software / Data Flow

Experiment run on HPLC in walk-away mode.

CDS generates chromatogram results.

Automated analysis, graphing, and reporting.

Report output formats: RTF, DOC, HTML, PDF.

Experiment Design

Ready-to-runmethods & sequences

File-less Data Exchanges

Steps 1 and 2 Step 3

Step 4

Step 5

46

Internal Column /External Solvent

SwitchingFusion AE

+ CDS

Waters Acquity

Case Study Hardware Framework –

UPLC System

47

Original Traditional HPLC MethodAU

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

Minutes1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00

4.6 X 150 X 5 µ

YMC Basic40/40/20 ACN/Methanol/ 2% Ammonium acetate pH 4.51.5 ml/min flowColumn Temperature 25 °C10 µ

injection

14 Compounds, including 2 APIs, 11 related impurities, and 1 process impurity

48

Experiment Variable Range or Level Settings

Gradient Time (min) 5.0 — 10.0

Gradient Slope (% Organic) 20.0 — 95.0 (solubility considerations)

pH 2.00, 4.5, 7.0

Column Type Three Columns:BEH C18 2.1 X 100BEH Phenyl 2.1 X 100Shield RP 2.1 X 100

Organic Solvents Mobile Phase A1-1: 0.05% TFA Buffer, pH 2.00Mobile Phase A1-2: 20 mM Ammonium Acetate Buffer, pH 4.45Mobile Phase A1-3: 10 mM Sodium Phosphate Dibasic Buffer, pH 6.80

Mobile Phase B1: 50% Acetonitrile, 50% Methanol

Step 1

–

Experiment Setup

49

50

100

2.0 7.0pH

Final %Organic

OFAT and

Experimental Design RegionExperimental Design Region Qualification

Center Point Used for Design Region Qualification Trial

50

AU

0.00

0.05

0.10

0.15

0.20

Minutes2.00 4.00 6.00 8.00 10.00

5.46

9

6.24

46.

459

6.88

17.

067

7.20

47.

292

7.49

47.

588

7.79

27.

920

8.20

38.

412

Gradient Conditions:Slope = 5% –

95%.Time = 7.5 min.

pH = 4.5

λ

=

@250nm

Col. Temp = 70°C

Flow Rate = 0.3 ml/min.

Results define that %Organic starting pointshould be increased –

New slope: 50% -

95%

Experimental Design Region Qualification

51

Software maps the experimental design to the study factors.

Important –

design region samplingof Numeric

factors is repeatedfor each level of each Categoricalfactor.

Step 2

–

Generate Design and Export it to the CDS

52

Automatically reconstruct experimental design within the Empower

chromatography data software

(CDS) as instrument methods and sample sets (sequences).

Step 2

–

Generate Design and Export it to the CDS

53

Fusion AE + CDS

CDS

Solvent Valve Assembly

4-RelayPanel

LANLAC/E Card

Network

Step 3

–

Run the experiment trials on the LC

54

Step 3

–

Integrate chromatograms

55

Step 4

–

Import Wizard. Auto-computed Trend Responses

56

Software automatically imports results from the CDS.

ImportFrom CDS

Step 4

–

Import Results from CDS

57

)x()x*x()x()x(Peaks .No 2221122

111110

pH (X1

= 6.5) Gradient Time (X2 = 9.0)

Predicted Result

Step 5

–

Model Results

58

Software generates and applies mathematical models to predict the optimum analytical method.

At right is a graphical representation of a model –

in this case the model of study factor effects on a given compound’s Tailing Factor response.

Note –

response is highly interactive and non-linear

Step 5

–

Model Results

59

Resolution Maps.

Note region of good Resolution (Red) changes for different pairs of compounds in the contour plots below.

Step 5

–

Graphically Represent Results from CDS

–

60

Step 5

–

Automated Numerical Search for Optimum Method

61

Step 5

–

Numerical Solution Search –

Best Conditions

62

An Overlay graph of all responses for which method performance goals are defined is automatically generated.

For this presentation we will “build”

the overlay graph one response at a time.

Step 5

–

Graphical Solution Search –

Best Region Overall

63

Note:

Shaded region

indicates pHand Gradient Time and pH combinations that do NOT

meet performance requirements.

Overlay Graphics

Fusion AE Overlay Graph.

Each color on the graph corresponds to a response for which goals have been defined.

A region shaded with a given color shows the study variable level setting combinations that will NOT meet the goals for the corresponding response.

Note: the

un-shaded region

corresponds to level setting combinations that meet all response goals.

64

2 response goals

Overlay Graphics

65

Overlay Graphics

Unshaded Region WithPredicted Best Settings:

Gradient Time = 9.5 minpH = 7.0Column = C18

66

Analyze Results to Define Variable Levels for Optimization.

Predicted best conditions chromatogram.Results define center-point conditions for optimization experiment.

AU

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

Minutes0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50

4.07

8 4.42

8

4.74

74.

927

5.10

45.

252

5.36

75.

508

5.72

5

5.96

1

6.17

4

6.55

1

67

Experiment Variable Range or Level Settings

Pump Flow Rate (mL/min) 0.1 — 0.5 (Constant level in Screening Design was 0.25 mL/min)

Gradient Slope(Starting Point % Organic) 50.0 — 80.0 Endpoint = 95%

Gradient Time (min) 5.0 — 10.0

pH 6.50, 7.10

Column Type One Column:BEH C18 2.1 X 100

Organic Solvents Mobile Phase A1: 10 mM Sodium Phosphate Dibasic Buffer, pH 6.50Mobile Phase A2: 10 mM Sodium Phosphate Dibasic Buffer, pH 7.10

Mobile Phase B: 50% Acetonitrile, 50% Methanol

Optimization Experiment –

Design

68

Automated Numerical Search for Optimum Method

69

)x()x*x()x()x(R 2221122

111110s

DOE Models are Mean Response Predictors

Pump Flow Rate (X1

= 1.0) Single LevelSetting

Single LevelSetting% Organic (X2 = 80)

Single Prediction = Mean Result

Rs

X = 2.87—

70

Overlay Graphics –

Mean Performance

Edges of Failure

7176.0 77.0 78.0 79.0 80.0 81.0 82.0

83.0

Setpoint Error:

The robustness of an analytical procedure is a measure of its capacity to remain unaffected by small variations in method parameters…

ICH Q2A –

Robustness

Distribution of Variation in % Organic around setpoint in normal use due to statistically random error.

Actual % Organic achieved in one assay.

% Organic Setpoint

72

Mean Performance Versus Robustness

96.0 97.0 98.0 99.0 100.0 101.0 102.0 103.0 104.0

API Concentration (%)

LAL UAL

Methods A and B -

Same Mean resultX

Method A -

Large Response Variation

Method B -

Small Response Variation

73

Mean Performance Versus Robustness -

Surrogate

74

Process Flow

= variation around setpoint

Separation(Column)

LSL USL

API Amount

6σVariation

The LC System as a Process in a Box

Raw Material(Mobile Phase

Pumps)

HeatingChamber

(Column Oven)

At-LineMeasurement

(Detector)

75

Process Capability -

Quantified

iationvar6LSLUSLcp

Process Capability

(Cp

)

This is a direct, quantitative measure of process robustness used routinely in Statistical Process Control (SPC) applications. The classical SPC definition

of “Inherent Process Capability”

(Cp

) is

USL and LSL

= Specification Limits (tolerance width).

6σ

Variation

= ±3σ

process output variation.

Traditional Goal ≥

1.33

(standard goal based on setting the USL and LSL at±4σ

of process output variation).

76

Monte Carlo Simulation = Predicted Variation

Variation AroundSetpoint

Variation AroundSetpoint

Step 2

–

Predict Variation at Run 1 Level Settings

Rs

Pump Flow Rate (X1) % Organic (X2)

)x()x*x()x()x(R 2221122

111110s

77

Tolerance Width Delta(±

distance) = 1.00

.I.CLSLUSLcp

e.g., Peak Resolution ±3σ

confidence interval of 1.50:

331

501002

122623

871873

.

.

...

..pc

1.87 2.87 3.87

USP Resolution

Step 3

–

Compute Robustness Cp for Run 1

∆

6σ

2.12 3.62

78

Step 4

–

Repeat Steps 1 -

3 for all Experiment Runs

Resolution RobustnessMean Resolution

Robustness can be calculated for each key performance metric.

79

Mean Performance

and Robustness

prediction models can be linked to a

numerical or graphical optimizer to identify one or more combinations of

variable level settings that meet or exceed mean performance and

performance robustness goals defined for each response.

Step 5

–

Generate Prediction Model of Robustness Cp

80

Edges of Failure

Design Space

–

Mean Performance

81

Design Space

–

Mean Performance + Robustness

82

2.40

9

2.64

7

2.96

2

3.27

4

3.62

1

3.83

0

3.93

4

4.02

8

4.16

3

Imp

A -

4.27

4

Imp

B -

4.45

8

AP

I 1 -

4.70

5

5.00

7

AP

I 2 -

5.19

8

5.51

3

Last

peak

- 5.

695

AU

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

Minutes2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60

Experimentally Verify Predicted Optimum Conditions.

QbD Approach -

Final Chromatogram.

AU

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

Minutes1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00

Trial-and-Error -

Final Chromatogram.

83

Are we doing QbD?

A Best Practices Checklist

1. Does my study address all critical parameters in combination ?

3. Does my study address interactions and complex parameter effects ?

4. Do my study variable ranges ensure good signal-to-noise ratio ?

2. Does my study address the entire experimental design region

?

5. Is my design free of aliasing of study factor effects ?

6. Am I making effective use of automation to support my study

?

7. Will the results data enable accurate quantitative effects estimation ?

8. Am I able to characterize robustness performance ?

84

The Fusion AE QbD-based Approach Presented Today:

Greatly facilitates QbD through:

- Automation

-

Statistically valid experimentation

-

Novel data treatments

Provides quantitative knowledge of all critical parameter effects

Enables establishing Design Space for both:

-

Mean Performance (setpoint optimization)

-

Process Robustness (operating space)

Required time for the work is dramatically reduced

Success promotes the use of QbD

Conclusions

85

End of Presentation

Thank You for inviting us.

And

Thanks' for attending!

86

1.

ICH Q8 -

Guidance for Industry, Pharmaceutical Development, May 2006.

2.

ICH Q8(R1), Pharmaceutical Development Revision 1, November 1, 2007.

3.

Cornell, John A., Experiments With Mixtures, 2nd Edition, John Wiley and Sons, New York, 1990.

4.

Christian, Robert P., Casella, George, (2004), Monte Carlo Statistical Methods: Second Edition, Springer Science+Business

Media Inc., New York

5.

Dong, Michael W., Modern HPLC for Practicing Scientists, John Wiley and Sons, Hoboken, New Jersey, 2006.

6.

Gavin, Peter F., Olsen, Bernard A., J. Pharm. Biomed. Anal. 46 (2007), 431-441.

7.

Juran, J.M., Juran on Quality by Design, (Macmillan, Inc., 1992).

8.

Montgomery, Douglas C., Design and Analysis of Experiments, 6th Edition, John Wiley and Sons, New York, 2005.

9.

Myers, Raymond H. and Montgomery, Douglas C., Response Surface Methodology, John Wiley and Sons, New York, 1995.

10.

Rathmore, A.S., Branning, R., and Cecchini, D., Design Space for Biotech Products. BioPharm

International, 20(5), April 2007.

11.

Rathmore, A.S., Saleki-Gerhardt, A., Montgomery, S.H., and Tyler, S.M., Quality by Design: Industrial Case Studies on Defining and Implementing Design Space for Pharmaceutical Processes –

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References

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