Issues in Non-Clinical Statistics Stan Altan Chemistry, - - PowerPoint PPT Presentation

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Stan Altan

Chemistry, Manufacturing & Control Statistical Applications Team Department of Non-Clinical Statistics

Issues in Non-Clinical Statistics

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Outline

Introduction Regulatory Considerations Impacting Statistical Practices in Non-Clinical Development (Two Issues)

Stability Analysis Issues and Controversies Equivalence Approach to Bioassay Potency Testing

Issues in the Statistical Analysis of a Non- standard Design (The N-1 Design)

Excipient Compatibility Studies

Wrap-up

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Pharmaceutical Product Development: Discovery through Launch

Lead Opt Compound Selection Formulation Development Safety Assessment Phase I First

in humans

Phase IIa

Proof of biological activity in humans

Phase IIb Phase III Registration NDA/MAA Submission Approval & Launch

Discovery Non-Clinical /Pre-Clinical

Clinical Research and Commercialization

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• Active Pharmaceutical Ingredient (API)
• fundamental physical and chemical properties of

the drug molecule and other derived properties:

pKa,solubility,melting point,hygroscopicity

• Chemical stability through degradation studies
• Oral absorption potential of API evaluated based on the

API aqueous solubility throughout the pH range of the GI Tract and the permeability of the compound in an in-situ rat intestinal loop or CaCo-2 model.

• Polymorphism, particle size and surface characteristics

Information Needed for Formulation Development Project

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Biopharmaceutics Classification System

BCS Class I: High Solubility & High Permeability Solubility > 1 mg/mL; Permeability > 6 x 10-5 cm/s BCS Class II: Low Solubility & High Permeability Solubility < 1 mg/mL; Permeability > 6 x 10-5 cm/s BCS Class III: High Solubility & Low Permeability Solubility > 1 mg/mL; Permeability < 6 x 10-5 cm/s BCS Class IV: Low Solubility & Low Permeability Solubility < 1 mg/mL; Permeability < 6 x 10-5 cm/s

CLASS BOUNDARIES

• HIGHLY SOLUBLE when the highest dose strength is soluble in < 250

ml water over a pH range of 1 to 7.5.

• HIGHLY PERMEABLE when the extent of absorption in humans is

determined to be > 90% of an administered dose, based on mass- balance or in comparison to an intravenous reference dose.

• RAPIDLY DISSOLVING when > 85% of the labeled amount of drug

substance dissolves within 30 minutes using USP apparatus I or II in a volume of < 900 ml buffer solutions.

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Stability Analysis : Issues and Controversies

Introduction

Objectives of a Stability Study Kinetic Models

Design of Stability Studies Stability Models

Fixed and Mixed effects Case Study

Bayesian Approach

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Introduction

Stability is defined as the capacity of a drug substance or a drug product to remain within specifications established to ensure its identity, strength, quality, and purity throughout the retest period or expiration dating period

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Purpose of Stability Testing To provide evidence on how the quality of a drug substance or drug product varies with time under the influence of a variety of environmental factors (such as temperature, humidity, light, package)

To establish a re-test period for the drug substance or an expiration date (shelf life) for the drug product

To recommend storage conditions Control focused on lot mean

Introduction

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Kinetic Models (API) (Underlying Mechanism)

Orders 0,1,2

where C0 is the assay value at time 0

When k1 and k2 are small,

1 2 ) 2 ( ) 1 ( ) (

1 ) ( ) ( ) (

1

  

                      t k C t C e C t C t k C t C

t k

t k C C ) t ( C and t k C C ) t ( C

2 2 ) 2 ( 1 ) 1 (

       

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Basic Design

Randomly select containers/dosage units at time

• f manufacture, minimum of 3 batches, stored at

specified conditions related to zones I,II,III,IV requirements At specified times 0,1,3,6,9,12,18,24,36,48,60 months, randomly select dosage units and perform assay on composite samples Basic Factors : Batch, Strength, Storage Condition, Time, Package Additional Factors: Position, Drug Substance Lot, Supplier, Manufacturing Site, ...

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Development Stability Study

Description of Data

Assay measurements at 0, 1, 3, 6, 9,12 months 3 Batches held at 25C/60%RH and 30C/65%RH and 40C/75%RH storage conditions, 3 package configurations

Specification limits: 90 – 110% Label Claim (w/w)

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Expiration Date

Regression Model (Fixed Terms) If bi < 0, the expiration date (TED) at condition i is the solution to the equation (roots of a quadratic)

LSL = lower specification limit, t(,df) is the (1-)th quantile of the t-distribution with df degrees of freedom.

) (

) , ( ED i df ED i

T b A Var t T b A LSL      



ij ij i ij

e t b A y    

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Intersection of specification limit with lower 1- sided 95% confidence bound on the batch mean

Expiration Date

Time (Months) Concentration % Label 24 18 12 9 6 3 1 104 102 100 98 96 94 92 90 90

Variable LCLM Pred Obs_Assay True_Conc

Shelf Life Scatterplot of Observed Assay, True Concentration, Lower CL vs Time

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Regulatory Model ICH Q1E (nb Batches, nc Conditions)

Models 1,2,3 (Fixed Terms)

1.

Fit individually by Batch and Condition (nb * nc models)

2.

Fit by Batch, include all Conditions (fit nb constrained intercept models)

3.

Fit all Batches and Conditions (fit 1 model, constrained batch intercepts, with/without constrained slopes)

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Regulatory Models (ICH Q1E)

Index i=Batch, j=Condition, k=Time

Model Specification

Type Number Form Number Fixed Parameters Number Variance Parameters 1

ijk ijk ij ij ijk

T B A y     

2*nb*nc nb*nc

2

ijk ijk ij i ijk

T B A y     

nb*nc+nb nb

3a

ijk ijk ij i ijk

T B A y     

nb*nc+nb 1

Fixed 3b

ijk ijk j i ijk

T B A y     

nc+nb 1

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Issues with Regulatory Models

Pooling across batches of drug Product

Intercepts and Slopes at p=0.25

Unrealistic to assume batch potencies are identical at release (time or manufacture), batches are going to be ‘different’, so why test for equality? Residual error term used for pooling across Intercepts – Why should this be the criterion for poolability? Multiple error terms possible if models 1,2 chosen P=0.25 ignores levels of process and analytical variability Cannot power a stability study design – emphasis is on estimation of degradation rates Ignores the fact that the Chemistry is independent of batch, same API, rate constant is property of the molecule

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Issues with Regulatory Models

Are the regulatory guidelines reflective of current technology and statistical practice? This is the right time to question the pooling paradigm Equivalence approach not a way out Are we stuck in a Hypothesis Testing /Equivalence Testing rut?

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Mechanistic basis exists to forego pooling tests (constrained models)

Assume a fixed common temperature-condition specific slope based on kinetic considerations Assume different batch-specific Intercepts

Main requirement is to estimate the parameters and account for incipient variation in such a way that control over the lot mean is assured.

Pooling across batches

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Mixed Model

If one can assume that drug product batches arise from a fixed manufacturing process, then one can regard the batches as the primary independent statistical units. Statistical model needs to estimate :

Process Mean at time of Manufacture Rate parameter Variance Structure Process (Lot-Lot) Analytical Variation

Measurement error, Extraneous sources

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The mixed effects model provides a coherent modeling framework in a compact way consistent with the manufacturing process

Acknowledges all sources of variation, simple but flexible variance structure Consistent with the basic philosophy that batch is the conditionally independent primary statistical unit (subject specific effects) A natural representation of a batch process, direct lead- in to process simulations, bootstrapping, post commercialization studies Easily extended to multiple fixed factors under study

Main objection – small number of batches

Mixed Effects Model

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Mixed Effects Model

Models 4, 5 (Mixed Models, with 1 or 2 Random Terms)

4.

Random Term in the Intercept

5.

Random Terms in Intercept and Slopes

Correlation not likely for API, may be for

• thers

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Mixed Effects Model

Index i=Batch, j=Condition, k=Time

Model Specification

Type Number Form Number Fixed Parameters Number Variance Parameters 4

ijk ijk j i ijk

T B y         ) (

nc+1 2

Mixed 5

 

ijk ijk i j i ijk

T B y           ) (

nc+1

3

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Case study: Data Listing

Condition Month Batch B1 Batch B2 Batch B3 25C-60RH 99.7 99.0 99.4 25C-60RH 1 100.0 99.4 100.5 25C-60RH 3 99.1 99.2 99.7 25C-60RH 6 98.8 99.5 99.7 25C-60RH 9 98.7 98.7 99.4 25C-60RH 12 98.7 98.6 99.3 30C-65RH 1 100.4 99.9 101.7 30C-65RH 3 99.6 99.4 100.0 30C-65RH 6 99.3 99.5 99.6 30C-65RH 9 98.2 98.2 98.9 30C-65RH 12 98.0 97.4 98.5

24 Time (Months) Assay (%LC)

12 9 6 3 102 101 100 99 98 12 9 6 3 102 101 100 99 98 B1 B2 B3 condition 25C-60RH 30C-65RH

Panel variable: Batch

Stability Profiles

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Results from 5 Models

Type Model Number Fixed Params. Rate Intercept

2

ˆ e 

2 2 ˆ

, ˆ

 

 

Res DF 25C 30C 25C 30C 25C 30C 1 12

• 1.23
• 0.60
• 0.61
• 2.21
• 1.97
• 2.03

99.7 99.3 99.9 100.2 99.8 100.6 0.10 0.10 0.17 0.14 0.34 0.77 4 2 9

• 1.62
• 1.08
• 1.87
• 1.98
• 1.87
• 1.90

100.0 99.7 100.5 0.14 0.20 0.42 8 3a 9 same same same 0.25 24 Fixed 3b 5

• 1.35
• 1.91

99.9 99.7 100.5 0.22 28 4 3

• 1.35
• 1.91

100.0 0.22 0.12, - 28 Mixed 5 3

• 1.35
• 1.91

100.0 0.22 0.12, 0 26

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Shelf Life Estimates

Model 25C/60RH 30C/65RH

Fixed Models

• 1. Batch and Condition specific

Intercept, Slope, Error 60 32

• 2. Batch specific Intercept,

Slopes, Error 51 41

• 3a. Batch specific Intercept,

Slopes, Common error across Batches 49 43

• 3b. Batch specific Intercept,

Condition Specific Slopes, Common error across Batches 65 49 Mixed Models

• 4. Combined across Batches,

Conditions (Mixed model with a single Random Coefficient) 67 51

• 5. Combined across Batches,

Conditions (Mixed model with two Random Coefficients) 67 51

27 Time (Months) Assay (%LC) 24 18 12 6 102 101 100 99 98 97 96 95 24 18 12 6 25C-60RH 30C-65RH

Assay vs Time on Stability - M4

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Bayesian Approach

Provides mechanism to include prior information to the statistical analysis

• f current data and to update model

parameter estimates as new data are collected A more natural way to approach to CMC decision making in terms of a posterior predictive distribution

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Hierarchical Model

Random Intercept Model Add (prior) distribution on the unknown parameters, m, j , 

2 ,  2

) , ( ~ ) , ( ~ ) (

2 2  

     m    m N X N Y X Y

i ijk j i ijk ijk ijk j i ijk

     

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Prior Distributions

Expert opinion

Process mean is likely between 99% and 101% Lot to lot variance is likely between 0.1 and 0.5 Flat prior on the yearly degradation rates Analytical variance is likely between 0.1 to 1.0

~ (100, 0.1) N m

2 1

~ (10, 2)









1 2

, ~ ( , ) I    

2 1

~ (6, 2)









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Parameter Estimates

Estimate 95% Confidence Interval Mean (Median) 95% Credible Interval m 100 99.2 , 100.8 100 99.6 , 100.5  

• 0.11
• 0.16 , -0.07
• 0.11
• 0.16 , -0.06

 

• 0.16
• 0.21 , -0.11
• 0.16
• 0.21 , -0.11





0.12 0.21 (0.20) 0.11 , 0.38 



0.22 0.27 (0.26) 0.17 , 0.42 Frequentist Bayesian Parameters

Method Storage Condition 25C 30C Frequentist 67 51 Bayesian 65 50 Expiration Date

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Summary

Current regulatory guidelines are being challenged in view of current technologies and scientific understanding – needs continued discussion Bayesian framework is available – needs further discussion in relation to reasonable priors, integrating scientific judgment

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Equivalence Approach to Bioassay Potency Testing

Introduction Modeling of Potency Curves Equivalence vs. Equality Issues

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Definition of Bioassay

WHO/NIBSC, J. Immunol. Methods (1998), 216, 103-116. International consensus, Dev. Biol. Standard. (1999) vol 97: "A bioassay is defined as an analytical procedure measuring a biological activity of a test substance based on a specific, functional, biological response of a test system” Finney, 3rd Edition (1978) Statistical Method in Biological Assay

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Examples of Assay Dose-Response Curves

Assay Type A Assay Type B Assay Type C

Day1 Day2 1 unit 1 unit Product induced response 1 unit Product induced response 1 unit Product induced response

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Parallelism of Dose-Response Curves

The definition of relative potency requires the test sample and standard have an identical type of response within the assay. Two parallel response lines should be observed (any displacement between the curves is related to their relative activities.) Non-parallelism indicates that standard and test material are not acting similarly and any definition of potency is not valid.

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Four Parameter Logistic

       

1 ) log( ) log( exp 1 1 ,

3 4 2 1 2 3 2 1 2

4

         



                

i i i

x x x f

where  = (1,2,3,4), 1 = asymptote as the concentration x  0 (for 4 >0), 2 = asymptote as x  , 3 = concentration corresponding to response halfway

between the asymptotes,

4 = slope parameter.

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Variance Function

Variability modeled as a function of mean response to capture heteroscedasticity: where is the variance function with parameter , is a scale parameter. Correct specification is important for calculating standard errors of parameter estimates. Power of the mean is commonly used: where . Generalized least squares (GLS) method is used to estimate the parameters (Giltinan and Ruppert).

 

 

2 2

( ) , ,

i i

Var y g f x    

 

 

2

, ,

i

g f x  

2

  

 

2

, ,

i i

g f x



  m 

( )

i i

E y m 

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Extend Model 1 to the comparison of multiple curves, say standard, test preparations. This is the context of potency testing.

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Constrained Four-Parameter Logistic

Conditions of Similarity:

s1=t1,

s2=t2,

s4=t4,

lower upper parallelism asymptote asymptote

and only s3, t3 vary. Let *

s3 = log s3 , * t3 = log t3.

Under these conditions, the constrained model is given by:

 

 

1 2 2 * 4 3

(2 ) 1 ex p lo g (lo g )

i i s i t i t s

y I x I x               

where t = *

s3-* t3.

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Current EQUALITY Approach for Similarity Testing of Dose-Response Curves

For parallel-line assays, similarity is assessed using a statistical hypothesis test of equal slopes (test of Parallelism):

Ho: S - T = 0, Ha: S - T ne 0

Test Statistic : T = Difference in slopes / Std Error(Difference) Conclude equality if |T| falls below a critical value. Problems with current approach

1.

The greater the precision, greater sensitivity to declare even a very small difference as significant. t-test in this case penalizes a more precise assay

2.

For assays with poor precision, it is hard to conclude even substantially different slopes as different.

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Proposed Changes in USP Chapter <111> (Design and Analysis of Biological Assays)

Focus on analysis – design and validation issues moved to other chapters Preferred method for combination of independent assays is unweighted averaging Non-linear mixed effects models (4 and 5-parameter Logistic)

Method of similarity testing of dose-response curves is shifted from an equality to an equivalence approach

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Proposed EQUIVALENCE Approach for Similarity Testing

„Equivalence Limits‟ are established that represent a measure

• f acceptable “closeness” in the slope estimates

H0 : The two slopes are not equivalent: T - S) < DL or (T - S) > DU Ha : The two slopes are equivalent. DL (T - S)  DU, where DL and DU are the equivalence limits. Confidence Intervals (CI) for the difference in slopes can be used to test equivalence: If CI‟s fall within the equivalence limits then

• ne

concludes similarity in dose-response curves.

Challenges of the Equivalence Approach

What to choose as the measure of ‘nonparallelism’

slope difference, ratio of slopes 3 or 4 parameters for 4&5 logistic curves

How to determine the ‘equivalence limits’ Knowledge/experience for product and assay? Historical data that compare the STND to itself? Provisional capability-based equivalence limits tolerance intervals on slope differences of sample replicates? Lack of enough data during assay development Highly variable assays such as In-Vivo may not be able to satisfy a CI criterion

use acceptance interval for the point estimate (rather than the CI)?

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Bioassay Potency Testing Summary

Equivalence approach replacing the traditional equality approach for similarity testing means that assay precision will have to be characterized very carefully during assay development Assay design will play a more important role, number of plates Further discussion is needed on a coherent approach to establishing equivalence criteria for dose response curve similarity testing

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Excipient Compatibility Studies - N-1 Design

Introduction Construction Analysis Issues

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Introduction

Prior to development of any dosage form of a drug candidate, fundamental physical and chemical properties of the drug molecule and other derived properties are studied. This information will provide possible approaches in formulation development and this early phase is known as Preformulation. Excipient Compatibility studies fall within this early phase and emphasis is on excipient effects

• n chemical and physical properties of the drug

formulation (API stability in particular).

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Introduction

Objective Carry out a stability study on drug- excipient combinations to identify the most stable formulation. Complete (or close to complete) combinations are preferred over binary formulations. Economic incentive to formulate early.

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Balanced Incomplete Block Designs

Consider a BIBD, the simplest BIBD has 3 treatments

with parameters

t treatments = 3 k exp units/block = 2 b number of blocks = 3 r number of reps/trtmt = 2

 number of blocks each pair of treatments occur = 1

BIBD defined by (t-1) = r(k-1)

1(3-1) = 2(2-1) = 2

Treatment Block A B C 1 x x 2 x x 3 x x

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Balanced Incomplete Blocked Factorial Designs (or N-1 Designs)

Suppose instead of treatments A,B,C, we have say 3 classes of factors, say F1, F2, F3, each with 2 levels, and we form factorial designs of each pair of factors, denoted Dij, ij, i,j=1,2,3, j>i, then

D12 = 2x2 factorial design of factors F1 and F2 D13 = 2x2 factorial design of factors F1 and F3 D23 = 2x2 factorial design of factors F2 and F3

Then the N-1 design is the collection of these 3 factorial designs. The N-1 Design can be considered a factorial extension of the BIBD idea but not subject to the restrictions in the BIBD parameters.

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General Construction of an N-1 Design

Given F1, F2,…,Fp factors, so that each factor has say li levels, i=1,2,…,p, (li 1) construct k factorial designs, the 1,2,…i-1,i+1,…k-th design denoted by D12…I-1,I+1,…k (full factorial design of all factors minus the ith factor), then the N-1 design is the collection of all such factorial designs. The total number of observations will be given by

An N-1 Design has more points than the corresponding full factorial Design So why do an N-1 design?

1 2 3 1 1 1

... ...

k i i k i

N l l l l l l

  

 

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Geometric 23 N-1 Design Y = 10*C Example Data + 10*A*C (0 means Absent) + N(0,16)

Group A B C Y

1 1 1 1 1

• 1

2

• 1

1 6

• 1
• 1
• 6

2 1 1 22 1

• 1 -14
• 1

1

• 5
• 1
• 1

6 3 1 1 5 1

• 1
• 7
• 1

1 16

• 1
• 1 -10

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23 N-1 Design

Response = Mean + main effects + 2 way interactions Consider each factorial as a group, then an error term can come from the group differences and group interactions and replication if available. Solve normal equations for a non-orthogonal analysis

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Example 23 N-1 Design

SAS Output Error(MS)=14.68

So Source urce DF Type I SS Mean Square A 2 13.17 6.58 B 2 5.63 2.81 C 1 496.13 496.13 A* A*B 3 89.38 29.79 A* A*C 2 573.38 286.69 B* B*C 1 49.00 49.00 So Source urce DF Type III SS Mean Square A 1 12.50 12.50 B 1 1.13 1.13 C 1 496.13 496.13 A* A*B 1 42.25 42.25 A* A*C 1 552.25 552.25 B* B*C 1 49.00 49.00

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Non-geometric N-1 Design

Four Factors Active +

Filler + F = 4 Disintegrant + D = 2 Lubricant + L = 2 Flow Enhancer E = 1

Ignore Mixture Aspect of Design

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Non-geometric Design

Can it be a 4x2x2x1 Factorial Design 16 combinations? N-1 Design 4+8+8+16 = 36 combinations

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Analysis Issues

Can the group interactions form a meaningful error term? Should replication be designed into the study? Geometric designs, the usual non-

• rthogonal analysis is straightforward and

probably acceptable. For non-geometric N-1 designs, what does

• ne do when a factor has only 1 level (Flow

Enhancer example). Fractionate to get a main effects design from a combined N-0/N-1.

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Wrap-up

Many issues in non-clinical statistical applications We live in exciting times with the advent

• f new technologies and methods leading to

a continuous source of statistical problems, especially in Non-Clinical applications Rutgers students and staff are at the forefront of solving these problems Thank you!

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Acknowledgements

J&J PRD Non-Clinical Statistics CM&C Statistical Applications Team

Ray Buck Hans Coppenolle Oscar Go Areti Manola Yan Shen Jyh-Ming Shoung

CM&C Client Groups at J&J PRD