Recent Method Development in Establishing Equivalence Limits for

Bioassay Parallelism Testing

Harry Yang, PhDSr. Director in Statistics, Non-Clinical Biostatistics, Translational Sciences

MedImmune, LLC

Midwest Biopharmaceutical Statistics Workshop, May 21 – 23, 2012, Muncie, Indiana

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Parallelism Testing

A broad concept

Can be difficult

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Source: Steve Novick, GSK, 2011 MWBS

An Example

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Parallelism Testing for Bioassay

Linear case

log10 Concentration

Ass

ay R

espo

nse

StandardTest

5

Parallelism Testing for Bioassay (Cont’d)

Nonlinear case

log10 Concentration

Assa

y Re

spon

se

StandardTest

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Metric of Non-parallelism

Difference in model parameters Slope (Hauck et al. 2005) Dilution effect (Schofield, 2000) Lower, upper asymptotes and Hillslope at EC50 (Jonkman and

Sidik, 2009) Upper asymptote, “effect window”, slope at EC50 (Yang and

Zhang, 2012)

Difference in dose-response curves Residual sum of squares (Gottschalk and Dunn, 2005) Difference at each concentration level (Liao, 2011) Difference in entire concentration region of interest (Novick, Yang

and Peterson, 2011)

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Significance Test verus Equivalence Test (Yang and Zhang, 2011)

)()()( EQSIG CRCRF

).()()( EQSIG PRPRG

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ROC Curve Analysis: A Unified Method for Method Comparison

Area under the curve (AUC) = Probability[ metric of non-parallel curves > metric of parallel curves]

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Equivalence Test vs. Significance Test

With right selections of equivalence limits, the former outperforms the latter

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Equivalence Approach

Equivalence test (Hauck et al, 2005;

Lansky, 2009; Draft USP Ch. <111>,

OCT 2006)

H0: vs. H1:

Parallel when 90% confidence

interval falls within equivalence

bounds

Equivalent to two one-sided t-

tests

Claim to reward precise assays0

equivalence bounds +/-∆

|| RT || RT

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Impact of Equivalence Limits Sensitivity (Se) and Specificity (Sp)

Se = Pr[Test non-parallel | True non-parallel curves] Sp =Pr[Test parallel | True parallel curves]

-/+∆

True non-parallelTrue

parallel

∆ Se Sp0 1.00 0.001 1.00 0.502 0.50 1.003 0.00 1.00

0 1 2 3

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How to Choose Equivalence Limits?

Capability-based method (Hauck et al, 2005) Test reference standard against itself Provisional Appropriate early in assay life cycle Need to be revised as more data become available

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Equivalence Bounds

Non-parametric method (Hauck et al, 2005) Use n pairs of historical parallel 4-PL curves

Construct n intervals for each of

The equivalence bound is given by

}...,,1,{oflargest2theand

),,1max(Let

...,,1),,(

niVV

UCLLCL

V

niUCLLCL

ind

ii

i

ii

321 ,, rrr

),1( VV

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Drawback of Capability-based Method

No direct linkages between the acceptance limits and product quality

Unsure consumer’s risk is protected

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ROC Curve Method Sensitivity (Se) and Specificity (Sp)

Se = Pr[Test non-parallel | True non-parallel curves] Sp =Pr[Test parallel | True parallel curves]

Best trade-off between Se and Sp can be made by choosing equivalence limits

∆

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Optimizing Limits Based On AUC

Choose equivalence limits to achieve the maximum overall accuracy of the assay parallelism testing

An Alternative Method Based on Risk Analysis

Two curves are Parallel Non-parallel

Accept L0 L1

Reject L2 L3

Choose cut point, Δ, to minimize the mean risk:

R(Δ) = pL0Sp(Δ) + (1-p)L1[1-se(Δ)] + pL2[1-sp(Δ)] +(1- p)L3Se(Δ)

where p is the prevalence of the two dose response curves of test sample and reference standard being parallel.

True status

Test

out

com

e

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Advantages of Risk-based Approach

Risk management approach in line with quality by design principles

Tie parallelism testing to assurance of product quality

Render flexibility in assigning different “weight” factors to non-parallelism and parallelism claims, pending on other factors such as intent of use of the product under testing

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Conclusions

Establishing equivalence limits is an important aspect of parallelism testing

Capability-based method can be used to set up provisional limits

ROC curve analysis can be used to make best tradeoff consumer’s and producer’s risk

A decision theory method can be used to give different treatment to consequences of parallelism and non-parallelism claims

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Acknowledgement

Steve Novick

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References Gottschalk PG, Dunn JR (2005). Measuring parallelism, linearity, and

relative potency in bioassay and immunoassay data. Journal of Biopharmaceutical Statistics, 15, 237-463.

Hauck WW, Capen RC, Callahan JD, De Muth JE, Hsu H, Lansky D, Sajjadi NC, Seaver SS, Singer RR, Weisman D (2005). Assessing parallelism prior to determining relative potency. PDA Journal of Pharmaceutical Science and Technology, 59: 127-137.

Jonkman J and Sidik K(2009). Equivalence testing for parallelism in the four-parameter logistic model. Journal of Biopharmaceutical Statistics, 19 (5): 818 – 837.

Liao J. (2011).Assessing similarity in bioanalytical methods. PDA J. of Pharm. Sci. and Tech.m 65 55-62.

Novick S, Yang H and Peterson J (2011). A Bayesian approach to parallelism testing in bioassay. Submitted for publication.

Yang H and Zhang L (2011). Evaluation of parallelism test methods using ROC analysis. Statistics in Biopharmaceutical Research.

Yang H et al (2012). Implementation of parallelism testing for 4PL logistic model in bioassays. PDA J. of Biopham. Sci & Technol. Vol. 66, No. 3.