recent method development in establishing equivalence limits for bioassay parallelism testing
DESCRIPTION
Recent Method Development in Establishing Equivalence Limits for Bioassay Parallelism Testing. Harry Yang, PhD Sr. Director in Statistics, Non-Clinical Biostatistics, Translational Sciences MedImmune, LLC Midwest Biopharmaceutical Statistics Workshop, May 21 – 23, 2012, Muncie, Indiana. - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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.