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
Parallelism Testing
 A broad concept
 Can be difficult
2
An Example
Source: Steve Novick, GSK, 2011 MWBS
3
Parallelism Testing for Bioassay
Assay Response
 Linear case
Standard
Test
log10 Concentration
4
Parallelism Testing for Bioassay
(Cont’d)
Assay Response
 Nonlinear case
Standard
Test
log10 Concentration
5
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)
G( )  PRSIG ( )  PREQ ( ).
F ( )  CR SIG ( )  CR EQ ( )
7
ROC Curve Analysis: A Unified Method
for Method Comparison
 Area under the curve (AUC) = Probability[ metric of nonparallel curves > metric of parallel curves]
8
Equivalence Test vs. Significance Test
 With right selections of equivalence limits, the former
outperforms the latter
9
Equivalence Approach

Equivalence test (Hauck et al, 2005;
equivalence bounds +/-∆
Lansky, 2009; Draft USP Ch. <111>,
OCT 2006)

H0:

Parallel when 90% confidence
| T   R | 
vs. H1:
| T   R | 
interval falls within equivalence
bounds

Equivalent to two one-sided ttests

Claim to reward precise assays
0
10
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-parallel
True parallel
0
1
2
∆
0
1
2
3
Se
1.00
1.00
0.50
0.00
Sp
0.00
0.50
1.00
1.00
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
r1 , r2 , r3
( LCLi , UCLi ), i  1, ...,n
1
Let Vi  max(
, UCLi ),
LCLi
and V  the2 nd largest of {Vi , i  1, ...,n}

The equivalence bound is given by
(
1
, V)
V
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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
14
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
∆
15
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
True status
Test outcome
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.
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 nonparallelism claims
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Acknowledgement
 Steve Novick
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References
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
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
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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.
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