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

 A broad concept  Can be difficult

Parallelism Testing

2

An Example

Source: Steve Novick, GSK, 2011 MWBS 3

Parallelism Testing for Bioassay

 Linear case log 10 Concentration Standard Test 4

Parallelism Testing for Bioassay (Cont’d)

 Nonlinear case log 10 Concentration Standard Test 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) 6

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

G

(  ) 

PR SIG

(  ) 

PR EQ

(  ).

F

(  ) 

CR SIG

(  ) 

CR EQ

(  ) 7

ROC Curve Analysis: A Unified Method for Method Comparison

 Area under the curve (AUC) = Probability[ metric of non parallel curves > metric of parallel curves] 8

Equivalence Test vs. Significance Test

 With right selections of equivalence limits, the former outperforms the latter 9

 Equivalence test

(Hauck et al, 2005; Lansky, 2009; Draft USP Ch. <111>, OCT 2006)

  H 0 : | 

T

 

R

|   vs. H 1 : | 

T

 

R

|   Parallel when 90% confidence interval falls within equivalence   bounds Equivalent to two one-sided t tests Claim to reward precise assays

Equivalence Approach

equivalence bounds +/ ∆

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 parallel True non-parallel ∆ Se Sp 0 1.00

0.00

1 1.00 0.50

2 0.50 1.00

3 0.00 1.00

0

1 2 3 11

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 12

Equivalence Bounds

    Non-parametric method (Hauck et al, 2005) Use

n

pairs of historical parallel 4-PL curves Construct

n

intervals for each of

r

1 ,

r

2 ,

r

3 (

LCL i

,

UCL i

),

i

 1 , ...,

n

Let

V i

and

V

 max( 1 ,

UCL i

),

LCL i

 the 2

nd

largest of {

V i

,

i

 1 , ...,

n

} The equivalence bound is given by 1 (

V

,

V

)

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 16

An Alternative Method Based on Risk Analysis

Two curves are

True status

Parallel Non-parallel Accept L 0 L 1 Reject L 2 L 3 Choose cut point,

Δ

, to minimize the mean risk: R(

Δ

)

= p

L 0

Sp( Δ) + (1-p)

L 1

[1-se( Δ)] + p

L 2

[1-sp( Δ)] +(1- p)

L 3

Se( 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 18

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 19

 Steve Novick

Acknowledgement

20

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.

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