Recent Method Development in Establishing Equivalence Limits for Bioassay Parallelism Testing

1. 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

2. Parallelism Testing • A broad concept • Can be difficult eSlide - P4815 - MedImmune Template

3. An Example Source: Steve Novick, GSK, 2011 MWBS eSlide - P4815 - MedImmune Template

4. Parallelism Testing for Bioassay • Linear case eSlide - P4815 - MedImmune Template

5. Parallelism Testing for Bioassay (Cont’d) • Nonlinear case eSlide - P4815 - MedImmune Template

6. 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) eSlide - P4815 - MedImmune Template

7. Significance Test verus Equivalence Test (Yang and Zhang, 2011) eSlide - P4815 - MedImmune Template

8. ROC Curve Analysis: A Unified Method for Method Comparison • Area under the curve (AUC) = Probability[ metric of non-parallel curves > metric of parallel curves] eSlide - P4815 - MedImmune Template

9. Equivalence Test vs. Significance Test • With right selections of equivalence limits, the former outperforms the latter eSlide - P4815 - MedImmune Template

10. 0 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 assays equivalence bounds +/-∆ eSlide - P4815 - MedImmune Template

11. 0 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] -/+∆ ∆ Se Sp 0 1.00 0.00 1 1.00 0.50 2 0.50 1.00 3 0.00 1.00 True non-parallel True parallel 1 2 3 eSlide - P4815 - MedImmune Template

12. 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 eSlide - P4815 - MedImmune Template

13. 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 13 04/14/2008 – 6:00pm eSlide - P4815 - MedImmune Template eSlide - P4815 - MedImmune Template

14. Drawback of Capability-based Method • No direct linkages between the acceptance limits and product quality • Unsure consumer’s risk is protected eSlide - P4815 - MedImmune Template

15. 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 ∆ eSlide - P4815 - MedImmune Template

16. Optimizing Limits Based On AUC • Choose equivalence limits to achieve the maximum overall accuracy of the assay parallelism testing eSlide - P4815 - MedImmune Template

17. An Alternative Method Based on Risk Analysis True status 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 standardbeing parallel. Test outcome

18. 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 eSlide - P4815 - MedImmune Template

19. 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 eSlide - P4815 - MedImmune Template

20. Acknowledgement • Steve Novick eSlide - P4815 - MedImmune Template

21. 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. eSlide - P4815 - MedImmune Template