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Recent Method Development in Establishing Equivalence Limits for Bioassay Parallelism Testing

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.

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Recent Method Development in Establishing Equivalence Limits for Bioassay Parallelism Testing

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  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

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