Non-inferiority And Equivalence - PowerPoint Presentation

1. Non-inferiority And EquivalenceDesign considerations and sample sizeDemonstrated on

2. Head of StatisticsnQuery Lead ResearcherFDA Guest SpeakerGuest LecturerWebinar HostHOSTED BY: Ronan Fitzpatrick

3. AGENDABackgroundNon-inferiority TestingEquivalence TestingConclusions and Discussion

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6. BackgroundPart 1

7. Non-inferiority & equivalence about if new trt. similar to existing trt.Common in generics & medical devicesNon-inferiority: Not Inferior to ControlDirect effect measure w/ “good” directionNeed NI margin below which is “inferior”Equivalence: Equivalent to ControlCommonly indirect effect measure w/ no “good” direction e.g. bioequivalence CI to fall between lower & upper limitsBackgroundSource: C Pater (2004)

8. Non-inferiority TestingPart 2

9. Non-inferiority TestingNon-inferiority testing is where hypothesis test that treatment no worse than standard by a specified marginSelect non-inferiority margin based on expertise & dataFDA: Fixed fraction (M2) of active control effect (M1)Very common for generics or medical devices and usually compare treatment vs control (e.g. RLD) w/o placeboMost often used for continuous outcome (parallel or cross-over) but available for proportions, survival, counts

10. “Calculation of the sample size was based on a margin of non-inferiority for in-segment late luminal loss of 0.16 mm. This value is equal to 35 percent of an assumed mean (±SD) late luminal loss of 0.46±0.45 mm in diabetic patients after the implantation of a sirolimus stent, as found in an analysis of a series of diabetic patients treated with sirolimus stents at participating centers in the 10 months that preceded the initiation of the study. Using a one-sided α level of 0.05, we estimated that 99 patients per group were needed to demonstrate noninferiority of the paclitaxel stent with a statistical power of 80 percent. Expecting that up to 20 percent of the patients would not return for follow-up coronary angiography, we included 250 patients in the study.”Source: A. Dibra et. al. (2005) ParameterValueSignificance Level (1-sided)0.05Expected Difference 0Non-Inferiority Margin-0.16Standard Deviation0.45Power80%Dropout Rate20%Worked Example 1

11. Non-inferiority DiscussionSize of the NI margin can take into account other considerations other than standard trt. effect sizeSafety profile, secondary endpoints, easier administrationBut in general, conservative NI margin is encouraged (FDA)Strong assumption for 2-trt. design that standard trt. effect size retained from its approval (assay sensitivity)May need to replicate previous study conditions very closelyMay need additional evidence/data for regulatory approvalNote closely related “Superiority by Margin” hypothesis

12. Three Armed TrialsHave Experiment (A), Reference (R) & Placebo (P) groups Direct evaluation of assay sensitivity (“gold standard”)Concurrent placebo only allowable if it is ethical to do soNeed to test H1(a): E/R > P and then H1(b) E > NIMCan simplify to a “ratio of differences” test: (E-P)/(R-P) > θFramework of Wald-type test for retention of effect Can use same approach for means, props, survival, ratesCan also find optimal allocation for given alternative

13. Three Armed Trials1Means (Homoscedatic)Pigeot et al. (2003)2Means (Heteroscedatic)Hasler et al. (2008)3ProportionsKieser and Friede (2007)4Survival/Time-to-EventMielke et al. (2009)5Counts/Rates (Poisson)Mielke and Munk (2009)6Counts/Rates (Negative Binomial)Mütze et al. (2016)7Non-ParametricMütze et al. (2016)

14. Worked Example 2ParameterValueSignificance Level (1-Sided)0.025Experimental Arm Mean1.56Reference Arm Mean1.56Placebo Arm Mean0 Non-inferiority Ratio0.5Common Standard Deviation2.5Power80%Allocation Proportion (E:R:P)0.38:0.38:0.24“It was assumed that the placebo-adjusted effect for both treatment groups was 1.56% and that the placebo-adjusted effect for the oral rsCT tablets must be at least 0.5 times the placebo-adjusted effect for the ssCT nasal spray for the study to demonstrate the non-inferiority of the oral rsCT tablets to the ssCT nasal spray. Thus we wished to have 95% confidence that the oral tablets were not less than one-half as effective as nasal spray. Assuming an SD of 2.5%, power of 80%, and a two-sided 5% level of significance, it was determined that approximately 133 patients were required for each of the active treatment groups and 84 patients were needed for the placebo treatment group.”

15. Equivalence TestingPart 3

16. Test if treatment equivalent to ControlBioequivalence (Cmax, AUC) tests commonBut widely used for direct measures tooMethod: “Two One-sided Tests” (TOST)H0: ΔTrue< ΔL or ΔTrue > ΔU, H1: ΔL< ΔTrue < ΔUTest both null hypotheses at one-sided αNB: Type I error is equal to one-sided α But TOST ≈ Confidence Interval Method2 x TOST α = Confidence Level of IntervalFor example: 0.05 TOST α = 90% Interval Other approaches proposed but not widely used (Lindley, Berger, Westlake)Equivalence TestingSource: lesslikely.comSource: CMBJ, Impax Labs

17. Definition of equivalence and which effect(s)/measure(s) to use?Average, Individual, Population Equivalence; Which of AUC, Cmax, Tmax?Equivalence IssuesCross-over trials common for bioequivalence but can do others2x2 is “classic” but replicates common 2x3,2x4; William’s Designs if 3/4 trt Bioequivalence bounds often from regulator, otherwise expertiseMost Common: 0.8-1.25 for GMR (AUC) but issues if NTID or HVDBe aware of issues/reqs. with highly variable and NTID drugsDifferent reqs from FDA/EMA/others: Bounds from CV, Replicate designs…

18. “The sample size for the study was determined with reference to the relevant, recent literature available on the pharmacokinetics of sildenafil, in particular the results of a study conducted after administration of two 25 mg capsules of Viagra film-coated tablets in a population of 12 male subjects. The highest coefficient of variance for the pharmacokinetic parameters Cmax and AUC was estimated to be 0.383 … Fixing the significance level α at 5% and the hypothesized test/reference mean ratio to 1, 50 subjects were considered sufficient to attain a power of 80% to correctly conclude the bioequivalence between the two formulations within the range 80.00%–125.00% for all parameters (Cmax and AUC).”Source: nejm.orgParameterValueSignificance Level0.05Lower Equivalence Limit0.8Upper Equivalence Limit1.25Mean Ratio1Coefficient of Variation0.383Power (%)80Worked Example 3Source: Radicioni M et al (2016)

19. Discussion and ConclusionsNI & Equivalence test if new trt. similar to standard trt.Non-inferiority = “No worse than”; Equivalence = “Equal to”NI if direct monotonic effect & can “redo” std. trt. trialNI margin requires careful consideration, cost-benefit balanceThree arm trials since have direct comparison to placeboFlexible framework available but only if ethical to give placeboEquivalence if trt. is “equivalent” on “indirect” effectBioequivalence typical use-case (AUC, Cmax) but beware issues

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25. ReferencesSenn, S. (2002). Cross-over trials in clinical research (2nd Edition). John Wiley & Sons.Pater, C. (2004). Equivalence and noninferiority trials–are they viable alternatives for registration of new drugs?(III). Current controlled trials in cardiovascular medicine, 5(1), 8.Food and Drug Administration Non-inferiority clinical trials to establish effectiveness. Guidance for industry. November 2016. https://www.fda.gov/downloads/Drugs/Guidances/UCM202140.pdfBlackwelder, W.C., 2002. Showing a Treatment Is Good Because It Is Not Bad: When Does ‘Noninferiority’ Imply Effectiveness?. Control Clinical Trials, 23, pp. 52–54.Chow, S.C., Shao, J., 2006. On Non-Inferiority Margin and Statistical Tests in Active Control Trial.” Statistics in Medicine, 25, pp. 1101–1113.Fleming, T.R., 2008. Current Issues in Non-inferiority Trials. Statistics in Medicine, 27, pp. 317-332.Althunian, T.A., de Boer, A., Groenwold, R.H. and Klungel, O.H., 2017. Defining the noninferiority margin and analysing noninferiority: an overview. British journal of clinical pharmacology, 83(8), pp.1636-1642.Dibra, A., et al (2005). Paclitaxel-eluting or sirolimus-eluting stents to prevent restenosis in diabetic patients. New England Journal of Medicine, 353(7), 663-670.

26. ReferencesI. Pigeot, J. Schäfer, J. Röhmel, D. Hauschke., 2003. Assessing non-inferiority of a new treatment in a three-arm clinical trial including a placebo. Statistics in Medicine, 22, pp. 883-899.M. Kieser, T. Friede., 2007. Planning and analysis of three‐arm non‐inferiority trials with binary endpoints. Statistics in Medicine, 26, pp. 253-273.M. Hasler, R. Vonk, L.A. Hothorn., 2008. Assessing non-inferiority of a new treatment in a three-arm trial in the presence of heteroscedasticity. Statistics in Medicine, 27, pp. 490-503.M. Mielke, A. Munk, and A. Schacht., 2008. The assessment of non‐inferiority in a gold standard design with censored, exponentially distributed endpoints. Statistics in Medicine, 27, pp. 5093-5110.M. Mielke and A. Munk., 2009. The assessment and planning of non-inferiority trials for retention of effect hypotheses-towards a general approach. arXiv:0912.4169Mielke, M., 2010. Maximum Likelihood Theory for Retention of Effect Non-Inferiority Trials (Doctoral dissertation, Niedersächsische Staats-und Universitätsbibliothek Göttingen).T. Mütze, A. Munk, T. Friede., 2016. Design and analysis of three‐arm trials with negative binomially distributed endpoints. Statistics in Medicine, 35, pp. 505-521.

27. ReferencesT. Mütze, F. Konietschke, A. Munk, T. Friede., 2017, A studentized permutation test for three-arm trials in the `gold standard’ design. Statistics in Medicine, 36, pp. 883-898.Binkley, N., Bolognese, M., Sidorowicz‐Bialynicka, A., Vally, T., Trout, R., Miller, C., Buben, C.E., Gilligan, J.P., Krause, D.S. and Oral Calcitonin in Postmenopausal Osteoporosis (ORACAL) Investigators, 2012. A phase 3 trial of the efficacy and safety of oral recombinant calcitonin: the Oral Calcitonin in Postmenopausal Osteoporosis (ORACAL) trial. Journal of bone and mineral research, 27(8), pp.1821-1829.Food and Drug Administration Statistical approaches to establishing bioequivalence. Guidance for industry. 2001. https://www.fda.gov/media/70958/downloadEuropean Medicines Agency, CHMP. Guideline on the Investigation of Bioequivalence. London; 2010 Jan 20.www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2010/01/WC500070039.pdfFood and Drug Administration Draft Guidance on Progesterone. 2001. https://www.accessdata.fda.gov/drugsatfda_docs/psg/Progesterone_caps_19781_RC02-11.pdfSchuirmann DJ. A Comparison of the Two One-Sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability. J Pharmacokinet Biopharm. 1987; 15(6): 657–80. Senn, S. (2001). Statistical issues in bioequivalence. Statistics in Medicine, 20, 2785-2799.

28. ReferencesKirkwood TBL. Bioequivalence testing—a need to rethink. Biometrics 1981; 37:589–591.Berger R, Hsu J. Bioequivalence trials, intersection-union tests, and equivalence confidence sets. Statistical Science 1996; 11:283–319O’Quigley, J. and C. Baudoin, General approaches to the problem of bioequivalence. The Statistician, 1988. 37: p. 51-58.Westlake WJ. Symmetrical confidence intervals for bioequivalence trials. Biometrics 1976; 32:741–744Lindley DV. Decision analysis and bioequivalence trials. Statistical Science 1998; 13:136 –141.Schütz, H., Reference-scaled Average Bioequivalence. Bebac https://bebac.at/lectures/Moscow2016-3.pdfTóthfalusi L et al. Evaluation of the Bioequivalence of Highly-Variable Drugs and Drug Products. Pharm Res. 2001;18(6): 728–33.Radicioni, M., Castiglioni, C., Giori, A., Cupone, I., Frangione, V. and Rovati, S., 2017. Bioequivalence study of a new sildenafil 100 mg orodispersible film compared to the conventional film-coated 100 mg tablet administered to healthy male volunteers. Drug Design, Development and Therapy, 11, p.1183.