The document discusses non-inferiority and equivalence trial designs, focusing on statistical considerations and sample size calculations for clinical trials. It highlights methods for testing whether new treatments are comparable to existing treatments, including fixed margin approaches and the two one-sided tests for bioequivalence. The document also details worked examples and considerations for trial design, emphasizing FDA guidelines and statistical power requirements.

1. Non-inferiority And Equivalence
Design considerations and sample size
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3. AGENDA
1. Background
2. Non-inferiority Testing
3. Equivalence Testing
4. Conclusions 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 devices
Non-inferiority: Not Inferior to Control
•Direct effect measure w/ “good” direction
•Need NI margin below which is “inferior”
Equivalence: Equivalent to Control
•Commonly indirect effect measure w/ no
“good” direction e.g. bioequivalence
•CI to fall between lower & upper limits
Background
Source: C Pater (2004)

8. Non-inferiority TestingPart 2

9. Non-inferiority Testing
Non-inferiority testing is where hypothesis test that
treatment no worse than standard by a specified margin
Select non-inferiority margin based on expertise & data
 FDA: 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 placebo
Most 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)
Parameter Value
Significance Level (1-sided) 0.05
Expected Difference 0
Non-Inferiority Margin -0.16
Standard Deviation 0.45
Power 80%
Dropout Rate 20%
Worked Example 1

11. Non-inferiority Discussion
Size of the NI margin can take into account other
considerations other than standard trt. effect size
•Safety profile, secondary endpoints, easier administration
•But 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 closely
•May need additional evidence/data for regulatory approval
Note closely related “Superiority by Margin” hypothesis

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

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

14. Worked Example 2
Parameter Value
Significance Level (1-Sided) 0.025
Experimental Arm Mean 1.56
Reference Arm Mean 1.56
Placebo Arm Mean 0
Non-inferiority Ratio 0.5
Common Standard Deviation 2.5
Power 80%
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 Control
•Bioequivalence (Cmax, AUC) tests common
•But widely used for direct measures too
Method: “Two One-sided Tests” (TOST)
•H0: ΔTrue< ΔL or ΔTrue > ΔU, H1: ΔL< ΔTrue < ΔU
•Test both null hypotheses at one-sided α
•NB: Type I error is equal to one-sided α
But TOST ≈ Confidence Interval Method
•2 x TOST α = Confidence Level of Interval
•For example: 0.05 TOST α = 90% Interval
•Other approaches proposed but not widely
used (Lindley, Berger, Westlake)
Equivalence Testing
Source: lesslikely.com
Source: 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 Issues
Cross-over trials common for bioequivalence but can do others
2x2 is “classic” but replicates common 2x3,2x4; William’s Designs if 3/4 trt
Bioequivalence bounds often from regulator, otherwise expertise
Most Common: 0.8-1.25 for GMR (AUC) but issues if NTID or HVD
Be aware of issues/reqs. with highly variable and NTID drugs
Different 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.org
Parameter Value
Significance Level 0.05
Lower Equivalence Limit 0.8
Upper Equivalence Limit 1.25
Mean Ratio 1
Coefficient of Variation 0.383
Power (%) 80
Worked Example 3
Source: Radicioni M et al (2016)

19. Discussion and Conclusions
NI & 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. trial
NI margin requires careful consideration, cost-benefit balance
Three arm trials since have direct comparison to placebo
Flexible framework available but only if ethical to give placebo
Equivalence if trt. is “equivalent” on “indirect” effect
Bioequivalence typical use-case (AUC, Cmax) but beware issues

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25. References
Senn, 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.pdf
Blackwelder, 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. References
I. 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:0912.4169
Mielke, 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. References
T. 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/download
European 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.pdf
Food and Drug Administration Draft Guidance on Progesterone. 2001.
https://www.accessdata.fda.gov/drugsatfda_docs/psg/Progesterone_caps_19781_RC02-11.pdf
Schuirmann 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. References
Kirkwood 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; 11:283–319
O’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; 32:741–744
Lindley 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.pdf
Tóthfalusi 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.