2016 Youngju Pak PhD Biostatistician ypaklabiomedorg Session 2 Understanding Equivalence and Noninferiority testing Testing Inequality vs Equality Testing Inequality Ha meantreatment mean control 0 ID: 545526
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Slide1
Biostatistics Case Studies 2016
Youngju Pak, PhD.
Biostatisticianypak@labiomed.org
Session 2Understanding Equivalence and Noninferiority testingSlide2
Testing Inequality v.s. Equality
Testing InequalityHa: | mean(treatment ) - mean (control ) | ≠ 0H0: | mean(treatment ) - mean (control ) | = 0
Testing equivalence Ha : δ 1< mean(
trt 1) – mean (trt2) < δ 2H0 : mean(trt 1) – mean (trt2) ≤
δ
1 or mean(trt 1) – mean (trt2) ≥ δ 2, δ 1 & δ 2 is called “Equivalence Margin
Testing
Noninferority
, noninfiority ity marginSlide3
Case Study
Ophthalmology 2006; 113:70-76
.Slide4
AbstractSlide5
Primary Outcome and Study Size
Study Size - Page 72 bottom of column 1:
Primary Outcome - Page 72 middle of column 1
:
Needs Consensus
PI’s GambleSlide6
Non-Inferiority Study
Usually a new treatment or regimen is compared with an accepted treatment or regimen or standard of care.
The new treatment is assumed inferior to the standard and the study is designed to show overwhelming evidence that it is at least nearly as good, i.e., non- inferior. It usually has other advantages, e.g., oral vs. inj. A negative inferiority study fails to detect inferiority, but does not necessarily give evidence for non-inferiority.
The accepted treatment is usually known to be efficacious already, but an added placebo group may also be used. Slide7
How to determine Sample Size? For IOP study, we have
Ha
: mean IOP change uf – mean IOP change f < 1.5
H0: mean IOP change uf – mean IOP change f ≥ 1.5 thus, we are only interested in the upper limit of the difference
Non-inferiority one-sided T-test
Thus we reject the H
0 if Signal/ Noise < some clinical value.But N for a non-inferiority test require more complicated parameters such as the non-centrality parameter of the t-distribution (a Two One Sided T-test is usually used for the equivalence test ).Slide8
Let’s run a softwarefrom www.stat.uiowa.edu/~rlenth/Power
Information you will need Equivalence Margin
Non-Inferiority Margin(NIM) =1.5 for the IOP studyAssumed mean difference in change of IOP between two groups -> usually zero difference assumed but it is assumed 0.5 for the IOP studySD of changes of IOP = 3.5α (usually set to 2.5%) since the confidence level of the confidence interval is (100-2 x α) %Slide9
Sample size for IOP studySlide10
Three dimensional power curve for a non-inferiority testSlide11
How do we determine if the fixed method is non-inferior to the unfixed method?
Regardless of study aim – to prove treatments equivalent or to prove them different - inference can be based on:
Primary Outcome: IOP reduction D
= Duf – Df , where Df
= mean IOP reduction with fixed therapy
Typical superiority/inferiority study:
Compare to 0.Non-inferiority study: Compare to δ2, a pre-specified margin of equivalence (1.5 here).= 95% CI for D(=
Duf – Df ) = “true (population) values for D”Slide12
Typical Analysis: Inferiority or Superiority
H0
: Duf – Df = 0
H1: Duf – Df ≠ 0Aim: H1 → therapies differ
α
= 0.05 & N=2
•194 Power = 80% when Δ=1, SD=3.5
Fixed is inferior
= 95% CI for
D = “true (population) values for D”
Fixed is superior
0
0
D
u
–
D
f
[Not used in this paper]
0
No difference detected
D
u
–
D
f
D
u
–
D
fSlide13
Typical Analysis: Inferiority Only
H0
: Du – Df ≤ 0
H1: Du – Df > 0Aim: H1 → fixed is inferior
α
= 0.025 & N=2
•194 Power = 80% for when Δ=1, SD=3.5Fixed is inferior
= 95% CI for
D
u
–
D
f
= “true (population) values for D”
0
0
D
uf
–
Df
[Not used in this paper]
0
Inferiority not detected
D
uf
–
D
f
D
uf
–
D
f
(
α
= 0.05
→
N=2
•153
)Slide14
Non-Inferiority
H0:
Du – Df ≥ 1.5
H1: Du – Df < 1.5Aim: H1 → fixed is non-inferior
α
= 0.025 & N=2
•194 Power = 80% for When Δ= 0.5, NIM=1.5
Fixed is non-inferior
= 95% CI for
D
u
–
D
f
= “true (population) values for D”
0
0
D
uf
–
D
f
[As in this paper]
0
Non-Inferiority not detected
D
uf
–
D
f
D
uf
–
D
f
1.5
1.5
Fixed is
inferior
1.5Slide15
Inferiority and Non-Inferiority
Fixed is non-inferior
= 95% CI for
D
u
– Df = “true (population) values for D”
0
0
0
Neither is detected
D
uf
–
D
f
1.5
1.5
Fixed is inferior
0
1.5
Fixed is “non-clinically” inferior
D^
uf
=
9.0
D^
f
= 8.7
D^
= 0.3 95% CI = -0.1 to 0.7
Observed Results:
Fixed is non-inferior
0
1.5
1.5Slide16
Conclusions: General
“Negligibly inferior” would be a better term than non- inferior.
All inference can be based on confidence intervals. Pre-specify the comparisons to be made. Cannot test for both non-inferiority and superiority. Power for only one or for multiple comparisons, e.g., non-inferiority and inferiority. Power can be different for different comparisons. Very careful consideration must be given to choice of margin of equivalence (1.5 here). You can be risky and gamble on what expected differences will be (0.5 here), but the study is worthless if others in the field would find your margin too large. Slide17
FDA Guidelines : http://www.fda.gov/downloads/drugs/guidancecomplianceregulatoryinformation/guidances/ucm202140.pdf
Where,
M1= Full effect of the active control compare with the test drug
M
2
= NI MarginSlide18
Self-Quiz
Give an example in your specialty area for a superiority /inferiority study. Now modify it to an equivalence study. Now modify it to a non-inferiority study.
T or F: The main point about non-inferiority studies is that we are asking whether a treatment is as good or better vs. worse than another treatment, so it uses a one-sided test.Power for a typical superiority test is the likelihood that you will declare treatment differences (p<0.05) if treatments really differ by some magnitude Δ. Explain what power means for a non-inferiority study.
T or F: Last-value-carried-forward is a good way to handle drop-outs in a non-inferiority study. Explain. continuedSlide19
Self-Quiz
T or F: In a non-inferiority study, you should first test for non-inferiority with a confidence interval, and then use a t-test to test for superiority, but only if non-inferiority was established at the first step.
What is the meaning of the equivalence margin, and how do you determine it?
continuedSlide20
Self-Quiz
Suppose the primary outcome for a study is a serum inflammatory marker. If it’s assay is poor (low reproducibility), then it is more difficult to find treatment
differences in a typical superiority/inferiority study than for a better assay, due to this noise. Would it be easier or more difficult to find non-inferiority with this assay, compared to a better assay?Does the assumed treatment difference (0.5 here) for power calculations have the same meaning as the difference used for power calculations in a typical superiority/inferiority study?