margin selection and result interpretation in non ... 2/204/s204 02_gang chen.pdf · 2nd dia china...

2nd DIA China Annual Meeting | May 16-19, 2010 | Beijing, China

Margin Selection and Result

Interpretation in Non-inferiority Trials

Gang Chen, Ph.D.

Director, Biostatistics

Johnson & Johnson


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Outline:

• Introduction

• Non-inferiority (NI) margin

• Hypotheses and sample size - Example

• Result interpretation

• Major questions


Introduction:

• Why need NI trials: ethical consideration in conducting a placebo controlled trial when some active treatments are available. The purpose of a NI trial is usually to show a new treatment is effective or similar to an active control in terms of efficacy but with better toxicity profile or other benefit.

• Margin for NI trials - in general

– More stringent margin required for testing a new (different) drug.

– A relative wider margin can be used if the objective of NI trial is to test two same drugs with different doses, route of administration etc.

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• Definition of NI margin (FDA Guidance):

– M1: the entire control effect

– M2: a proportion of the M1 which is the largest

clinically acceptable difference (M2 <= M1)


• What should be M1?

– Point estimate – Liberal?

– Lower limit of 95% CI – conservative?

• What should be M2?

– M2 = M1*(1-δ0 ), where δ0 is a given proportion of retention

– 20%, 50%, 75% of M1?

Drug Information Association www.diahome.org 5



Then 2 different statistical hypotheses associated with NI

margin can be formulated:

Defining:

– θ1 = true treatment effect

– θ2 = true control effect (with estimate M1)

• Synthesis: H0: θθθθ1 / θθθθ2 < 1-δδδδ0 vs. Ha: θθθθ1 / θθθθ2 ≥ 1- δδδδ0

• Fixed Margin: H0: θθθθ1 < M1(1-δδδδ0)=M2 vs. Ha: θθθθ1 ≥ M2


• Which NI hypothesis should be formulated with same objective of a NI trial

– With more efficient design (less sample size)?

– With more reliable NI conclusion?



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Example (oncology trial):

• 2:1 randomization SC:IV

• Primary endpoint: RR after 4 cycles

• Study in North America and Europe


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• Objective: to show similar response rate (RR) for SC and IV

– Alpha: 1-sided 0.025– Power 80%

– RR form historical studies: 50% with 95% CI (43%, -)– Control effect M1 defined: 43%

– Margin (δ0 ) = 60 % RR retention – Margin (M1) = (1-60%) X 43% ~ 17% in RR

– Possible NI hypothesis:

RR_SC/RR_IV < 40% vs. RR_SC/RR_IV=1, OR

RR_SC - RR_IV < -17% vs. RR_SC = RR_IV


Sample size:

• Fixed margin:

– 344 (-15% margin or 28% RR)

– 770 (-10% margin or 33% RR)

– 1204 (-8% margin or 35% RR)

• Synthesis:

– 92 (50% retention or 21.5% RR)

– 168 (60% retention or 25.8% RR)

– 512 (75% retention or 32.3% RR)



• Example discussion: With the same objective, the sample size almost increased about 50% in a fixed

margin design Why?

– Researches done in 1990s: lack of power for

fixed margin is due to larger variances used in

fixed margin test.



• Example discussion: Synthesis (retention) vs. fixed margin, which one is more reliable in this setting?

17% fixed margin vs. (1-60%) retention margin

– Fixed margin: M2=17% (relative to 43% RR) may be

“too larger” if in current NI trial the observed control

RR is lower, e.g., observed RR = 30% - a 17% margin in control RR is too large relative to a 30%

control effect and NI conclusion is questionable.



• Synthesis margin (1- δ0 ) = 40% (40% of control effect) may be “more reliable” in above example:

• If in current NI trial the observed control RR = 30% -

then a relative margin is 12% (.4X30%) in control RR

which still leads to a reasonable NI conclusion.



• Example discussion: Synthesis (retention) vs. fixed margin (with binary variable)

– Retention margin:

• Highly associated with current control effect

• More statistical test power

– Fixed margin:

• Determined based on historical control data which may be different from current trial

• Lower stat power

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• Result interpretations: with an appropriate NI margin

and a significant NI test, what can (should) we conclude?

– In a superiority trial: e.g., if observed HR =1.25 in OS, and superiority test p < 0.025(1-sided), we can conclude that the treatment significantly improves OS by 25% and this will be included in the package insert:

“Drug X can reduce 20% risk of death in MM patients (HR=.8, 95%CI (.64, .92))”



However, in a NI trial:

– If the test is significant > margin then can (should)

we conclude similarly to what we do for a superiority trial?

– Example: if observed HR=1 in OS, and NI test p

<0.025(1-sided) against the NI margin selected, what can we claim: “non-inferiority” or “not worse

than the control” or “equivalence”?



Back to Oncology Example:

– to show SC_RR=IV_RR

– to rule out the worst case SC_RR/IV_RR <= 40%

• With a significant NI test of the study, if the observed

ratio SC_RR/IV_RR = 1, i.e., RR is the same for SC and IV arm than can we conclude:

– the RR is similar between SC and IV treatment with a 95%CI ….

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More result interpretations: what if the NI test is significant

but at the same time it also becomes significant NI test?

Three major possible reasons:

1. Large margin

2. Large sample size

3. Small variation



1. A “too large” margin is what we should avoid in NI design. In this case, the significance of a NI test is not

interpretable and NI can not be concluded. As

discussed before, a reasonable (may be conservative) margin should be at most 1/2 of the lower limit of 95%

CI of control effect.



2. Lager sample size: by the large sample theory any difference will be significant when sample size goes to

infinity. In this case, important judgment is whether this

small difference is clinically meaningful. If not, NI claim is reasonable.



3. Small variation: the variation associated with the point estimate is relatively small (e.g., lab data measure with

high assessment accuracy). In this case stat significance

is easy to achieve although the NI difference(margin) is appropriate.



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• Major Questions:

– M1 assessment:

• If limited historical trials on control drug

• If population change or medical practice change

• If historical trials on control were not compared with placebo

• Point estimate or lower limit of XX%CI.

– M2 determination:

• What is appropriate discount of M1 (0% - ?% ) to define a margin



• Major Questions:

– What NI hypothesis should be formulated?

– How do we interpret NI results: Should a NI

trial always be “conservative” in terms of

result interpretation?


Thanks


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