Non-Inferiority and Superiority-by-Margin Test

The non-inferiority and superiority-by-margin test is a one-sided test of whether a treatment's mean or proportion is not worse than, or better by more than, a control's by a prespecified margin.

비열등성·우월성(한계) 검정은 처리군의 평균이나 비율이 대조군보다 미리 정한 한계 이상 나쁘지 않은지, 또는 한계 이상 좋은지를 판정하는 단측 검정입니다.

How do I show that a new treatment is not worse than the standard by more than 10 percentage points?

새 치료법이 기존 치료법보다 10%포인트 이상 나쁘지 않다는 것을 어떻게 보이나요?

A non-inferiority test sets the null hypothesis that the treatment is worse than the control by at least the margin and rejects it when the one-sided test is significant, which matches the lower limit of the (1 - 2 alpha) confidence interval lying above the negative margin. Means are tested with a Welch t statistic and binary outcomes with the Farrington-Manning score statistic, on either a difference or a ratio scale.

When to use Non-Inferiority and Superiority-by-Margin Test

• A new treatment, product or process should be shown not to be meaningfully worse than an established one.
• You want to show that a treatment is better than control by more than a clinically or practically relevant margin.
• The margin was fixed before the data were collected.

When to use something else

• You want to show that two treatments are equivalent in both directions; use the equivalence test (TOST).
• No justified margin exists; use an ordinary two-sample test with a confidence interval.

Assumptions and requirements

• The two groups are independent random samples.
• The margin was chosen in advance on clinical or practical grounds.
• For means, the sample means are approximately normal; for proportions, counts are large enough for the score approximation.

What the analysis reports

• Estimated difference or ratio (treatment versus control)
• (1 - 2 alpha) confidence interval and the boundary it is compared with
• Welch t or Farrington-Manning z, degrees of freedom when relevant, and the one-sided p value
• Conclusion (non-inferior, superior by the margin, or not shown)

How to report it

With a non-inferiority margin of [value], the difference between [treatment] and [control] was [value], 95% CI [[lower], [upper]], [t or z] = [value], one-sided p = [value], so non-inferiority was [shown / not shown].

Related methods

• Equivalence Test (TOST)
• Independent Samples t-test
• Two-Proportion Z Test

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