# Sample size calculation for non-inferiority and superiority

#### kumarnaidu

##### New Member
Dear all,
I am little bit confused with dual statements which I read in the literatures and books. Some says that Non-inferiority studies requires more sample size than superiority study and other states vice versa. Can anybody guide me what is correct here?

Also as per some experts the case where the treatment of interest appears slightly less effective than the control treatment the sample size for a superiority study is significantly smaller than that of the equivalent and non-inferiority study. How it is possible if test is less effective how come we prove its superiority over reference?

#### hlsmith

##### Omega Contributor
I believe the issue may be that a Superiority Test could be constructed as a one-sided test. non-inferiority may be a two-sided. Meaning you divide alpha by 2 and expect the the difference could be less or more. It has been awhille since I have done those tests, so you should verify if this is true or not.

#### kumarnaidu

##### New Member
Hi, thanks for the reply. As I understand both Non inferiority and Superiority used one-sided test.
For e.g. If higher value is bad; For proving non-inferiority upperlimit of CI (diff) should be less than margin. and for proving superiority it should be less than zero ultimately you will get CI completely below zero.
HA(NI):M1-M2<Margin
HA(Sup):M1-M2<0

#### hlsmith

##### Omega Contributor
I must have been thinking of the equivalency version!

#### ted00

##### New Member
In all examples I've seen, the math is the same between non-inferiority and superiority power/sample-size formulas, with the distinction coming from the subject domain context ... part of the problem might be that there is not (I'm not aware of?) a clear and general definition of what exactly "non-inferiority" and "superiority" means since, again, it depends on the context.

edit: I have heard people assert that one or the other requires larger sample size because (for some reason I'm not clear on) the measurement variance isn't the same.