### Differences between Non-inferiority, Superiority, Super-superiority and Equivalence designs

#### Non-inferiority

#### When we compare a new treatment or device vs a reference treatment or device, and when inferences about superiority cannot be demonstrated, a desirable strategy
could be to assess that the new treatment or device is at minimum "not acceptably worse" than the reference treatment or device.

To do that we need to define a threshold of "not unacceptably worse", i.e., the non-inferiority margin. In other words,
the maximum tolerable difference for which is acceptable to claim non-inferiority. The non-inferiority margin is determined based
on statistical analisis and clinical judgement. For instance, it is quite common to consider a non-inferiority margin of 0.1 logMAR in studies where the primary
estimate is Best Corrected Distance Visual Acuity. For the analysis of such study design, we need to look at the inferior 95% confidence limit of our main estimate,
if the limit is smaller than the non-inferiority margin, we cannot claim non-inferiority. If it is greater, we can accept the non-inferiority hypothesis.
For instance, let's imagine the non-inferiority margin for our primary estimate is -0.1 logMAR, the mean difference between both groups is 0 with a 95% confidence interval
that ranges from -0.12 to 0.12 logMAR. In this particular case we cannot claim non-inferiority because -0.12 is smaller than -0.1 logMAR.

#### Superiority

#### If we want to compare two treatments or measurements methods and we want to see if one is superior to another, a superiority
design is a good approach. There is no need to define a superior or inferior margin. Typically, this design is analyzed by means of a paired t-test (in a cross-over design),
independent t-test (in a parallel design) or their equivalent non-parametric tests: Wilcoxon Signed-Rank test and Mann-Whitney U, respectively.

#### Super-Superiority

#### This design is analogous to the non-inferiority but instead of an inferior margin we have to define a superior margin. This design is utilised to show that two treatments are different by a certain amount.

#### Equivalence

#### This design combines the non-inferiority with the super-superiority designs. Both a non-inferior and a super-superior margins have to be defined.
If the mean (or median) difference between treatments plus the 95% confidence interval fall within both superior and inferior limits, we can say that both treatments or measurement methods are equivalent.

### Differences between a Cross-over or Parallel designs

####
In a crossover design, each subject receives all treatments/measurement methods. Usually one group starts receiving treatment/measurement method A and followed by treatment/measurement method B. It is common
to leave a wash-out period between treatments.

In a parallel design, one group receives treatment/measurement method A and another group receives treatment/measurement method B. In this design is important subject allocation in each group. Randomization can play a very
important role in this designs, and actually for small sample sizes (less than 100 subjects) advanced randomization methods might be necessary to ensure a balanced allocation in both groups.

### How to compute the sample size calculation in a Non-inferiority design? and in a Superiority, Super-Superiority and Equivalence designs?

#### Sample size calculation depends on the type of hypothesis (i.e., non-inferiority, superiority, super-superiority or equivalence), the type of design
(i.e., parallel or crossover), and the type of estimate (i.e., proportion or mean/median). These three factors can be combined and result in a different sample size calculation formula.
Try for free any of these cases with our sample size calculation app.