Kreara

Hypothesis testing

In studies concerned with detecting an effect (e.g. a difference between two treatments, or relative risk of a diagnosis if a certain risk factor is present versus absent), sample size calculations are important to ensure that if an effect deemed to be clinically meaningful exists,then there is a high chance of it being detected, i.e. that the analysis will be statistically significant. If the sample is too small, then even if large differences are observed, it will be impossible to show that these are due to anything more than sampling variation. There are different types of hypothesis testing problems depending on the goal of the research.

Let μS = mean of standard treatment, μT = mean of new treatment, and δ = the minimum clinically important difference.

1. Test for Equality: Here the goal is to detect a clinically meaningful difference/effects is such a difference/effects exists
2. Test for Non-inferiority: To demonstrate that the new drug is as less effective as the standard treatment (ie the difference between the new treatment and the standard is less than the smallest clinically meaningful difference)
3. Test for Superiority: To demonstrate that the new treatment is more superior that standard treatment (ie the difference between the new treatment and the standard is greater than the smallest clinically meaningful difference).
4. Test for equivalence: To demonstrate the difference between the new treatment and standard treatment has no clinical importance

It is important to note that
the test for superiority is often referred to as the test for clinical superiority
If δ = 0, it is called the test of statistical superiority
Equivalence is taken to be the alternative hypothesis, and the null hypothesis is nonequivalence