Area Under Curve (AUC)
In the field of pharmacokinetics, the area under the curve (AUC) is the area under the curve in a plot of concentration of drug in plasma against time.
In real-world terms the AUC (from zero to infinity) represents the total amount of drug absorbed by the body, irrespective of the rate of absorption. This is useful when trying to determine whether two formulations of the same dose (for example a capsule and a tablet) release the same dose of drug to the body.
AUC becomes useful for knowing the average concentration over a time interval, AUC/t. Also, AUC is referenced when talking about elimination.
The amount eliminated by the body = clearance (volume/time) * AUC (mass*time/volume).
Another application that we recently found is when we try to establish the equivalence of two asthma formulations and their superiority over placebo. Here are some links if you
a. want to learn how we can use integration to find the AUC
b. A small SAS macro to calculate AUC using trapezoidal rule
c. Use proc expand to find out the AUC
Hypothesis testingIn 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
In the field of pharmacokinetics, the area under the curve (AUC) is the area under the curve in a plot of concentration of drug in plasma against time.
