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Chapter 390

Area Under Curve

Introduction

Suppose you are studying a drug that influences plasma concentration. A popular method of looking at the

absorption and elimination properties of the drug is to follow the plasma concentration across time. When the

concentration values are plotted on the vertical axis, the time values are plotted on the horizontal axis, and the

points are joined with a line, a curve results. One method of making comparisons among different types of drugs

and different doses of the same drug is to compute the area under the curve (AUC).

AUC is computed by the trapezoidal rule as follows:

AUC = 1 n-1

2 (Ti+1 - Ti )(Ci+1 + Ci - 2B)

i =1

where Ti is the ith time value, Ci is the ith concentration value, n is the number of time values, and B is the baseline

value. The area between the baseline and the curve is computed by this formula.

The AUC should be calculated from zero to a time at which the concentration has returned to its regular levels.

Also, when making comparisons, you should ensure that all AUC's are computed for the same time intervals.

Data Structure

Two different data structures may be used to store data for analysis by this procedure. In the first format, the X

(time) values are stored in one variable and the Y (concentration) values are stored in other variables, one variable

per group. The AUC dataset is in this format.

In the other format, the X values are stored in one variable, group values are stored in a second variable, and the

measurements are stored in a third variable. The data in the AUC dataset was reorganized to be in this format in

the AUC1 dataset.

Format Type 1

AUC dataset

Time P1 P2 P3

05 4 6

1 15 14 17

2 20 16 22

3 21 18 23

4 21 17 25

5 19 15 22

10 15 12 18

50 6 3 7

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Area Under Curve

Format Type 2

AUC1 dataset

Time Subject Concentration

0 P1 5

1 P1 15

2 P1 20

3 P1 21

4 P1 21

5 P1 19

10 P1 15

50 P1 6

0 P2 4

1 P2 14

2 P2 16

3 P2 18

4 P2 17

5 P2 15

10 P2 12

50 P2 3

0 P3 6

1 P3 17

2 P3 22

3 P3 23

4 P3 25

5 P3 22

10 P3 18

50 P3 7

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Area Under Curve

Example 1 - Calculating Area Under the Curve (Multiple Y

Columns)

This section presents a tutorial of calculating the AUC for three individuals labeled P1, P2, and P3. The responses

for each individual are contained in separate columns. The data are contained on the AUC dataset.

Setup

To run this example, complete the following steps:

1 Open the AUC example dataset

? From the File menu of the NCSS Data window, select Open Example Data.

? Select AUC and click OK.

2 Specify the Area Under Curve procedure options

? Find and open the Area Under Curve procedure using the menus or the Procedure Navigator.

? The settings for this example are listed below and are stored in the Example 1 settings template. To load

this template, click Open Example Template in the Help Center or File menu.

Option Value

Variables Tab

Y Variable(s) ........................................... P1-P3

X Variable ............................................... Time

Reports Tab

AUC Report ............................................ Checked

Data Report ............................................ Checked

3 Run the procedure

? Click the Run button to perform the calculations and generate the output.

Area Section

Area Section with Baseline = 0

Area Under Y Time at Time Time

Y Variables Curve Max Max of Y Min Max Count

P1 594 21 3 0 50 8

P2 442 18 3 0 50 8

P3 701 25 4 0 50 8

This report shows the area under curve as well as supporting information.

Y Variables

This gives the value of the Y variable (if multiple Y variables were specified) or the value of the break variable (if

a break variable was specified).

Area Under Curve

The is the area under the curve calculated in the interval between Time Min and Time Max. It is calculated using

the trapezoidal formula presented earlier.

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Title: Area Under Curve

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