This program can be used to calculate the area under a curve, or the average function value over a range, by the trapezoidal method (e.g. for AUC and bioavailability), or the fraction of the range above a threshold (e.g. proportion of treatment time with plasma levels above a critical drug concentration).
Suppose a function f(x) is well defined and can be integrated over a range x1 =< x =< x2. Then the area over this range can be defined as an integral, namely
Area = integral of f(x) between x1 and x2.If a model equation f(x) is not available or cannot be fitted then the area under the curve can be estimated by the trapezoidal rule when values are given for x and y. This is equivalent to using the lines joining up adjacent (x,y) pairs as an approximation to y = f(x). The average value of f(x) between x1 and x2 can be defined as
Average = Area/(x2 - x1),which can then be calculated from the area-estimate.
Sometimes it is required to estimate the fraction of the range of x where f(x) lies above or below a given threshold, and this program also calculates such parameters. To simplify the calculation and to avoid any ambiguities, it is supposed that y_values are all nonnegative, and that x_values are in nondecreasing order but not necessarily equally spaced. A linear interpolation is used if the limit values of x1 or x2 do not correspond to any actual x_values in the current data set.
At the start of each run you will be asked if you want to re-set Begin = Xmin, End = Xmax. If you accept, the program will automatically initialise (x1,x2) for the calculation of areas and average values to the extreme values set by the range of the current data as each new data set is entered. That is
x1 = Xmin x2 = Xmax.However, you can temporarily alter limits interactively for any current data set. This mode of program operation should be selected when the average and/or area is required over the complete range for each data set. If you do not select this option, you set the range by choosing (x1,x2) values for limits which will remain fixed until you change them. This ensures that areas and averages use the same range for all the data sets, but note that x1 and x2 are always adjusted temporarily if necessary to lie in the range (X-min,X-max). Similarly, you can select the option to set the y-theshold equal to the smallest y-value for each individual data set, or you can set a default value interactively. Initial defaults are set by the first data set entered.
Use a baseline for measurement so that all y-values are positive, then prepare a data file as a matrix with a column of x in nondecreasing order, and a corresponding column of y values, e.g. using program MAKMAT. Alternatively you can prepare a curve fitting file using the program MAKFIL, and then edit this if required using EDITFL, or you can transfer data from a spreadsheet by using the clipboard or a macro.
Important points to remember
Xmin Smallest x_value in the current data set Xmax Largest x_value in the current data set Ymin Smallest y_value in the current data set Ymax Largest y_value in the current data set x1 lower critical x_value (>= Xmin and < x2) x2 upper critical x_value (<= Xmax and > x1) Xstart maximum of x1 and Xmin (but =< Xmax) Xstop minimum of x2 and Xmax (but >= Xmin) Above X_length above threshold (also as % of total X_range) Below X_length below threshold (also as % of total X_range) Ytest Threshold y_critical_value Yarea Area under y points between Xstart and Xstop Ymean (Yarea)/(Xstop - Xstart)