© John Wiley & Sons, Inc.

FIGURE 19-6: The blood concentration of an intravenous drug decreases over time in one participant.

PK theory is well-developed and predicts under a set of reasonable assumptions that the drug

concentration (Conc) in the blood following a bolus infusion should vary with time (Time) according

to the equation:

where

is the elimination rate constant.

is related to the elimination half-life (λ) according to the

formula:

, where 0.693 is the natural logarithm of 2. So, if you can fit the preceding

equation to your Conc-versus-Time data in Table 19-2, you can estimate

, from which you can

calculate

. You can also estimate

, from which you can calculate λ.

The preceding equation is nonlinear and includes parameters, with

appearing in the exponent.

Before nonlinear regression software became widely available, analysts would take a shortcut by

shoehorning this nonlinear regression problem into a straight-line regression by working with the

logarithms of the concentrations. But that approach can’t be generalized to handle more complicated

equations that often arise.

Running a nonlinear regression

Nonlinear curve-fitting is supported by many modern statistics packages, like SPSS, SAS,

GraphPad Prism, and R (see Chapter 4). It is possible (though not easy) to set up calculations in

Microsoft Excel. In addition, the web page http://StatPages.info/nonlin.html can fit any

function you can write involving up to eight independent variables and up to eight parameters.