CHAPTER 19 Other Useful Kinds of Regression 285

Using equivalent functions to fit the

parameters you really want

It’s inconvenient, annoying, and error-prone to have to perform manual calcula-

tions on the parameters you obtain from nonlinear regression output. It’s so much

extra work to read the output that contains the estimates you need, likeC 0 and the

ke rate constant, then manually calculate the parameters you want, like Vd and λ.

It’s even more work to obtain the SEs. Wouldn’t it be nice if you could get Vd and

λ and their SEs directly from the nonlinear regression program? Well, in many

cases, you can!

Because nonlinear regression involves algebra, some fancy math footwork can

help you out. Very often, you can re-express the formula in an equivalent form

that directly involves calculating the parameters you actually want to know.

Here’s how it works for the PK example we use in the preceding sections.

Algebra tells you that because V

Dose C

d

/

0^{, then C}

Dose Vd

0

/

. So why not use

Dose /Vd instead of C 0 in the formula you’re fitting? If you do, it becomes

Conc

Dose v

e

d

k Time

e

. And you can go even further than that. It turns out that

a first-order exponential-decline formula can be written either as e ^{k Time}

e

or as the

algebraically equivalent form 2

1 2

Time t /

.

FIGURE 19-8:

Nonlinear model

fitted to drug

concentration

data.

© John Wiley & Sons, Inc.