From the original description of this example, you already know that Dose = 10,000 μg, so you can

substitute this value for Dose in the formula to be fitted. You’ve already estimated λ (variable tHalf)

as 4 hours. Also, you estimated

as about 50 μg/dL from looking at Figure 19-6, as we describe

earlier. This means you can estimate

(variable Vd) as

, which is 200 dL. With these

estimates, the final R statement is

which produces the output shown in Figure 19-9.

FIGURE 19-9: Nonlinear regression that estimates the PK parameters you want.

From Figure 19-9, you can see the direct results for Vd and tHalf. Using the output, you can estimate

that the Vd is

(or

liters), and λ is

hours.

Smoothing Nonparametric Data with LOWESS

Sometimes you want to fit a smooth curve to a set of points that don’t seem to conform to a common,

recognizable distribution, such as normal, exponential, logistic, and so forth. If you can’t write an

equation for the curve you want to fit, you can’t use linear or nonlinear regression techniques. What

you need is essentially a nonparametric regression approach, which would not try to fit any

formula/model to the relationship, but would instead just try to draw a smooth line through the data

points.

Several kinds of nonparametric data-smoothing methods have been developed. A popular one, called

LOWESS, stands for Locally Weighted Scatterplot Smoothing. Many statistical programs can perform

a LOWESS regression. In the following sections, we explain how to run a LOWESS analysis and

adjust the amount of smoothing (stiffness) of the curve.

Running LOWESS

Suppose that you discover a new hormone called XYZ believed to be produced in women’s ovaries

throughout their lifetimes. Research suggests blood levels of XYZ should vary with age, in that they

are low before going through puberty and after completing menopause, and high during child-bearing

years. You want to characterize and quantify the relationship between XYZ levels and age as

accurately as possible.

Suppose that for your analysis, you are allowed to obtain 200 blood samples drawn from consenting

female participants aged 2 to 90 years for another research project, and analyze the specimens for

XYZ levels. A graph of XYZ level versus age may look like Figure 19-10.