284 PART 5 Looking for Relationships with Correlation and Regression

In Figure 19-7, the output first restates the model being fitted. Next, what would

normally be called the coefficients table is presented, only this time, it is labeled

Parameters. It has a row for every adjustable parameter that appears in the func-

tion. Like other regression tables, it shows the fitted value for the parameter under

Estimate, its standard error (SE) under Std. Error, and the p value under Pr(>|t|)

indicating whether that parameter was statistically significantly different from

zero. The output estimatesC 0 at 59 5

2 3

.

.

μg/dL and ke at 0 163

0 0164

1

.

.

hr

because first-order rate constants have units of per time. From these values, you

can calculate the PK parameters you want:»

» ^{Volume of distribution: V}

Dose / C

10,000

g / 59.5 g / dL

168 dL

0

d

,

or 16.8 liters. Since this amount is several times larger than the blood volume

of the average human, the results indicate that this drug is going into other

parts of the body besides the blood.»

» ^{Elimination half-time: λ = 0.693/ke = 0.693/0.163hr1, or 4.25 hours. This}

result means that after 4.25 hours, only 50 percent of the original dose is left

in the body. After twice as long, which is 8.5 hours, only 25 percent of the

original dose remains, and so on.

How precise are these PK parameters? In other words, what is their SE? Unfortu-

nately, uncertainty in any measured quantity will propagate through a mathemat-

ical expression that involves that quantity, and this needs to be taken into account

in calculating the SE. To do this, you can use the online calculator at https://

statpages.info/erpropgt.html. Choose the estimator designed for two vari-

ables, and enter the information from the output into the calculator. You can cal-

culate that the Vd

16 8

0 65

.

.

liters, and

4 25

0 43

.

.

hours.

R can be asked to generate the predicted value for each data point, from which you

can superimpose the fitted curve onto the observed data points, as in

Figure 19-8.

R also provides the residual standard error (labeled Residual std. err. in Figure 19-7),

which is defined as the standard deviation of the vertical distances of the observed

points from the fitted curve. The value from the output of 3.556 means that the

points scatter about 3.6 μg/dL above and below the fitted curve. Additionally, R

can be asked to provide Akaike’s Information Criterion (AIC), which is useful in

selecting which of several possible models best fits the data.