FIGURE 19-7: Results of nonlinear regression in R.

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 function. 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 estimates

at

μg/dL and

at

because first-order rate

constants have units of per time. From these values, you can calculate the PK parameters you want:

Volume of distribution:

, 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? Unfortunately, uncertainty in

any measured quantity will propagate through a mathematical 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

variables, and enter the information from the output into the calculator. You can calculate that the

liters, and

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.