| Section 2 - Applied Pharmacokinetics |
Introduction
The traditional use of measured drug levels (ie., a posteriori drug dosing) is to estimate the patient's pharmacokinetic parameters from the measured drug levels without relying in any way on the population model. An example of a posteriori dosing is the Sawchuk and Zaske method of aminoglycoside serum level analysis.
The Bayesian approach incorporates both sets of data for estimating the patient's pharmacokinetic parameters. It uses the a priori pharmacokinetic parameters of the population model as the starting estimate for an individual; it then adjusts these estimates based on the patient's measured drug levels, taking into consideration the variability of the population parameters and the variability of the serum level measurement. Our population model is not discarded, rather it is incorporated into the estimation procedure. The serum level data is interpreted in light of both the variability of the population model the variability of the serum level measurement itself.
The appeal of the Bayesian approach is that it mimics human thinking. Before deciding what to do, our intuition first tries to for see all the possibilities that might arise. Then, we judge how likely each is, based on both what we see and all our past experiences. Human intuition is good at judging what pieces of information are relevant to a question, but very unreliable in judging the relative cogency of different pieces of information. Bayes' theorem tells us quantitatively just how cogent every piece of information is, however it is not always able to discern whether a piece of information is relevant. Let's look at a practical example.
Practical application
If we plug those levels into the traditional Sawchuk and Zaske equations, we get a Vd of 1.13 L/kg and half-life of 22.8 hours, giving an ideal dose of 340mg every 61 hours. Obviously this is not the proper dosage recommendation.
If we select the Bayesian algorithm for this set of levels, we get a Vd of 0.36 L/kg and half-life of 7.5 hours, giving an ideal dose of 112mg every 20 hours. Okay, that's a more reasonable dose than before, but let's dig a little deeper into this scenario.
An experienced pharmacokineticist would realize at first glance that these levels are just not right, they don't jive with what one would expect from this patient. Because any number of things could have gone wrong, your first step is to find out what when wrong from the nursing and lab staffs. You find out that the over-worked nurse hung the dose late. The hurried phlebotomist drew the trough "on time", but didn't notice that the infusion was already in progress.
Now that we know the "trough" is not a trough at all, what is the next step? If we throw out the trough level that we know is wrong, and use only the peak, we get a Vd of 0.32 L/kg and half-life of 5 hours, giving an ideal dose of 103mg every 14 hours. This is obviously the most reasonable of the three alternatives.
The lesson to take from this example is to never use bad data. Even a sophisticated Bayesian algorithm can not completely overcome bad data. The software engineer's cliche, "garbage in = garbage out", still applies. We must look at all "unusual" serum level data in a critical light.
Precautions
Likewise, outlying patients in a population (ie, those patients whose pharmacokinetic parameters lie outside of the 95th percentile of the population) may be put at risk.
And, as shown in the example above, bad data will corrupt the analysis. As is always the case, the computerized algorithms outlined below can only assist in the decision-making process and should never become a substitute for rational clinical judgement.
Pharmacokinetic formulas
CPss = (MD / t_{inf } x Vd x k_{el} ) x (1 - e^{-kel x tinf} /1 - e^{-kel x tau} ) x e^{-kel x t}
where
CPss = [k_{0} (k_{12}-k_{d}) (1 - e^{kd x tinf}) e^{kd x t})] / [V_{c} x k_{d} (k_{d}-k_{el}) (1 - e^{kd x tau})] +
[k_{0} (k_{el}-k_{21}) (1 - e^{kel x tinf}) e^{kel x t})] / [V_{c} x k_{el} (k_{d}-k_{el}) (1 - e^{kel x tau})]
where
| Section 2 - Applied Pharmacokinetics |