# Bayesian Schmayesian

The revised vancomycin guidelines are currently in the comment phase, and peaks are cool again. With two levels a Bayesian algorithm is not required, the calculations can easily be done the old fashioned way. How did we do kinetics back in the seventies, before desktop PC’s? The answer: 3-cycle semi-log graph paper, get yours here

Computer-less AUC-guided dosing

1. Ensure no vacomycin on board, then give a 20mg/kg load.
2. Draw a post-distribution level (1 to 2 hours after the end of the infusion).
3. Calculate the creatinine clearance in order to estimate the vancomycin half-life (see table below).
4. Draw a vancomycin level at the estimated half-life.
5. Plot the results and connect the dots (see the idealized example below).
6. The half-life is the time it takes for the serum level to drop by half.
7. Calculate the elimination rate from this known relationship: Kel = 0.693 / Half-life
8. Estimate the volume of distribution from this basic pk equation: Vd = Dose/Peak

How to estimate vancomycin half-life

 CrCl Half-life (hrs) 140 6 100 8 70 12 50 16 35 24 25 32 < 25 pulse dosing (?)

An idealized example

Using the pk parameters derived from the semi-log plot we can then estimate the dose required to reach a target 24-hr AUC by using the known relationships between pk terms:
Clearance = Kel * Vd (L/hr)
24-hr AUC = Daily dose/Clearance (mg*hr/L)
= (Dose * (24 / Interval)) / (Kel * Vd)

Ideally we re-dose vancomycin at the half-life, rounded for practicality

The target range for 24-hr AUC is 400 to 550, therefore the initial target would be the midpoint: 475.
Dose = (475 * Kel * Vd) / (24 / Interval)
From the above example:
Dose = (475 * 0.058 * 50) / (24 / 12)
= 686 mg

Round to a practical dose and recheck your 24-hr AUC output.
From the above example, round to 750mg:
24-hr AUC = (Dose * (24 / Interval)) / (Kel * Vd)
= (750 * ( 24 / 12)) / (0.058 * 50)
= 519 mg*hr/L

Finally, estimate the steady-state trough using the standard pk equation:
Css(trough) = Css(peak) * e -kel*tau
From the above example.
Trough = 15.5 mg/L

Understand the limitations

Please realize that vancomycin kinetics are multi-compartmental. The one-compartment model does not capture the distribution phase(s) thus it under-estimates the true 24-hr AUC by 5 to 10%. What does this mean in practice? First, if the calculated 1-compartment AUC is 400, then you can be assured that you have hit the minimum 24-hr AUC target. Second, if your estimated 24-hr AUC is greater than 550 then the dose is likely to be above the AKI risk threshold.

Enjoy.