Bayesian Method:
Break Down Complex Mathematical Concepts into the ABC of Pharmacy

PrecisePk Pharm. D. Team
December 4, 2020

Have you heard that the 2020 revised vancomycin guideline specifically recommends Bayesian approach as a method of choice to measure and monitor AUC? Have you ever wondered what is the Bayesian algorithm and why it is considered the preferred approach by ASHP, the Infectious Disease Society of America, the Pediatric Infectious Disease Society, and the Society of Infectious Disease Pharmacists?

PrecisePK has been a leader in the field of Bayesian Dosing for over 30 years. Let us take a deep dive into the benefits of Bayesian methods and the concepts behind it.

Benefit #1: You only need one serum level to estimate the patient’s AUC. This means less collection time required from the phlebotomy, the ability to achieve target concentration early on during the course of treatment, and reducing the patient’s pain and discomfort with venipunctures, and the likelihood of infection that we would potentially expose the patient to. So why the Bayesian method can predict drug concentration accurately using only one level?

Bayesian algorithm fits an appropriate population PK model, known as Bayesian’s priori, to the patient data (i.e. actually measured vancomycin serum levels). Priori models are clinically validated, informative, and are used to describe the clinician’s prior understanding of how the population responds to therapy. On the contrary, the first-order PK equation-based approach requires two levels to draw a line and uses the trapezoidal approximation to estimate an AUC. Furthermore, Bayesian incorporates different sources of information and the associated uncertainty including priori information (population model and the range of variability expected to be in the population), posterior information (all plasma concentration data points and the assay error), patient factors and covariates (demographics) to obtain the most likely results (individual parameters and posterior models). In other words, it strikes a balance between the priori and the posteriori to select a drug dosage regimen. The outcome is obtained from the tug of war between the priori population PK parameters (Vd, CL) and the observed serum level. In a nutshell, just like human behavior, Bayesian uses prior knowledge and experiences to make well-informed decisions under unexpected circumstances.

Benefit #2: You can use levels that are obtained anytime during the dosing interval. This cuts down on the cumbersome associated with interdepartmental coordination between nursing, pharmacy, and phlebotomy to synchronize blood test with drug administration and offers flexibility with the timing of lab draw. So why Bayesian method can utilize samples taken at a random time?

The calculation involved in the First-order PK equations assumes steady-state pharmacokinetic parameters; thus, the trapezoidal approximation only provides a static estimation of AUC. Bayesian method with fully embedded population PK models considers individual variation in pharmacokinetics over a dosing period. Therefore, it does not just capture one concentration point in time that may often not occur in the future, but rather a full plasma vs time profile.

Benefit #3: The program enables you to build PK model specifically for your local population  The most compelling aspect of Bayesian philosophy is the ability to learn. As more patients’ data become available, our understanding of the PK parameters of interest evolves, and the posterior model is updated incrementally. Bayesian method uses machine learning to design models that fit specifically to the local patients at your respective institutions.

Interpretation of results obtained from the Bayesian algorithm with Precise PK

AE is a 50-year-old male  (Ht=5’8’’, Wt=200 lbs, SCr=1.4 mg/dL) with a PMH of diabetes, HTN, CAD is admitted to the ER for fever, chills and right leg cellulitis. Previous blood cultures were positive for gram-positive cocci in cluster. His temperature is elevated to 101F and his WBC was 20,000 cells/ mm3. Pt was started on 1,000 mg vancomycin IV Q12H. A peak level drawn on day 4 of therapy at 1 PM was 30.5mg/L and a trough level drawn on day 5 of therapy at 00AM was 13 mg/L. At this point, patient’s respiratory culture is positive for MRSA w/ a vancomycin MIC of 1mg/L. Pt’s Symptoms are improving and SCr has decreased to 0.9 mg/dL. Is the current dosing adequate to achieve a trough of >=15 mg/dL?

PrecisePK uses general populations that are representative of the patient’s description to compute the predicted population PK parameters are shown in the table above. As the Bayesian program fits the population PK model to the patient’s measured levels (associated with the approximated half-life of 11 hours as concentration was almost halved from 11/29/20 1300 to 11/30/20 0000), the patient’s PK parameters were calculated accordingly.

Steady state analysis shows that current regimen 1000 mg IV Q12H yields trough 12.29 mg/L and AUC24/MIC 495.61 meets the target for cellulitis, thus adequate.

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