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

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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 the American Society of Health-System Pharmacists (ASHP), the Infectious Disease Society of America (IDSA), the Pediatric Infectious Disease Society (PIDS), and the Society of Infectious Disease Pharmacists (SIDP)?

PrecisePK has been a leader in the field of Bayesian Dosing for over 35 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 collections required from phlebotomy, the ability to achieve target concentration within the first 24-48 hours, and the reduction of patient’s pain and discomfort associated with venipunctures, and the decreased risk of exposure to infections for the patient. So why can the Bayesian method  predict drug concentrations accurately using only one level?

PrecisePK's drug dosage regimen is a balance of the Bayesian priori and the observed values in the individual.

Bayesian algorithm fits an appropriate population pharmacokinetic (PK) model, known as Bayesian’s priori, to the patient data. Priori models are clinically validated and informative, and are used to describe the clinician’s prior understanding of how the population responds to therapy. In contrast, first-order PK equation-based approaches require two serum levels to draw a graph and uses the trapezoidal approximation to estimate an AUC. Furthermore, Bayesian incorporates different sources of information such as priori information (population model and the range of variability expected to be in the population), posteriori 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. Bayesian uses prior knowledge and experiences to make well-informed decisions under unexpected circumstances.

First order pharmacokinetics of vancomycin requires two serum levels to draw a curve and predict AUC. The Bayesian method incorporates prior information and only requires one serum to predict future values.

Benefit #2: You can use levels that are obtained anytime during the dosing interval. This cuts down on inconveniences associated with interdepartmental coordination between the nursing, pharmacy, and phlebotomy departments to synchronize blood tests with drug administration and offers the flexibility with the timing of lab draws. So how can the Bayesian method 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, including non-steady state levels. Therefore, it does not just capture one concentration point in time, but rather a full concentration 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 its ability to learn from specific population sets. 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.

Sample Case of interpreting the results obtainded from PrecisePK's Bayesian algorithm

AE is a 50-year-old male  (Ht=5’8’’, Wt=200 lbs, SCr=1.4 mg/dL) with a PMH of diabetes, HTN, and CAD. He is admitted to the ER for fever, chills and right leg cellulitis. Blood cultures are positive for Gram-positive cocci in clusters. His temperature is elevated at 101F and his WBC is 20,000 cells/ mm3. The patient is started on vancomycin 1,000 mg IV Q12H. A peak level drawn on day 4 of therapy at 1300 is 30.5mg/L and a trough level drawn on day 5 of therapy at 0000 is 13 mg/L. At this point, the patient’s respiratory culture is positive for MRSA with a MIC of 1mg/L. His symptoms are improving and SCr has decreased to 0.9 mg/dL. Is the current dosing adequate to achieve a target efficacy of 400-600 mg*h/L?

PrecisePK's Population and individual patient's a priori information including volume of distribution (Vd), creatinine clearance (CL), and half life (T1/2),.

PrecisePK uses general populations that are representative of the patient’s description to compute the predicted population PK parameters as shown in the table above. As the Bayesian program fits the population PK model to the patient’s measured levels, the patient’s PK parameters were calculated accordingly.

Steady state analysis shows that the current regimen of vancomycin 1,000 mg IV Q12H yields trough levels of 12.29 mg/L and AUC24/MIC of 495.61 mg*h/L meets the target for cellulitis, thus adequate for efficacy and resolution of the infection.

PrecisePK therapeutic drug monitoring report displayed after or during a dosing regimen summarizing population and individual PK parameters, serum levels, and dosage history.

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