# Predictive Performance of Bayesian Methods to Forecast Vancomycin Concentration for Therapeutic Drug Monitoring in Critically Ill Pediatric Patients

## TL;DR

This study compares Bayesian methods and a first-order pharmacokinetics approach to predict vancomycin levels in critically ill children, finding that a weighted-flattened Bayesian method performs best.

## Contribution

The study introduces a weighted-flattened Bayesian algorithm that improves prediction accuracy for vancomycin concentrations in pediatric patients.

## Key findings

- The weighted-flattened Bayesian algorithm reduced relative bias by 12.66% compared to the conventional Bayesian model.
- Using one or two blood concentration measurements in Bayesian forecasting yielded similar prediction accuracy.
- The first-order PK method had lower bias than conventional Bayesian algorithms but higher than the weighted-flattened approach.

## Abstract

Background: This study aimed to evaluate different Bayesian algorithms and the first-order pharmacokinetics (PK) equation approach for forecasting vancomycin concentrations in critically ill pediatric patients and to identify influencing factors. Methods: A cohort of 110 patients with 568 therapeutic drug monitoring (TDM) blood samples was included. Three Bayesian algorithms, i.e., conventional, flattened, and weighted-flattened, using one or two historical values of either blood concentrations measured at the peak, trough, or middle (mid) of the dosing interval, were applied to forecast the concentrations of the next TDM occasion. The first-order PK approach, according to the Sawchuk–Zaske method, was used with two levels. The forecasting performance was assessed via relative bias (rBias) and relative root mean squared error (rRMSE) between the forecasted and observed levels. A linearmixed-effects model was employed to identify potential influencing factors on the rBias and rRMSE. Results: All methods showed negative rBias values of less than −20% and had relatively similar rRMSE of about 40%. First-order PK had lower bias than the conventional and flattened Bayesian algorithm (−10% vs. −15%), but higher bias than the weighted-flattened Bayesian algorithm (rBias −5%). Multivariate analysis using the linear mixed-effects model revealed that the type of forecasting algorithms significantly impacted the predictability. The weighted-flattened Bayesian algorithm significantly improved the rBias by 12.660% (95% CI: 10.131–15.194, p-value < 0.001) and decreased the rRMSE by 2.099% (CI 95% 3.779–0.418, p-value = 0.014) compared to the conventional Bayesian model. Either using one (mid or trough) or two concentrations in Bayesian forecasting yielded comparable rBias and rRMSE. Conclusion: The weighted-flattened Bayesian estimation method with solely one blood level is appropriate for forecasting the vancomycin concentration during therapeutic drug monitoring in critically ill children.