The Bayesian pharmacokinetic approach maximizes prior information about a population in pharmacokinetic calculations to improve pharmacokinetic parameter estimations and dosing predictions when drug levels are available. A large data set is used to extract the mean pharmacokinetic parameters and their standard deviations for a population. Equations are derived to calculate parameter values for an individual patient.
For a one-compartment open model, the mean volume of distribution and mean clearance are determined with their standard deviations or coefficient of variations and the equations used to estimate an individual patient's values. Accuracy of a Bayesian forecasting program is largely determined by the robustness and generalizability of the population model used.
Model Development Requirements: One compartment models can be constructed with a large number of patients (~100) with varying degrees of renal function when a post dose peak and trough are drawn for each patient (Shingde RV 2019).
"Bayesian methods can use serum levels obtained at anytime."
This is not related to the Bayesian Method, but is related to software design.
"Bayesian methods can incorporate changes in renal function and volume of distribution."
This is not related to the Bayesian Method, but is related to software design.
"Bayesian methods allow accurate and reliable AUC estimates with trough-only data."
This is only possible when richly sampled data is used as a Bayesian prior. Richly sampled models have eight or more levels drawn throughout the dosage interval to capture the distribution and elimination phases for each patient during model development and a large number of patients are included in the analysis. Most published models are based on small populations with limited peaks and trough sampling and usually with only trough sampling. It is advisable to review the original publications and vendor documentation for verification of the sampling used during model development. Otherwise a peak and trough are required to adequately calculate the AUC in a Bayesian or non-Bayesian model. First-order analytic equations are as accurate as Bayesian methods of AUC calculations.
The first two statements are a function of software design and not Bayesian analysis. Any computerized pharmacokinetic program can perform these functions if designed with appropriate nonlinear least squares regression routines. Most commonly the method of superposition is applied to allow for changes in doses, dosage intervals, lengths of infusions, and time of serum levels, and serum creatinines during data fitting. Data fitting is possible with steady state or non-steady state levels at any point in time.
Once serum levels are determined after a known drug dosage history for an individual, these values (means and standard deviations of PK parameters) are included in the data fitting minimization calculation of prediction errors.
SSE = [Sum for all levels (LevelMeasured − LevelPredicted)2 / (SDfor assay)2] + [Sum for all PK parameters (Population Mean − Fit Value)2 / (SDof parameter)2]
SSE = [Sum of all levels (LevelMeasured − LevelPredicted)2 / (CVAssay × LevelMeasured)2] + [Sum for all parameters (Population Mean − Fit Value)2 / (CV × Population Mean)2]
The SSE (Sum of Square of Errors) becomes more heavily weighted towards the actual serum levels as more levels are obtained.
| Population Mean | Calculated pharmacokinetic parameter mean for the patient based on the derived population pharmacokinetic equations. For example, if vancomycin's one-compartment open model population mean Vd is 0.65 L/kg of total body weight and the patient weighs 100 kg, then 65 liters is the population mean value for the patient. |
| Coefficient of Variation (CV) for parameters | May be found in the literature and is typically 30-40% |
| Fit Value | The fit value for the parameter that minimizes the sum of the square of the errors for the above equation |
| Level Predicted | The level calculated for the fit values of the pharmacokinetic parameters |
| Standard Deviation (SD) | Coefficient of variation × Mean |
| Coefficient of Variation (CV) | Standard Deviation / Mean |
| Coefficient of Variation (CV) | CV = Standard Deviation / Mean |
| Standard Deviation (SD) | SD = Coefficient of variation × Mean |
The applied Bayesian model needs to match the population or patient to which it is later applied. If it doesn't, Bayesian calculations will be erroneous and may negatively impact patient outcomes.
Clinical Judgment: If actual levels are consistently higher or lower than the predicted levels, the model does not fit the patient and more emphasis should be placed on the actual measured levels when making dosing adjustments.