Bias and Uncertainty of Monte Carlo Simulations with Beta-Lactams
Bulitta, J.(1), T. P. Lodise(2), G. L. Drusano(3), M. Kinzig-Schippers(1), U. Holzgrabe(4), F. Sörgel(1,5)
(1)IBMP, Nürnberg, Germany; (2)Albany College of Pharmacy, Albany, NY, USA; (3)Ordway Research Institute, Albany, NY, USA; (4)Univ. of Würzburg, Würzburg, Germany; (5)Univ. of Duisburg-Essen, Essen, Germany;
Objectives: The majority of published papers on Monte Carlo simulations (MCS) with beta-lactams use pharmacokinetic (PK) parameters from literature. Often, 1-compartment (1-C) models are used. The central tendency and variability of simulated and observed concentrations is rarely compared, e.g. by visual predictive checks. Some authors statistically compare the probability of target attainment (PTA), but do not account for uncertainty in PK parameters and MIC distributions. Our objectives: 1) To compare selection criteria for population PK models to be used for MCS, 2) to quantify the influence of model misspecification on PTAs, and 3) to quantify the uncertainty in PTAs.
Methods: We compared the log-likelihood, residual plots, and visual predictive checks as model selection criteria for two real data examples. To study the effect of model misspecification, we simulated plasma concentrations of a typical beta-lactam by a 2-C model and re-estimated the PK parameters for a 2-C and a 1-C model, and by non-compartmental analysis. Uncertainty in PK parameters and MIC distributions was quantified by nonparametric bootstrapping. Based on data from 48 simulated subjects (20 observations/subject), we re-estimated the PK parameters for 3,000 bootstrap datasets with n=12, 24, or 48 subjects. We derived the PTA for each bootstrap dataset by MCS. We used the PKPD target time above MIC over a dose interval of >= 40% or >= 70% and calculated the expected value of PTA against bacteria from specific MIC distributions.
Results: Visual predictive checks best assured adequate predictive performance. Model misspecification had a pronounced effect on MCS. The PTAs for a specific MIC distribution relative to the true 2-C model were within [-1.0% to 0.3%] [range] for the re-estimated 2-C model, within [-40% to -5.9%] for the re-estimated 1-C model, and within [0.5% to 25%] for the MCS with non-compartmental variables. Due to uncertainty in PK parameters and in MIC distributions, the width of the 90% confidence interval of the expected PTA for a specific MIC distribution with 50 samples was <=36% (for n=12 subjects), <=25% (n=24), and <=19% (n=48).
Conclusions: Visual predictive checks should be performed to qualify a population PK model for MCS, as model misspecification can severely bias the PTAs. Uncertainty in PK and MIC distributions needs to be considered for a statistical comparison of PTAs. A sound statistical comparison of PTAs based on literature PK data is hardly possible.