Malin Andersson 1,2, Charlotte Kloft 1, Robin Michelet 1
1 Freie Universität Berlin, Institute of Pharmacy, Dept. of Clinical Pharmacy & Biochemistry (Berlin, Germany), 2 Graduate Research Training program PharMetrX (Berlin/Potsdam, Germany)
Introduction: The β-lactam/β-lactamase inhibitor combination piperacillin/tazobactam (PIP/TAZ) is a widely used empirical therapy in critical ill patients. The minimum inhibitory concentration (MIC) of PIP/TAZ is the standard metric for pharmacodynamic (PD) evaluations of this combination. As an alternative to the MIC, the β-lactamase inhibitor concentration-dependent MIC (MICcBLI) has been incorporated into a population pharmacokinetic/PD modelling framework to account for in vivo fluctuations of the TAZ concentration, not reflected by the standard MIC [1]. By applying the MICcBLI framework in a simulation-based setting, investigations for optimised antibacterial strategies for PIP/TAZ, accounting both for individual patient characteristics and the effect of TAZ on the antibacterial effect of PIP can be performed.
Objectives: As a first step towards optimised antibacterial strategies for PIP/TAZ, a global variance-based sensitivity analysis was performed to elucidate the impact of the respective PD parameter and its contribution to the uncertainty of the model output (MICcBLI prediction) and thereby identify key parameters reflecting isolate-specific characteristics for subsequent simulation studies.
Methods: Two PD models for PIP/TAZ were investigated: initial and extended. Both models followed an inhibition type Imax model and were parameterised with MIC0 (MIC at TAZ=0), Imax (maximum inhibitory effect), IC50 (TAZ concentration for half-maximum effect), and H (Hill coefficient) [2]. The extended PD model included an additional inhibition term with the parameters (with k as total number of parameters) Imax2 and IC50,2. A global variance-based sensitivity analysis was performed to obtain first-, second-, and total-order Sobol’-based sensitivity indices [3, 4]. The indices provided the fraction of total output variance explained by one parameter alone (first-order effect), the first-order effect of the parameter with its interaction with all other parameters (total-order effect), and the fraction of total output variance explained by interaction of two parameters (second-order effect). A Latin hypercube sampling method was used to sample 10 000 (k=4) or 1000 000 (k=6) samples (N) to create N(k+2) Sobol’ matrices. Sobol’ indices were calculated for first-, second-, and total-order effect utilising the “saltelli” [5] (first-, second-order effect) and the “jansen” [6] (total-order effect) estimators in the R package sensobol [7]. The parameter values for the Sobol’ indices were leveraged in a local sensitivity analysis, where the respective parameter was fixed to the values obtained in the global sensitivity analysis and the remaining parameters were estimated on in vitro MICcBLI data to obtain the change in sum of squared residuals utilised as the objective function [1].
Results: For the initial PD model (k=4), the respective Sobol’ index for the first-order effect indicated that mostly the parameters MIC0, Imax, and IC50 contributed to the total output variance. The respective Sobol’ index was TAZ concentration dependent: The MIC0 contributed to the total outcome variance at lower TAZ concentrations, IC50 at intermediate TAZ concentrations, and Imax with increasing TAZ concentration. The first- and total-order effect only differed for Imax and IC50. The second-order effect indicated that the total output variance at intermediate TAZ concentrations was due to an interaction between Imax and IC50. For the extended PD model (k=6), all parameters contributed to the total output variance, however, at different TAZ concentration levels. The Sobol’ indices indicated that the H parameter’s total-order effect exceeded its first-order effect, reflecting interactions with the two IC₅₀ parameters (second-order effect). The local sensitivity analysis indicated that all parameters were identifiable for both models given the data.
Conclusions: A global sensitivity analysis using first-, second-, and total-order Sobol’ indices was performed to quantify the contribution of PD parameters to overall model output variability.
The impact of identified key parameters was dependent on the TAZ concentration. These findings could inform experimental design: different regions of the TAZ concentration space provided different information, underlining what has been postulated before, interaction experiments need a design with a relatively wide range of concentrations to ensure robust characterisation of the interaction [8]. Furthermore, the parameters remained well identifiable for an extended PD model. The integration of the sensitivity analyses underpinned the selection of key parameters important to further consider and incorporate for simulation purposes for analysing optimised dosing strategies for PIP/TAZ. In addition to selecting impactful parameters, by applying the global variance-based sensitive analysis approach, reasonable parameter values could be further selected and evaluated to reflect potential isolates with varying PD characteristics.
References:
[1] Andersson M, et al. J Antimicrob Chemother 2026; 81: dkaf406.
[2] Bhagunde P et al. Antimicrobial Agents and Chemotherapy 2012; 56: 2237.
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[5] Saltelli A et al. Computer Physics Communications 2010; 181: 259–70
[6] Jansen MJW. Computer Physics Communications 1999; 117: 35–43.
[7] Puy A et al. Journal of Statistical Software 2022; 102: 1–37.
[8] Wicha SG et al. Nat Commun 2017; 8: 2129.
Reference: PAGE 34 (2026) Abstr 12050 [www.page-meeting.org/?abstract=12050]
Poster: Drug/Disease Modelling - Infection