Impact of interaction model choice in PKPD analysis evaluating drug combination in TGI in vivo studies
Vincent Madelain
Servier
Objectives:
Combining drugs has become a usual strategy in oncology to improve treatment efficacy and/or reduce dose-related safety issue yet characterizing the respective activity of two or more drugs in combination remains often challenging. Despite rich literature on the interaction models, only few articles focus on quantitative properties and behavior of these models for in vivo PKPD analysis [1,2,3], which is often a key step for the evaluation of combination therapy. In this work, we aimed to identify relevant mathematical models to describe the PD interaction between two drugs and investigate their respective properties with application to tumor growth inhibition data from in vivo mouse models.
Methods: Candidate models were identified from literature, focusing on quantitative models relying on dose or concentration effect relationship, and not requiring mechanistic assumptions or previous knowledge to ensure applicability to various drug associations. First, a simple mathematical exploration was performed using isobologram plots for different sets of parameters, describing additivity and synergy.
As a second step, the candidate models were applied to a PKPD analysis, aiming to characterize the antitumoral activity of two drugs in a xenograft mouse model. In vivo study design consisted in 6 groups of 6 mice, allocated to one control group, two single agent groups and 3 combo groups, where the dose of one of the two drugs was varying while the second was kept constant. Drug A and B were administered respectively by IV and oral routes for 8 days, with QW and QD dosing interval respectively. PK sampling was done on D1 and tumor volume was measured every other day for 28 days. Sequential PKPD analysis was performed independently for the two drugs using control and single agent groups; then ability of each selected PD interaction model to characterize the combination effect was evaluated using BIC and stratified VPC. A second xenograft model with similar study design was used to confirm the obtained results.
Lastly, for the best performing models, simulations/re-estimation were run in order to evaluate the ability of these models to correctly identify a synergy pattern generated with different interaction models.
Results: Six mathematical models were identified from literature and described through isobologram: the interaction parameter model (IPM), the Bliss interaction model (BlissI), the zero-interaction potency model (ZIP), the Greco model, the general pharmacodynamic interaction model (GPDI) and two parametrizations of the Lp space model. Ability to describe the different interaction patterns varied across models.
PK profiles of drugs A and B were well described by a tricompartmental model with Michaelis Menten elimination and bicompartmental model with 0 order absorption and linear elimination respectively. No PK drug-drug-interaction was observed. Tumor volume growth was described with an exponential – linear tumor growth model where the effects of drug A and B concentrations as single agent were described with Emax model, inducing delayed death of tumoral cells after three transit compartments.
IPM, Bliss interaction, the two parametrizations of Lp space and GPDI consistently identified synergy between the 2 evaluated drugs. Similar BIC values were obtained with Bliss interaction, Lp space and GPDI model. GPDI was found numerically unstable due to the higher number of estimated parameters. IPM model was found equivalent or significantly worse depending on the direction of the interaction effect. Consistent results were obtained with the second dataset, where Lp space and Bliss interaction models both allowed to identify strong synergy.
The 4 models considered for simulation re-estimation procedure were IPM, BlissI and the two parametrization of LP space. All were able to accurately reestimate their respective model parameters describing the PD interaction, with higher variability for BlissI. When simulating with BlissI or IPM and reestimating with other models, reestimated parameters appeared slightly more biased for the BlissI and IPM, while Lp space appears the most robust.
Conclusions: This work suggest that BlissI and Lp space models can be used to characterize interaction in case of suspected strong synergy, without making assumption on the direction of the interaction. Further exploration would be required to identify the fittest models allowing to describe other interaction patterns.
References:
[1] Wooden et al., MuSyC is a consensus framework that unifies multi-drug synergy metrics for combinatorial drug discovery, Nat Commun. 2021 Jul 29;12(1):4607. doi: 10.1038/s41467-021-24789-z
[2]Wicha et al., A general pharmacodynamic interaction model identifies perpetrators and victims in drug interactions, Nat Commun. 2017 Dec 14;8(1):2129. doi: 10.1038/s41467-017-01929-y.
[3] Pearson et al., Drug Combination Modeling: Methods and Applications in Drug Development J Clin Pharmacol. 2023 Feb;63(2):151-165. doi: 10.1002/jcph.2128. Epub 2022 Sep 11.