Wouter Ahmed 1, Edmund J Gore 2, Coretta van Leer-Buter 2, Michel M R F Struys 1,3, Pieter J Colin 1, Douglas J Eleveld 1, Jeroen V Koomen 1,4
1 Department of Anaesthesiology, University Medical Center Groningen, University of Groningen (Groningen, The Netherlands), 2 Department of Medical Microbiology and Infection Prevention, University Medical Center Groningen, University of Groningen (Groningen, The Netherlands), 3 Department of Basic and Applied Medical Sciences, Ghent University (Ghent, Belgium), 4 Department of Pharmacology, Toxicology and Pharmacokinetics, Medicines Evaluation Board (Utrecht, The Netherlands)
Background: Personalized tacrolimus therapy after transplantation mainly revolves around targeting trough concentrations (C0) in whole-blood to a range that minimizes the risk of immune-related complications and adverse events. However, evidence for an optimal target C0 level is weak, with conflicting results being reported in literature [1]. In particular, C0 being a poor estimate of exposure, low informativeness of clinically relevant outcomes and suboptimal statistical methods may have contributed to difficulty with establishing an exposure-response relationship [2].
In this regard, joint modelling, which allows parameter estimation based on a joint likelihood function of the predictor and event outcome, seems promising. Indeed, it was shown that tacrolimus C0 is associated with lower rejection incidence in a joint model developed in kidney transplant recipients [2]. The current study continues the development of a previously presented joint model describing latent immune dynamics and multiple immune-related outcomes over a 6-year period after lung transplantation (LuTx) [3].
Methods: Data came from 88 patients who underwent LuTx at the University Medical Center Groningen between 2015 and 2017. Modelled outcomes were torque teno virus (TTV) load, the forced expiratory volume as % of predicted (FEV%), the (possibly repeated) occurrence of rejection/infection and a combined terminal event of a new transplant/death (Tx/D). Tacrolimus plasma C0 was predicted using a population pharmacokinetic model and used in the model as a time-varying covariate [4].
The base model was structured as follows: immune function was incorporated as a latent variable, described by a baseline parameter (fixed effect set to 1 for reasons of identifiability) proportional to an Imax-function (with Imax fixed to 1) that used tacrolimus C0 as input. For TTV and FEV%, indirect response models were specified and immunity was assumed to modulate their output rate constants (stimulatory for TTV and a bidirectional effect for FEV%). For the event outcomes, baseline hazards were kept constant and proportional hazards with immune(t) as predictor were assumed. The imposed direction of the immune effect was stimulatory for rejection, inhibitory for infection and bidirectional for death.
As a first step, model development focused on optimization of the continuous and latent variable model structure, keeping the hazard functions as is. Once fit to the continuous data was deemed acceptable, modifications to the hazard functions were considered. Model evaluation was based on classical goodness-of-fit plots, simulation-based metrics and the Bayesian information criterion (BIC). All models were fit using the SAEM algorithm as implemented in Monolix 2024R1.
Results: Starting from the base model, the assumption of steady state was relaxed for FEV% and an initial value estimated (dBIC:-1505.86). Thereafter, an estimated power was added to provide more flexibility in the shape of the bidirectional effect of immune on FEV% (dBIC:-44.47). Lastly, a linear time-dependency was incorporated that allowed immune function to increase past its initial value (dBIC:-344.93). The developed model showed no misspecification with respect to FEV%-fit and a slight tendency to overpredict peak TTV loads.
Based on the continuous outcome-optimized model, misfit was most evident for rejection. Therefore, alternative rejection baseline hazards were evaluated and fit improved with both Gompertz (dBIC:-54.44) and Weibull (dBIC:-84.43). An effect of immunity on the hazard could be estimated when log(immune) was delayed through an effect compartment. This link function gave reasonable fit when considered with a Gompertz baseline hazard (dBIC:-93.33), though convergence was unstable. No alterations were thus far made to the infection and Tx/D hazards, with fit for the latter being acceptable. For infection but not Tx/D, an effect of immunity was established.
Discussion: A joint model was developed that accurately describes TTV, FEV% and Tx/D dynamics after LuTx. Some indication was found that TTV production might stagnate at higher loads, though the mechanism (pharmacological or cell-limited) remains unclear with tested structures showing either misfit or unstable convergence. The time-dependency built into the model potentially extrapolates poorly to populations different from the one used to develop the model. Primarily because it is likely dependent on the specific immunosuppressive protocol used. Therefore, external validation and further development considering other immunosuppressive agents should precede model use in a clinical context. As a next step, rejection hazard development will continue by first considering alternative methods to delay immunity. Once the rejection submodel is finalized, hazard functions for infection and Tx/D will be optimized.
References:
1. Brunet, M., et al. (2019). Therapeutic Drug Monitoring of Tacrolimus-Personalized Therapy: Second Consensus Report. Therapeutic drug monitoring, 41(3), 261–307. DOI:10.1097/FTD.0000000000000640
2. Schagen, M. R., et al. (2025). Tacrolimus Exposure is Associated with Acute Rejection in the Early Phase After Kidney Transplantation: A Joint Modeling Approach. Therapeutic drug monitoring, 47(6), e82–e89. DOI:10.1097/FTD.0000000000001359
3. Ahmed, W., et al. (2025). Development of a mechanistic joint model describing multivariate continuous and event outcomes linked through a latent variable. [Poster abstract]. Population Approach Group Europe meeting 33. Abstr 11316. URL: www.page-meeting.org/?abstract=11316
4. Koomen, J. V., et al. (2023). A Joint Pharmacokinetic Model for the Simultaneous Description of Plasma and Whole Blood Tacrolimus Concentrations in Kidney and Lung Transplant Recipients. Clinical pharmacokinetics, 62(8), 1117–1128. DOI:10.1007/s40262-023-01259-x
Reference: PAGE 34 (2026) Abstr 12134 [www.page-meeting.org/?abstract=12134]
Poster: Drug/Disease Modelling - Other Topics