Wouter Ahmed1, Edmund J. Gore2, dr. Coretta van Leer-Buter2, dr. Pieter J. Colin1, dr. Douglas J. Eleveld1, dr. Jeroen V. Koomen1,3
1Department of Anesthesiology, University Medical Center Groningen, University of Groningen, 2Department of Medical Microbiology and Infection Prevention, University Medical Center Groningen, University of Groningen, 3Department of Pharmacology, Toxicology and Pharmacokinetics, Medicines Evaluation Board
Introduction/objectives: In the development of a joint model (JM), computational constraints often force the analyst to focus on a single continuous/event outcome combination [1]. While this allows for increased computational efficiency, information loss is inevitable as a result of condensing the complexity of disease to a few variables. Therefore, the costly modelling of all observed outcomes may in some cases be preferred to enhance both the inference that can be drawn and predictive power. Mechanistic JMs, based on systems of ordinary differential equations (ODEs), are particularly well suited to describing such multivariate outcome data [2]. This is because their structure is informed by biological knowledge and offers the flexibility to incorporate latent (i.e. unobserved) disease-related variables. As a result, correlations between outcomes are inherently accounted for since the equations describe the (un)observed dynamics of the disease under study [2,3]. The present work aims to develop a mechanistic JM of multiple immune-related continuous and event outcomes by quantifying the latent immune function dynamics in patients that underwent lung transplantation (LTx). Methods: 88 LTx recipients were included in the study and followed up from the time of LTx until 31-12-2022, a second transplant, or death, whichever occurred first. Tacrolimus dosages and observed plasma concentrations were used to predict trough plasma concentrations throughout the follow-up period based on a published pharmacokinetic model [4]. Surrogate outcomes for immune and lung graft function considered in model development were torque-teno virus (TTV) load and the forced expiratory volume in 1 second (FEV1), respectively. Included events were graft rejection (GR), infections requiring therapeutic intervention (ITI) and a combined terminal event of second transplant/death (Tx/D). Latent immune dynamics were described empirically either by constant, or time-driven linear, second-order polynomial, inverse Bateman and bi-linear models. More mechanistic structures were also tested and based on bacterial growth and killing models driven by an effect of immunosuppression [5]. Continuous outcomes were described by ODEs with zero-order production and first-order elimination rates, the latter of which incorporates the “immune function” as its rate constant. Event outcomes were modelled with parametric (repeated) time-to-event models assuming constant hazard functions with an effect of immune function. Model parameters were estimated using the SAEM algorithm implemented in Monolix2024R1. Convergence was assessed based on similarity in parameter estimation over multiple chains and seeds. When convergence was deemed satisfactory, model selection involved evaluation of corrected bayesian information criteria (BICc), standard error estimates and goodness-of-fit (GoF) plots. Results: The bi-linear model for immune function dynamics outperformed all other evaluated empirical functions both in terms of BICc (?BICc of -306.6 compared to next best) and GoF. Convergence issues arose for every empirical model when trying to estimate all fixed and random-effect parameters. Fixing the fixed effect for the baseline immune function to 0.5 (i.e. 50%) resolved these issues in all cases. Overall, the bi-linear model showed good fit for FEV1 and Tx/D, but predictive performance was suboptimal for the other outcomes (TTV & GR & ITI). Preliminary results show that the mechanistic model with an effect of predicted tacrolimus plasma concentration (median absolute percentage error of 30.9%) on the input rate (Kin) fit the data better than the second best empirical function in terms of GoF and BICc (?BICc: -53.01). No effect could be estimated for the use of immunosuppression different from tacrolimus (incorporated as indicator variable on the Kin). Conclusions: The developed JM gives a reasonable fit to the data considering the simplicity of functions specified for the outcome variables. In part this is due to the informativeness of the FEV1 data which drives the parameter estimates to provide a good fit for this outcome. Possibly, the ‘information borrowing’ that a latent component connecting all outcomes facilitates also aided in achieving a reasonable fit at this early stage. Future efforts should explore more plausible functions for the outcome models as well as other parameterizations and simpler structures for the mechanistic latent models.
1. D. Rizopoulos. (2012). Joint models for longitudinal and time-to-event data: with applications in R. Chapman & Hall/CRC. 2. Guedj, J., Thiébaut, R., & Commenges, D. (2011). Joint modeling of the clinical progression and of the biomarkers’ dynamics using a mechanistic model. Biometrics, 67(1), 59–66. 3. Kerioui, M., Bertrand, J., Bruno, R., et al. (2022). Modelling the association between biomarkers and clinical outcome: An introduction to nonlinear joint models. British journal of clinical pharmacology, 88(4), 1452–1463. 4. Koomen, J. V., Knobbe, T. J., Zijp, T. R., 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. 5. Minichmayr, I. K., Aranzana-Climent, V., & Friberg, L. E. (2022). Pharmacokinetic/pharmacodynamic models for time courses of antibiotic effects. International journal of antimicrobial agents, 60(3), 106616.
Reference: PAGE 33 (2025) Abstr 11316 [www.page-meeting.org/?abstract=11316]
Poster: Drug/Disease Modelling - Other Topics