Ali Issa 1, Tarjinder Sahota 2, Núria Buil-Bruna 2, Joseph Standing 1, Frank Kloprogge 1
1 University College London (London, United Kingdom), 2 GSK (Stevenage, United Kingdom)
Objectives:
Machine-learning (ML) models are increasingly proposed as rapid, automated alternatives to nonlinear mixed-effects (NLME) pharmacokinetic (PK) modelling. However, many ML PK studies emphasise individual fit or point-prediction error and do not report population predictive checks required for prospective trial simulation (e.g., VPC/NPDE), or allow PK-implausible dynamics (negative concentrations, oscillations, non-monotone decay) [1,2]. The objective of this work was to develop an automated population PK framework for IV bolus data that preserves pharmacometric realism by construction and supports prospective simulation without per-compound structural model selection. Specifically, we aimed to develop a model that (i) supports unconditional (marginal) population simulation for trial simulation diagnostics, (ii) enables reliable transfer across dosing regimens, and (iii) enforces positivity, dose linearity, and monotone post-bolus decay. We present ConstrainNODE-PK, a constrained neural impulse-response model that integrates inter-individual variability, standard diagnostics (VPC and NPDE), and amortised individualisation within a single reusable model class.
Methods:
IV-bolus concentrations were formulated as an impulse-response (convolution) popPK model. For subject i with random effects z_i (η_i), g(t|z_i) denotes the concentration–time profile after a unit IV bolus. For a dosing history with bolus doses D_k at times t_k, the predicted concentration is C(t|z)=sum_k D_k * g(t-t_k|z), so enforcing constraints on g directly enforces constraints on concentrations under any regimen. This is the same superposition principle used by linear compartment models, where g(t) is the model’s multi exponential unit bolus response and different regimens were handled by changing the dosing history rather than re-specifying the structural model. Instead of choosing a per-compound 1/2/3-compartment ODE, we used a single reusable kernel class with fixed order J across compounds. The base kernel was a constrained exponential mixture:
g_base(t|z) = (1/V) * sum_{j=1..J} w_j * exp(-lambda_j*t),
with V>0, w_j≥0, ∑w_j=1 and λ_j>0. With fixed order J, the constrained mixture can represent (and closely approximate) standard multi-exponential impulse responses typical of 1–3-compartment mammillary PK; unused components can shrink via w_j→0, while the constraints guarantee positivity, stability and monotone post-bolus decay under any regimen. Flexibility was added by multiplying by a monotone neural modulation term m(t|z)=exp(-s(t|z)) with s(t|z) constrained to be nondecreasing (implemented by parameterising s as a cumulative integral/sum of positive functions so that s′(t) ≥ 0 by construction); this preserved positivity and monotone decay while improving fit to multi-phase profiles with fixed J, and it avoided oscillations and unstable long-lag behaviour.
Between-subject variability was modelled as z~N(m(x),Ω), where Ω is the NLME-style IIV covariance and m(x)=m0+βx allows the prior mean to shift with a dose-level covariate x (standardised log(1+total daily dose)) while keeping Ω regimen-invariant, supporting dose proportionality and transfer to new schedules; residual unexplained variability was proportional (lognormal). Individual-conditional predictions (IPRED) used an amortised encoder to infer z from an individual’s DV (EBE-like), whereas unconditional population prediction (POP) used prior-predictive (‘trial simulation’) draws z~N(m(x),Ω) plus residual error (no DV conditioning) for VPC/NPDE.
We evaluated six truth-known simulated IV-bolus drugs (120 subjects/drug; 1–3-compartment disposition; single/multiple dosing; proportional residual variability) to enable ground-truth assessment of POP calibration and regimen transfer (QD→TID), since the data-generating truth is known. We also evaluated two clinical PK datasets (indomethacin, diazepam) to demonstrate applicability on real data. Data were split at the subject level (all records per subject kept together): 60% of subjects were used to estimate model parameters (training), 20% formed a validation set used only to guide early stopping and select modelling/tuning settings (to limit overfitting), and the remaining 20% were held out as unseen test subjects and used only once for the final reported predictive metrics and VPC/NPDE. We assessed (a) unseen-subject prediction under the same regimen, (b) true regimen transfer without retraining (train QD, test TID; same total daily dose), (c) time extrapolation beyond the sampling window, and (d) dose proportionality. IPRED accuracy was summarised by logRMSE and exposure errors (MdAPE for AUC0-t and Cmax). POP calibration used PI95 coverage and NPDE mean/SD, supported by GOF/VPC/NPDE plots. For simulated datasets, the NLME comparator was nlmixr2 (FOCEI) fitted with the true data-generating compartmental model [3]. We also compared against an unconstrained neural ODE baseline [4,5].
Results:
Across eight datasets (six simulated + indomethacin + diazepam), ConstrainNODE-PK achieved logRMSE(IPRED)=0.15-0.21 with near-nominal POP calibration: PI95=93.5-96.5%, NPDE mean ~0 and NPDE SD ~1. Predictions remained positive with monotone post-bolus decay, and time-extrapolation checks showed no oscillatory artefacts beyond the observed sampling grid.
On a representative simulated 2-compartment multiple-dose QD dataset (unseen test: 24 subjects), ConstrainNODE-PK achieved logRMSE(IPRED)=0.193, MdAPE(AUC0-t)=2.11% and MdAPE(Cmax)=21.34%, with POP calibration PI95=96.5%, NPDE mean=+0.007 and NPDE SD=0.949. On the same dataset, nlmixr2 achieved logRMSE(IPRED)=0.149, MdAPE(AUC0-t)=1.14% and MdAPE(Cmax)=16.52%, with PI95=94.25%, NPDE mean=-0.012 and NPDE SD=1.084.
ConstrainNODE-PK enabled genuine regimen transfer where dosing times/frequency change (QD->TID). When trained on a simulated 2-compartment QD regimen and evaluated on an unseen TID regimen, IPRED accuracy was comparable to nlmixr2 (logRMSE 0.169 vs 0.166) with improved exposure metrics (MdAPE AUC0-t 1.95% vs 4.53%; MdAPE Cmax 16.34% vs 20.22%). Under POP on the TID regimen (no DV conditioning), ConstrainNODE-PK remained well calibrated (NPDE mean +0.009; NPDE SD 0.975; PI95 95.6%), comparable to nlmixr2 (NPDE mean +0.014; NPDE SD 1.061; PI95 94.9%). The unconstrained neural ODE baseline showed acceptable in-window fit (logRMSE=0.240) but failed under POP on the unseen TID regimen (PI95 49.8%) and exhibited terminal-slope flattening on time extrapolation.
Conclusion:
ConstrainNODE-PK combines pharmacometric structure with constrained neural flexibility to provide an automated IV-bolus popPK framework that preserves positivity, dose linearity and monotone decay while avoiding per-compound compartment selection. Crucially, the framework targets reliable marginal (prior predictive) simulation: by separating IPRED from unconditional POP simulations, it enables standard GOF/VPC/NPDE and propagates IIV/RUV uncertainty under new regimens for prospective trial simulation and regimen comparison. In a six-drug truth-known simulation benchmark and two clinical datasets, ConstrainNODE-PK approached the performance of correctly specified NLME models and demonstrated unconditional population-level regimen transfer (QD->TID) in simulation without retraining. By using a single reusable model class with amortised individualisation and built-in constraints, ConstrainNODE-PK reduces manual model-building decisions and enables rapid, reproducible trial simulation–based prospective regimen evaluation when throughput limits or structural uncertainty make conventional NLME workflows impractical.
References:
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Reference: PAGE 34 (2026) Abstr 12112 [www.page-meeting.org/?abstract=12112]
Poster: Oral: Methodology - New Tools