Mats Jirstrand

Variational autoencoders (VAEs) combined with neural ordinary differential equations provide a flexible framework for exploring neural latent‐variable models in population pharmacokinetics. In this work, we investigate an empirical Bayes VAE formulation that integrates encoder–decoder architectures with covariate‐dependent population priors, enabling correlated latent representations and probabilistic inference. We evaluate the proposed framework using controlled simulation studies and a small clinical benchmark dataset. The simulation experiments assess the ability to recover known population structures and covariate effects, while the clinical study evaluates subject‐specific prediction and model diagnostics. In simulation studies with correlated individual parameters, the empirical Bayes VAE consistently captured population‐level variability, whereas a fixed‐prior VAE baseline exhibited systematic biases. In our experiments, extrapolation beyond the training dosing schedules showed more stable predictive behavior when using the proposed input–response normalization, relative to models trained without normalization, within a limited range. Diagnostic analyses indicated clear relationships between inferred latent variables and true parameters, and estimated observation noise was consistent with simulated values. In the clinical case study, cross‐validation experiments suggested predictive performance comparable to previously reported neural ODE–based approaches. Overall, the results illustrate the feasibility of combining empirical Bayes inference with neural ODE–based decoders for population modeling. The proposed framework should be viewed as a methodological proof‐of‐concept, highlighting both the potential and the current limitations of variational neural approaches in pharmacometric applications.

Clinical trials in asthma and chronic obstructive pulmonary disease often use exacerbation risk as the primary endpoint. However, exacerbations occur with low frequency, leading to long and costly clinical trials. Home‐measured spirometry, which is becoming more common, provides an alternative and has previously been used to shorten the necessary trial duration. In this work, we develop a mixed‐effects hidden Markov model (MEHMM) for analyzing home‐measured peak expiratory flow (PEF), combining an observation model with a latent two‐state disease process representing sustained periods of high and low PEF, respectively. An inference framework is implemented to estimate fixed and random effects together with measures of uncertainty. Data from a phase 2b dose‐finding study of velsecorat in asthma are used to investigate dose–response relationships, complemented by an extensive simulation study. The results demonstrate reliable estimation of parameters and identify statistically significant treatment effects on multiple model components. These findings support the use of latent disease‐state models for extracting meaningful information from home‐measured spirometry.

Diffusion models can be parameterized in terms of either score or energy function. The energy parameterization is attractive as it enables sampling procedures such as Markov Chain Monte Carlo (MCMC) that incorporates a Metropolis–Hastings (MH) correction step based on energy differences between proposed samples. Such corrections can significantly improve sampling quality, particularly in the context of model composition, where pre-trained models are combined to generate samples from novel distributions. Score-based diffusion models, on the other hand, are more widely adopted and come with a rich ecosystem of pre-trained models. However, they do not, in general, define an underlying energy function, making MH-based sampling inapplicable. In this work, we address this limitation by retaining score parameterization and introducing a novel MH-like acceptance rule based on line integration of the score function. This allows the reuse of existing diffusion models while still combining the reverse process with various MCMC techniques, viewed as an instance of annealed MCMC. Through experiments on synthetic and real-world data, we show that our MH-like samplers yield relative improvements of similar magnitude to those observed with energy-based models, without requiring explicit energy parameterization.

Background: In the field of precision nutrition, predicting high-dimensional metabolic response to diet and identifying groups of differential responders are two highly desirable steps towards developing tailored dietary strategies. However, proper data analysis tools are currently lacking, especially for complex settings such as crossover studies. Current methods of analysis often rely on matrix or tensor decompositions, which are well suited for identifying differential responders but lacking in predictive power, or on dynamical systems modelling, which may be used for prediction but typically requires detailed mechanistic knowledge of the system under study. Objectives: To remedy these shortcomings, we aimed to explore dynamic mode decomposition (DMD), which is a recent, data driven method for deriving low-rank linear dynamical systems from high dimensional data. Methods: To allow integration of complex data from several dietary inputs to the metabolic system, we combine parametric DMD (pDMD) with DMD with control (DMDc). The resulting method allows (i) to predict the postprandial metabolic response of a new diet given only the metabolic baseline and dietary input, and (ii) to identify inter-individual differences in metabolic regulation, useful in determining metabotypes, i.e., metabolic phenotypes in dynamic data. To our knowledge, this is the first time DMD has been applied to metabolomics data. Results: pDMDc enabled a data-driven construction of low-dimensional dynamical models, able to capture the underlying dynamics of the metabolome after three dietary challenges. We demonstrate the utility and accuracy of the model in a crossover study setting on both measured and simulated data. Using simulated data, metabolic response to a new diet was accurately predicted having trained on four diets, with an average cosine similarity score of 0.6 (SD = 0.27). In measured data, we identified previously published metabolic groups with 100% overlap. Discussion: Accurate predictions via pDMDc require data from several dietary exposures with large variation, which can be costly to collect to confirm the efficacy of the method. A possible remedy is to share data among individuals using the mixed-effects framework. Employing pDMDc paves the way towards using control theory to approach PN by estimating the optimal input given a target metabolite trajectory.

The global prevalence of type 2 diabetes mellitus (T2DM) has surged in recent decades, and the identification of differential glycemic responders can aid tailored treatment for the prevention of prediabetes and T2DM. A mixed meal tolerance test (MMTT) based on regular foods offers the potential to uncover differential responders in dynamical postprandial events. We aimed to fit a simple mathematical model on dynamic postprandial glucose data from repeated MMTTs among participants with elevated T2DM risk to identify response clusters and investigate their association with T2DM risk factors and gut microbiota. Data were used from a 12-week multi-center dietary intervention trial involving high-risk T2DM adults, comparing high- versus low-glycemic index foods within a Mediterranean diet context (MEDGICarb). Model-based analysis of MMTTs from 155 participants (81 females and 74 males) revealed two distinct plasma glucose response clusters that were associated with baseline gut microbiota. Cluster A, inversely associated with HbA1c and waist circumference and directly with insulin sensitivity, exhibited a contrasting profile to cluster B. Findings imply that a standardized breakfast MMTT using regular foods could effectively distinguish non-diabetic individuals at varying risk levels for T2DM using a simple mechanistic model.