Early prediction of engraftment outcomes in hematopoietic cell transplantation using neural ordinary differential equations

Background: Engraftment failure after allogeneic hematopoietic cell transplantation (HCT) is a complex event that traditional models struggle to predict due to dynamic interactions among microbiome composition, immune recovery, and clinical risk factors, especially with missing or irregular data. Neural Ordinary Differential Equations (Neural ODEs) address these limitations by treating patient trajectories as continuous-time evolutions, enabling effective learning from such sparse and irregularly sampled measurements where traditional discrete-time networks often fail. Methods: A synthetic cohort of 1,000 HCT patients over 42 days, modeling dynamic features (e.g. gut bacterial abundance, immune cell numbers) and static risk factors (e.g. age, HHV-6 status, conditioning intensity, initial microbiome diversity) was generated. Microbiome dynamics were governed by Lotka-Volterra equations, capturing predator-prey interactions between beneficial and pathogenic bacteria populations. Literature-derived parameters governed immune trajectories, ensuring biological plausibility. For prediction, a neural ODE framework that learns continuous-time dynamics from discrete, irregularly sampled data, enabling smooth visualization and extrapolation was utilized. The model was trained on only the first 3-7 days of data with class-weighted loss. Feature importance was assessed via permutation analysis. Results: Validation of the synthetic cohort (N=1,000) confirmed clinically realistic recovery trajectories; for instance, patients receiving myeloablative conditioning engrafted later (mean 20.8 days) than those receiving reduced-intensity conditioning (14.8 days). On this validated cohort, the neural ODE model achieved strong early prediction of Day 42 outcomes using only the first 3 days of data (AUC=0.96; recall=93.8%; precision=88.2%). Permutation feature importance analysis revealed that while early neutrophil dynamics were critical, the dynamics of the abundance of specific beneficial commensals and initial microbiome diversity were dominant predictive signals, outweighing static clinical factors. Conclusions: Neural ODEs provide a mechanistically grounded framework for learning from sparse, irregularly sampled longitudinal data while maintaining biological interpretability. Beyond HCT, this approach shows promise for dynamic prediction in cancer research where traditional recurrent architectures struggle with irregular time series. The continuous-time parameterization enables smooth trajectory interpolation offering advantages over standard discrete-time neural network models.