Federico L. Perlino | Searcharxiv

arXiv2026

Quantifying Uncertainty in Future Event Counts at Interim Analyses of Time-to-Event Trials, with an Application to Pediatric Oncology

Time-to-event endpoints are central to evaluating treatment efficacy across disease areas. In clinical trials with time-to-event endpoints, the information available for interim and final analyses is often determined by the number of observed events rather than by the number of enrolled patients. Interim monitoring therefore requires assessing how many additional events are expected to accrue by scheduled future analysis dates. Quantifying uncertainty around these counts is essential for assessing whether planned information levels are likely to be reached, anticipating delays or event overrunning, and supporting operational decisions while the trial is ongoing. This is especially relevant where event accrual is low as in pediatric hemato-oncology trials. Although methods for predicting time to endpoint maturation are well established, interval prediction for event counts at fixed calendar times remains less developed. We propose a patient-level framework for constructing such intervals at interim analyses of time-to-event trials. Conditionally on the interim data, the future count follows a Poisson--binomial law with patient-specific event probabilities; we estimate this law using a conditional parametric bootstrap. Under standard regularity conditions, the bootstrap is consistent and yields asymptotically calibrated prediction intervals. The framework accommodates staggered entry, patient-level covariates, administrative censoring, loss to follow-up, and possible dependence between entry dates and loss to follow-up, before conditioning on the realised interim data. We study its operating characteristics in simulation studies and illustrate the method using a real-world phase III trial in childhood acute lymphoblastic leukaemia.

stat.ME↗

arXiv2026

Deep Gaussian Processes on Directed Acyclic Graphs

Many real-world processes can be represented as compositions of functions along a directed acyclic graph (DAG). In causal modelling, these correspond to the underlying mechanisms; in engineering, to multiple fidelity levels; and in gene-regulatory networks, to transcription factors. These functions are partially observed across the DAG, with noisy and heterogeneously sampled measurements, posing significant challenges for reconstruction, uncertainty propagation, and inference. To tackle these challenges, we place priors over functions and naturally arrive at Deep Gaussian Processes over DAGs. We theoretically study their prior-collapse behaviour, and the effect of graph topology and intermediate observations on the preservation of information. We obtain almost-sure lower bounds on the asymptotic frequency of depths at which the distinction between inputs is preserved, identify broad kernel classes for which these hold, and prove an observation by \cite{dunlop2018} on the role of input connections. We offer a structured variational approximation that retains graph dependencies, preserves compositional uncertainty, and captures the explaining-away behaviour of colliders. Finally, we empirically validate our theoretical results and our methodology, and model a latent-collider DAG, a protein signalling network, and a multi-fidelity heavy-ion collision emulation task, attaining state-of-the-art performance while recovering low-fidelity contributions and yielding interpretability of the simulator hierarchy.

stat.ML↗