Inference for sparsely sampled Gauss-Markov processes under outcome-dependent dropout
Abstract
We consider sparsely observed functional data generated by a latent Gauss-Markov process modeled through a linear stochastic differential equation (SDE). Motivated by an application to tumor growth data, we allow for outcome-dependent dropout, where sampling terminates once the most recent observation exceeds a prescribed threshold. Such observation schemes arise naturally in longitudinal studies and violate the fundamental missing completely at random assumption commonly imposed in the analysis of partially observed functional data. We develop a likelihood-based estimation framework that, in contrast to existing moment-based methods, avoids the bias induced by outcome-dependent dropout. We establish convergence rates for the proposed estimators and show that they are mini-max optimal up to logarithmic factors, with the diffusion coefficient admitting a faster rate than the drift coefficients under a random initial condition for the SDE. An application to tumor growth data further demonstrates the advantages of a fully probabilistic functional data model for tasks beyond second-order inference, including prediction bands, first-passage times, and tumor-age estimation.
Related
- Inference for Generalized Almost Cyclostationary Processes with Unknown Lag-Dependent Cycle Frequencies
- Collaborative representations for targeted causal inference under outcome selection
- Studentized inference in randomized experiments when a few units dominate the outcome variation
- Semiparametric inference for a Target Outcome Leveraging Heterogeneous External Summaries of Auxiliary Outcomes
- Thermodynamic Cyclic Processes with Markov Samplers in Bayesian Inference
BibTeX
@misc{aue2026inference,
title = {{Inference for sparsely sampled Gauss-Markov processes under outcome-dependent dropout}},
author = {Alexander Aue and Siegfried Hörmann and Maximilian Ofner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23617},
eprint = {2609.23617},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23617},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inference for sparsely sampled Gauss-Markov processes under outcome-dependent dropout
AU - Alexander Aue
AU - Siegfried Hörmann
AU - Maximilian Ofner
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23617
UR - https://arxiv.org/abs/2609.23617
AB - We consider sparsely observed functional data generated by a latent Gauss-Markov process modeled through a linear stochastic differential equation (SDE). Motivated by an application to tumor growth data, we allow for outcome-dependent dropout, where sampling terminates once the most recent observation exceeds a prescribed threshold. Such observation schemes arise naturally in longitudinal studies and violate the fundamental missing completely at random assumption commonly imposed in the analysis of partially observed functional data. We develop a likelihood-based estimation framework that, in contrast to existing moment-based methods, avoids the bias induced by outcome-dependent dropout. We establish convergence rates for the proposed estimators and show that they are mini-max optimal up to logarithmic factors, with the diffusion coefficient admitting a faster rate than the drift coefficients under a random initial condition for the SDE. An application to tumor growth data further demonstrates the advantages of a fully probabilistic functional data model for tasks beyond second-order inference, including prediction bands, first-passage times, and tumor-age estimation.
ER -