Inference for sparsely sampled Gauss-Markov processes under outcome-dependent dropout

2026-09-20

AI Summary

研究通过线性随机微分方程处理稀疏观测的高斯-马尔可夫过程，开发了基于似然估计的方法来解决结果依赖性失访问题。

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.

Problem

• sparsely observed functional data
• outcome-dependent dropout
• Gauss-Markov process
• longitudinal studies
• likelihood-based estimation

Innovation

• likelihood-based estimation
• outcome-dependent dropout
• Gauss-Markov process
• convergence rates