Gaussian process (GP) regression is wildly known to be a flexible and non-parametric Bayesian approach for modeling data being generated from some latent smooth trajectory and observed at discrete time points with measurement noise. In the linear setting, it can be seen as a fully probabilistic and non-parametric model compared to the traditional linear mixed-effects model approach replying on parametric mean specifications.
In this talk we will present a solution to the GP regression setting when the some of the observations are subject to value-based censoring. We derive exact closed-formed expressions of the conditional posterior distributions of the latent mean functions in both the single-curve case, and also for common mean and the subject-specific deviations under a hierarchical Bayesian model. This is a novel result, as previous papers have termed this task analytically intractable.
Our method can accommodate left, right, and interval censoring, and is directly applicable as an empirical Bayes method or integrated in a Markov-Chain Monte Carlo sampler for full posterior inference. Our method is validated through extensive simulations, where it substantially outperforms naive approaches that either exclude censored observations or treat them as fully observed values. We give an application to a real-world dataset of longitudinal HIV-1 RNA measurements, where the observations are subject to left censoring due to a detection limit.