Fast Kalman Filtering and Forward–Backward Smoothing via a Low-Rank Perturbative Approach

Fitting joint models of longitudinal observations and time to event by sequential Bayesian updating

Joint modelling of longitudinal measurements and time to event, with longitudinal and event submodels coupled by latent state variables, has wide application in biostatistics. Standard methods for fitting these models require numerical integration to marginalize over the trajectories of the latent states, which is computationally prohibitive for high-dimensional data and for the large data sets that are generated from electronic health records. This paper describes an alternative model-fitting approach based on sequential Bayesian updating, which allows the likelihood to be factorized as the product of the likelihoods of a state-space model and a Poisson regression model. Updates for linear Gaussian state-space models can be efficiently generated with a Kalman filter and the approach can be implemented with existing software. An application to a publicly available data set is demonstrated.

Adaptive Sedation Monitoring From EEG in ICU Patients With Online Learning

Sedative medications are routinely administered to provide comfort and facilitate clinical care in critically ill ICU patients. Prior work shows that brain monitoring using electroencephalography (EEG) to track sedation levels may help medical personnel to optimize drug dosing and avoid the adverse effects of oversedation and undersedation. However, the performance of sedation monitoring methods proposed to date deal poorly with individual variability across patients, leading to inconsistent performance. To address this challenge we develop an online learning approach based on Adaptive Regularization of Weight Vectors (AROW). Our approach adaptively updates a sedation level prediction algorithm under a continuously evolving data distribution. The prediction model is gradually calibrated for individual patients in response to EEG observations and routine clinical assessments over time. The evaluations are performed on a population of 172 sedated ICU patients whose sedation levels were assessed using the Richmond Agitation-Sedation Scale (scores between -5 = comatose and 0 = awake). The proposed adaptive model achieves better performance than the same model without adaptation (average accuracies with tolerance of one level difference: 68.76% vs. 61.10%). Moreover, our approach is shown to be robust to sudden changes caused by label noise. Medication administrations have different effects on model performance. We find that the model performs best in patients receiving only propofol, compared to patients receiving no sedation or multiple simultaneous sedative medications.