  Learning temporal patterns from multivariate longitudinal data is challenging
especially in cases when data is sporadic, as often seen in, e.g., healthcare
applications where the data can suffer from irregularity and asynchronicity as
the time between consecutive data points can vary across features and samples,
hindering the application of existing deep learning models that are constructed
for complete, evenly spaced data with fixed sequence lengths. In this paper, a
novel deep learning-based model is developed for modeling multiple temporal
features in sporadic data using an integrated deep learning architecture based
on a recurrent neural network (RNN) unit and a continuous-time autoregressive
(CAR) model. The proposed model, called CARRNN, uses a generalized
discrete-time autoregressive model that is trainable end-to-end using neural
networks modulated by time lags to describe the changes caused by the
irregularity and asynchronicity. It is applied to multivariate time-series
regression tasks using data provided for Alzheimer's disease progression
modeling and intensive care unit (ICU) mortality rate prediction, where the
proposed model based on a gated recurrent unit (GRU) achieves the lowest
prediction errors among the proposed RNN-based models and state-of-the-art
methods using GRUs and long short-term memory (LSTM) networks in their
architecture.
