Fig. 1
Description of the problem setup and model architecture. (A) Problem setup. Based on the static variables of a specific patient (e.g. age, sex) and the history of clinical follow-up prior to extubation (e.g. SpO2, MAP), our model predicts 4 probabilities: the probability that the time-to-death (TTD) is shorter than 30 minutes, between 30 and 60 minutes, between 60 and 120 minutes, and longer than 120 minutes. The sum of these probabilities equals to 1 by design. BMI stands for body mass index, SpO2 for oxygen saturation, MAP for mean arterial blood pressure, Hgb for hemoglobin, and NE for norepinephrine. Note that we consider 5 static variables and 25 longitudinal variables, and only some are shown for illustration purposes. (B) Architecture of our ODE-RNN. The set of variables fed to the model consists of a concatenation of the longitudinal variables available at that observation time and a mask specifying which longitudinal variables are observed. Each clinical observation is sequentially processed by a gated recurrent unit (GRU) that incorporates the observation into the hidden state representation from the previous samples in the time series. Between observations, an ordinary differential equation (ODE) models the evolution of the patient’s hidden state continuously over time, which enables processing of variable temporal intervals between subsequent observations. The hidden state obtained after the whole time series is then complemented with the static variables to form the latent phenotype, a vector representation that summarizes the whole available information about the patient. The end classification is performed by using a multi-layer perceptron classifier (MLP) that predicts the TTD probabilities from the latent phenotype.
