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Delaying intubation for patients failing Bi-Level Positive Airway Pressure (BIPAP) may be associated with harm. The objective of this study was to develop a deep learning model capable of aiding clinical decision making by predicting Bi-Level Positive Airway Pressure (BIPAP) failure. This was a retrospective cohort study in a tertiary pediatric intensive care unit (PICU) between 2010 and 2020. Three machine learning models were developed to predict BIPAP failure: two logistic regression models and one deep learning model, a recurrent neural network with a Long Short-Term Memory (LSTM-RNN) architecture. Model performance was evaluated in a holdout test set. 175 (27.7%) of 630 total BIPAP sessions were BIPAP failures. Patients in the BIPAP failure group were on BIPAP for a median of 32.8 (9.2–91.3) hours prior to intubation. Late BIPAP failure (intubation after using BIPAP > 24 h) patients had fewer 28-day Ventilator Free Days (13.40 [0.68–20.96]), longer ICU length of stay and more post-extubation BIPAP days compared to those who were intubated ≤ 24 h from BIPAP initiation. An AUROC above 0.5 indicates that a model has extracted new information, potentially valuable to the clinical team, about BIPAP failure. Within 6 h of BIPAP initiation, the LSTM-RNN model predicted which patients were likely to fail BIPAP with an AUROC of 0.81 (0.80, 0.82), superior to all other models. Within 6 h of BIPAP initiation, the LSTM-RNN model would identify nearly 80% of BIPAP failures with a 50% false alarm rate, equal to an NNA of 2. In conclusion, a deep learning method using readily available data from the electronic health record can identify which patients on BIPAP are likely to fail with good discrimination, oftentimes days before they are intubated in usual practice.

Deep learning has demonstrated success in many applications; however, their use in healthcare has been limited due to the lack of transparency into how they generate predictions. Algorithms such as Recurrent Neural Networks (RNNs) when applied to Electronic Medical Records (EMR) introduce additional barriers to transparency because of the sequential processing of the RNN and the multi-modal nature of EMR data. This work seeks to improve transparency by: 1) introducing Learned Binary Masks (LBM) as a method for identifying which EMR variables contributed to an RNN model's risk of mortality (ROM) predictions for critically ill children; and 2) applying KernelSHAP for the same purpose. Given an individual patient, LBM and KernelSHAP both generate an attribution matrix that shows the contribution of each input feature to the RNN's sequence of predictions for that patient. Attribution matrices can be aggregated in many ways to facilitate different levels of analysis of the RNN model and its predictions. Presented are three methods of aggregations and analyses: 1) over volatile time periods within individual patient predictions, 2) over populations of ICU patients sharing specific diagnoses, and 3) across the general population of critically ill children.

We have two main objectives in this dissertation: (i) to analyze the splitting mechanism behind entropy stable finite difference approximations of conservative systems; and (ii) to investigate global error estimation for nonlinear, hyperbolic partial differential equations. For symmetrizable systems of conservation laws, Olsson used entropy functions to obtain rigorous stability estimates for a family of finite difference schemes that approximate the original equations [\"Summation by parts, projections and stability, III,\" RIACS Technical Report 95-06]. A key element behind the estimates and the resulting schemes is a splitting process which uses an entropy function to recast the flux derivative into a skew-symmetric form. Gerritsen applied the splitting concept to the compressible Euler equations [\"Designing an Efficient Solution Strategy for Fluid Flows,\" Ph.D. Dissertation, Stanford, 1996]. We studied the splitting process through a parameter which defines both the schemes and the family of entropy functions that was used by Gerritsen and Olsson for the Euler equations. Our analysis of this parameter enabled us to compare the schemes' behaviors relative to each other. Our results demonstrate the existence of an optimal value which minimizes errors. Both our theoretical analysis and computational examples show advantages of using the split schemes over their un-split counterparts. These benefits include greater accuracy and efficiency for the solution algorithm, and longer periods of integration. We also illustrate the split schemes' ability to compute the entropy solution when discontinuities (of different types) exist. Our analysis of both the stability estimates and entropy errors provides insights into these behaviors. We also derived an error estimate for the entropy function of symmetrizable hyperbolic systems. Like classical estimates for the computational error, the estimate for the entropy error reflects an accumulation of local truncation errors. We show that the computational and entropy errors converge in a similar fashion. Therefore, the entropy error estimate can be used to monitor and control global accuracy. Since the entropy error estimate utilizes variables already computed by the discretization kernel, it does not add any substantial cost to the solution algorithm. We also demonstrate the feasibility of using the entropy error estimate as a monitor function for local grid adaption purposes.

High Flow Nasal Cannula (HFNC) provides non-invasive respiratory support for critically ill children who may tolerate it more readily than other Non-Invasive (NIV) techniques. Timely prediction of HFNC failure can provide an indication for increasing respiratory support. This work developed and compared machine learning models to predict HFNC failure. A retrospective study was conducted using EMR of patients admitted to a tertiary pediatric ICU from January 2010 to February 2020. A Long Short-Term Memory (LSTM) model was trained to generate a continuous prediction of HFNC failure. Performance was assessed using the area under the receiver operating curve (AUROC) at various times following HFNC initiation. The sensitivity, specificity, positive and negative predictive values (PPV, NPV) of predictions at two hours after HFNC initiation were also evaluated. These metrics were also computed in a cohort with primarily respiratory diagnoses. 834 HFNC trials [455 training, 173 validation, 206 test] met the inclusion criteria, of which 175 [103, 30, 42] (21.0%) escalated to NIV or intubation. The LSTM models trained with transfer learning generally performed better than the LR models, with the best LSTM model achieving an AUROC of 0.78, vs 0.66 for the LR, two hours after initiation. Machine learning models trained using EMR data were able to identify children at risk for failing HFNC within 24 hours of initiation. LSTM models that incorporated transfer learning, input data perseveration and ensembling showed improved performance than the LR and standard LSTM models.