Survival models and longitudinal medical events for hospital readmission forecasting

Figures

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  Fig. 1. Censorship illustration with three example patients, each starting with their respective index hospitalization. Patient 1 is uncensored, as we understand their time-until-event (green-shaded area). Patients 2 and 3 are both censored, as Patient 2 moved away before experiencing an event, and Patient 3 remained event-free until the end of the study. Their respective time-until-censorships are shown using the red-shaded boxes. Some patients may never experience an adverse outcome

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  Fig. 2. Survival prediction and individual survival distributions. a A survival dataset is used to train a survival model, which can in turn provide insights into the future of a new patient. t represents the time-to-event, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \delta $$\end{document}δ is the censoring bit. b The structure of an Individual Survival Distribution (ISD). The x axis is measured in time, and the y axis denotes the probability of reaching that time event-free. The dotted lines show the prediction that this patient has a 50% chance of no readmission for 340 days; this is their median survival time. We can use such a “median survival time” as our prediction for that patient’s time-to-event, or (if desired) use the survival probability between two different points (e.g., the times associated with the probabilities 0.25 and 0.75) to report a prediction confidence interval

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  Fig. 3. Overview of procedures used for dataset procurement, model training, and model evaluation. A Procedure used to arrive at the final dataset of index admissions and study population. B Details of external cross-validation for evaluation

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  Fig. 4. Study and example patient timelines. The study timeline is split into three periods: the pre-index period for training Medical Concept Embeddings, the index period from which index admissions are selected, and the post-index period to examine at least one year of a patient’s future post-index-admission-discharge. The timeline for each patient is split into two periods: the lookback period of patient history (which includes all information until the index admission discharge) and the time-to-readmission (the period of readmission-free survival). Time-to-readmission is calculated from the discharge of the index admission to the day of the next admission. If time-to-readmission extends beyond the end of the study period, we instead compute time-to-censorship

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  Fig. 5. Architectures and inputs of models used in this study. A LACE baseline model taking the LACE score as input, B XGBoost and CoxPH models taking tabular features as input. The CoxPH risk score is combined with a baseline survival function to generate an individual survival distribution. C DNN and N-MTLR models taking tabular and/or sequence features as input

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  Fig. 6. The differing distributions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{(i)} $$\end{document}t(i) based on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\delta}^{(i)} $$\end{document}δ(i). Note that in “Time-to-Censorship”, the x-axis starts at 365 days, which is the censoring time of individuals whose index episode discharge coincided with the last day of the index period

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  Fig. 7. Comparisons of sequence-accepting models and the LACE baseline. The Deep Neural Network (DNN) uses a binary target, while N-MTLR uses a survival target to model an Individual Survival Distribution. Non-MCE Seq denotes the use of patient documents as one-hot vectors of medical codes. MCE Seq uses the unsupervised Medical Concept Embedding dictionary to represent codes as dense vectors to capture domain knowledge