Novel Deep Learning Approaches for Semi-Competing Risk Prediction
Salerno, Stephen
2023
Abstract
In the era of precision medicine, time-to-event outcomes such as time to death or disease progression are routinely collected, along with high-throughput covariates which defy classical survival regression models. Given challenges with high-dimensional survival data, recent emphasis has been placed on developing novel deep learning approaches for survival estimation and prognostication. However, many survival processes in real applications involve multiple competing events. Semi-competing risks, a variant of competing risk problems, have commonly been encountered in clinical studies. In this dissertation, we propose a series of deep learning approaches in this setting of semi-competing risks. Our motivation comes from the Boston Lung Cancer Survival Cohort study, a large cancer epidemiology cohort investigating the complex mechanisms of lung cancer. In Chapter II, we first propose a novel, multi-task deep neural network for semi-competing risks based on the illness-death model, a compartment-type model for the rates at which individuals transition between disease states. We develop our objective function based on the hazards of experiencing a disease progression or death from being event-free (e.g., from time of diagnosis) and the hazards of death following progression. Our deep learning model consists of three risk-specific sub-networks, respectively corresponding to the three possible state transitions, and a finite set of trainable parameters for specifying the baseline hazards and the degree of dependence among the three transition processes. We further introduce a novel framework for evaluating predictive performance in this setting by extending the widely used Brier score for censored univariate time-to-event data to the bivariate survival function. In Chapter III we further extend this method to allow the nonparametric estimation of our transition-specific baseline hazard functions. We propose a hybrid approach to deep learning via our so-called neural expectation-maximization (NEM) algorithm. By viewing the subject-specific frailty as a missing variable, the algorithm iterates between three steps. In the E-step, we update the conditional expectation of the frailties, given the data and current values for the model parameters. In the M-step, we estimate the jump sizes for the piecewise-constant baseline hazards, then fixing these quantities, update our estimates of the log risk functions and frailty variance as outputs of our neural network architectures in the N-step. While mortality is often the primary endpoint for studying the effect of a particular treatment or exposure, non-fatal events impact illness trajectories and treatment decisions related to disease management. The integration of causal inference into machine learning approaches has shown great promise for estimating the causal effects of treatments on survival outcomes, however, little work has been done in settings where a non-fatal event is potentially ‘truncated by death.’ In Chapter IV, we propose a deep learning approach for estimating the causal effect of a given treatment on a non-fatal outcome. We estimate the marginal survival function for the non-fatal event based on an Archimedean copula model and use a jackknife pseudo-value approach to circumvent the need for a complex loss function, whereby we estimate pseudo-survival probabilities at fixed time points as target values. We relate our pseudo-outcomes to our causal variable of interest and additional confounders in a deep neural network S-learner. Throughout, we provide a series of numerical studies to evaluate our proposed approach and apply our method to the Boston Lung Cancer Study. We conclude with some discussion on our current work and areas of future research.Deep Blue DOI
Subjects
Deep Learning; Semi-Competing Risks; Survival Analysis; Causal Inference; Lung Cancer; Risk Prediction
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