Survival regression aims to predict the time when an event of interest will take place, typically a death or a failure. A fully parametric method [18] is proposed to estimate the survival function as a mixture of individual parametric distributions in the presence of censoring. In this paper, We present a novel method to predict the survival time by better clustering the survival data and combine primitive distributions. We propose two variants of variational auto-encoder (VAE), discrete and continuous, to generate the latent variables for clustering input covariates. The model is trained end to end by jointly optimizing the VAE loss and regression loss. Thorough experiments on dataset SUPPORT and FLCHAIN show that our method can effectively improve the clustering result and reach competitive scores with previous methods. We demonstrate the superior result of our model prediction in the long-term. Our code is available at https://github.com/

In recent years, data-driven, deep-learning-based models have shown great promise in medical risk prediction. By utilizing the large-scale Electronic Health Record data found in the U.S. Department of Veterans Affairs, the largest integrated healthcare system in the United States, we have developed an automated, personalized risk prediction model to support the clinical decision-making process for localized prostate cancer patients. This method combines the representative power of deep learning and the analytical interpretability of parametric regression models and can implement both time-dependent and static input data. To collect a comprehensive evaluation of model performances, we calculate time-dependent C-statistics $$C_{\text {td}}$$ over 2-, 5-, and 10-year time horizons using either a composite outcome or prostate cancer mortality as the target event. The composite outcome combines the Prostate-Specific Antigen (PSA) test, metastasis, and prostate cancer mortality. Our longitudinal model Recurrent Deep Survival Machine (RDSM) achieved $$C_{\text {td}}$$ 0.85 (0.83), 0.80 (0.83), and 0.76 (0.81), while the cross-sectional model Deep Survival Machine (DSM) attained $$C_{\text {td}}$$ 0.85 (0.82), 0.80 (0.82), and 0.76 (0.79) for the 2-, 5-, and 10-year composite (mortality) outcomes, respectively. In addition to estimating the survival probability, our method can quantify the uncertainty associated with the prediction. The uncertainty scores show a consistent correlation with the prediction accuracy. We find PSA and prostate cancer stage information are the most important indicators in risk prediction. Our work demonstrates the utility of the data-driven machine learning model in prostate cancer risk prediction, which can play a critical role in the clinical decision system.

We describe a new approach to estimating relative risks in time-to-event prediction problems with censored data in a fully parametric manner. Our approach does not require making strong assumptions of constant baseline hazard of the underlying survival distribution, as required by the Cox-proportional hazard model. By jointly learning deep nonlinear representations of the input covariates, we demonstrate the benefits of our approach when used to estimate survival risks through extensive experimentation on multiple real world datasets with different levels of censoring. We further demonstrate advantages of our model in the competing risks scenario. To the best of our knowledge, this is the first work involving fully parametric estimation of survival times with competing risks in the presence of censoring.