Recent advance in score-based models incorporates the stochastic differential equation (SDE), which brings the state-of-the art performance on image generation tasks. This paper improves such score-based models by analyzing the model at the zero perturbation noise. In real datasets, the score function diverges as the perturbation noise ($\sigma$) decreases to zero, and this observation leads an argument that the score estimation fails at $\sigma=0$ with any neural network structure. Subsequently, we introduce Unbounded Noise Conditional Score Network (UNCSN) that resolves the score diverging problem with an easily applicable modification to any noise conditional score-based models. Additionally, we introduce a new type of SDE, so the exact log likelihood can be calculated from the newly suggested SDE. On top of that, the associated loss function mitigates the loss imbalance issue in a mini-batch, and we present a theoretic analysis on the proposed loss to uncover the behind mechanism of the data distribution modeling by the score-based models.

A smart healthcare system that supports clinicians for risk-calibrated treatment assessment typically requires the accurate modeling of time-to-event outcomes. To tackle this sequential treatment effect estimation problem, we developed causal dynamic survival model (CDSM) for causal inference with survival outcomes using longitudinal electronic health record (EHR). CDSM has impressive explanatory performance while maintaining the prediction capability of conventional binary neural network predictors. It borrows the strength from explanatory framework including the survival analysis and counterfactual framework and integrates them with the prediction power from a deep Bayesian recurrent neural network to extract implicit knowledge from EHR data. In two large clinical cohort studies, our model identified the conditional average treatment effect in accordance with previous literature yet detected individual effect heterogeneity over time and patient subgroups. The model provides individualized and clinically interpretable treatment effect estimations to improve patient outcomes.

With the ever-growing complexity of primary health care system, proactive patient failure management is an effective way to enhancing the availability of health care resource. One key enabler is the dynamic prediction of time-to-event outcomes. Conventional explanatory statistical approach lacks the capability of making precise individual level prediction, while the data adaptive binary predictors does not provide nominal survival curves for biologically plausible survival analysis. The purpose of this article is to elucidate that the knowledge of explanatory survival analysis can significantly enhance the current black-box data adaptive prediction models. We apply our recently developed counterfactual dynamic survival model (CDSM) to static and longitudinal observational data and testify that the inflection point of its estimated individual survival curves provides reliable prediction of the patient failure time.