Crowdsourcing digital health measures to predict Parkinson's disease severity: the Parkinson's Disease Digital Biomarker DREAM Challenge

Consumer wearables and sensors are a rich source of data about patients' daily disease and symptom burden, particularly in the case of movement disorders like Parkinson's disease (PD). However, interpreting these complex data into so-called digital biomarkers requires complicated analytical approaches, and validating these biomarkers requires sufficient data and unbiased evaluation methods. Here we describe the use of crowdsourcing to specifically evaluate and benchmark features derived from accelerometer and gyroscope data in two different datasets to predict the presence of PD and severity of three PD symptoms: tremor, dyskinesia, and bradykinesia. Forty teams from around the world submitted features, and achieved drastically improved predictive performance for PD status (best AUROC = 0.87), as well as tremor- (best AUPR = 0.75), dyskinesia- (best AUPR = 0.48) and bradykinesia-severity (best AUPR = 0.95)

Default Risk Modeling Beyond the First-Passage Approximation: Extended Black-Cox Model

We develop a generalization of the Black-Cox structural model of default risk. The extended model captures uncertainty related to firm's ability to avoid default even if company's liabilities momentarily exceeding its assets. Diffusion in a linear potential with the radiation boundary condition is used to mimic a company's default process. The exact solution of the corresponding Fokker-Planck equation allows for derivation of analytical expressions for the cumulative probability of default and the relevant hazard rate. Obtained closed formulas fit well the historical data on global corporate defaults and demonstrate the split behavior of credit spreads for bonds of companies in different categories of speculative-grade ratings with varying time to maturity. Introduction of the finite rate of default at the boundary improves valuation of credit risk for short time horizons, which is the key advantage of the proposed model. We also consider the influence of uncertainty in the initial distance to the default barrier on the outcome of the model and demonstrate that this additional source of incomplete information may be responsible for non-zero credit spreads for bonds with very short time to maturity.