Predicting the early risk of chronic kidney disease in patients with diabetes using real-world data.

Diagnostic procedures, therapeutic recommendations, and medical risk stratifications are based on dedicated, strictly controlled clinical trials. However, a plethora of real-world medical data exists, whereupon the increase in data volume comes at the expense of completeness, uniformity, and control. Here, a case-by-case comparison shows that the predictive power of our real world data-based model for diabetes-related chronic kidney disease outperforms published algorithms, which were derived from clinical study data.

Numerical solution of a conspicuous consumption model with constant control delay.

We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account.This non-standard optimal control problem is difficult to solve analytically, and solutions depend on the variable model parameters. Therefore, we use a numerical result-driven approach. We propose a structure-exploiting direct method for optimal control to solve this challenging optimization problem. In particular, we discretize the uncertainties in the model formulation by using scenario trees and target the control delays by introduction of slack control functions.Numerical results illustrate the validity of our approach and show the impact of uncertainties and delay effects on optimal economic strategies. During the recession, delayed optimal prices are higher than the non-delayed ones. In the normal economic period, however, this effect is reversed and optimal prices with a delayed impact are smaller compared to the non-delayed case.