A Framework for Data-Driven Explainability in Mathematical Optimization

Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the perception of optimization software as a black box. Although well understood by scientists, this lacks easy accessibility for practitioners. Hence, we advocate for introducing the explainability of a solution as another evaluation criterion, next to its objective value, which enables us to find trade-off solutions between these two criteria. Explainability is attained by comparing against (not necessarily optimal) solutions that were implemented in similar situations in the past. Thus, solutions are preferred that exhibit similar features. Although we prove that already in simple cases the explainable model is NP-hard, we characterize relevant polynomially solvable cases such as the explainable shortest-path problem. Our numerical experiments on both artificial as well as real-world road networks show the resulting Pareto front. It turns out that the cost of enforcing explainability can be very small

Data-driven Distributionally Robust Optimization over Time

Stochastic Optimization (SO) is a classical approach for optimization under uncertainty that typically requires knowledge about the probability distribution of uncertain parameters. As the latter is often unknown, Distributionally Robust Optimization (DRO) provides a strong alternative that determines the best guaranteed solution over a set of distributions (ambiguity set). In this work, we present an approach for DRO over time that uses online learning and scenario observations arriving as a data stream to learn more about the uncertainty. Our robust solutions adapt over time and reduce the cost of protection with shrinking ambiguity. For various kinds of ambiguity sets, the robust solutions converge to the SO solution. Our algorithm achieves the optimization and learning goals without solving the DRO problem exactly at any step. We also provide a regret bound for the quality of the online strategy which converges at a rate of $\mathcal{O}(\log T / \sqrt{T})$, where $T$ is the number of iterations. Furthermore, we illustrate the effectiveness of our procedure by numerical experiments on mixed-integer optimization instances from popular benchmark libraries and give practical examples stemming from telecommunications and routing. Our algorithm is able to solve the DRO over time problem significantly faster than standard reformulations

Obeticholic acid for the treatment of non-alcoholic steatohepatitis: interim analysis from a multicentre, randomised, placebo-controlled phase 3 trial

Background Non-alcoholic steatohepatitis (NASH) is a common type of chronic liver disease that can lead to cirrhosis. Obeticholic acid, a farnesoid X receptor agonist, has been shown to improve the histological features of NASH. Here we report results from a planned interim analysis of an ongoing, phase 3 study of obeticholic acid for NASH. Methods In this multicentre, randomised, double-blind, placebo-controlled study, adult patients with definite NASH,non-alcoholic fatty liver disease (NAFLD) activity score of at least 4, and fibrosis stages F2–F3, or F1 with at least oneaccompanying comorbidity, were randomly assigned using an interactive web response system in a 1:1:1 ratio to receive oral placebo, obeticholic acid 10 mg, or obeticholic acid 25 mg daily. Patients were excluded if cirrhosis, other chronic liver disease, elevated alcohol consumption, or confounding conditions were present. The primary endpointsfor the month-18 interim analysis were fibrosis improvement (≥1 stage) with no worsening of NASH, or NASH resolution with no worsening of fibrosis, with the study considered successful if either primary endpoint was met. Primary analyses were done by intention to treat, in patients with fibrosis stage F2–F3 who received at least one dose of treatment and reached, or would have reached, the month 18 visit by the prespecified interim analysis cutoff date. The study also evaluated other histological and biochemical markers of NASH and fibrosis, and safety. This study is ongoing, and registered with ClinicalTrials.gov, NCT02548351, and EudraCT, 20150-025601-6. Findings Between Dec 9, 2015, and Oct 26, 2018, 1968 patients with stage F1–F3 fibrosis were enrolled and received at least one dose of study treatment; 931 patients with stage F2–F3 fibrosis were included in the primary analysis (311 in the placebo group, 312 in the obeticholic acid 10 mg group, and 308 in the obeticholic acid 25 mg group). The fibrosis improvement endpoint was achieved by 37 (12%) patients in the placebo group, 55 (18%) in the obeticholic acid 10 mg group (p=0·045), and 71 (23%) in the obeticholic acid 25 mg group (p=0·0002). The NASH resolution endpoint was not met (25 [8%] patients in the placebo group, 35 [11%] in the obeticholic acid 10 mg group [p=0·18], and 36 [12%] in the obeticholic acid 25 mg group [p=0·13]). In the safety population (1968 patients with fibrosis stages F1–F3), the most common adverse event was pruritus (123 [19%] in the placebo group, 183 [28%] in the obeticholic acid 10 mg group, and 336 [51%] in the obeticholic acid 25 mg group); incidence was generally mild to moderate in severity. The overall safety profile was similar to that in previous studies, and incidence of serious adverse events was similar across treatment groups (75 [11%] patients in the placebo group, 72 [11%] in the obeticholic acid 10 mg group, and 93 [14%] in the obeticholic acid 25 mg group). Interpretation Obeticholic acid 25 mg significantly improved fibrosis and key components of NASH disease activity among patients with NASH. The results from this planned interim analysis show clinically significant histological improvement that is reasonably likely to predict clinical benefit. This study is ongoing to assess clinical outcomes

Additional file 5 of Worldwide clinical practices in perioperative antibiotic therapy for lung transplantation

Additional file 5. Answers to Case 3

Additional file 8 of Worldwide clinical practices in perioperative antibiotic therapy for lung transplantation

Additional file 8 Answers according to large et small volume centers. The groups were defined on the median of lung transplants performed in 2017 (n = 28). LTx: lung transplantation

Additional file 6 of Worldwide clinical practices in perioperative antibiotic therapy for lung transplantation

Additional file 6. Answers to Case 4

Additional file 2 of Worldwide clinical practices in perioperative antibiotic therapy for lung transplantation

Additional file 2. Raw anonymized answers of the 99 participant