A Bayesian Nonparametric Conditional Two-sample Test with an Application to Local Causal Discovery

For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These algorithms are often applied to datasets containing binary variables, which indicate the 'context' of the observations, e.g. a control or treatment group within an experiment. In these settings, conditional independence testing with $X$ or $Y$ binary (and the other continuous) is paramount to the performance of the causal discovery algorithm. To our knowledge no nonparametric 'mixed' conditional independence test currently exists, and in practice tests that assume all variables to be continuous are used instead. In this paper we aim to fill this gap, as we combine elements of Holmes et al. (2015) and Teymur and Filippi (2020) to propose a novel Bayesian nonparametric conditional two-sample test. Applied to the Local Causal Discovery algorithm, we investigate its performance on both synthetic and real-world data, and compare with state-of-the-art conditional independence tests

COVID-19 among heart transplant recipients in Germany: a multicenter survey

Aims Heart transplantation may represent a particular risk factor for severe coronavirus infectious disease 2019 (COVID-19) due to chronic immunosuppression and frequent comorbidities. We conducted a nation-wide survey of all heart transplant centers in Germany presenting the clinical characteristics of heart transplant recipients with COVID-19 during the first months of the pandemic in Germany. Methods and results A multicenter survey of all heart transplant centers in Germany evaluating the current status of COVID-19 among adult heart transplant recipients was performed. A total of 21 heart transplant patients with COVID-19 was reported to the transplant centers during the first months of the pandemic in Germany. Mean patient age was 58.6 +/- 12.3 years and 81.0% were male. Comorbidities included arterial hypertension (71.4%), dyslipidemia (71.4%), diabetes mellitus (33.3%), chronic kidney failure requiring dialysis (28.6%) and chronic-obstructive lung disease/asthma (19.0%). Most patients received an immunosuppressive drug regimen consisting of a calcineurin inhibitor (71.4%), mycophenolate mofetil (85.7%) and steroids (71.4%). Eight of 21 patients (38.1%) displayed a severe course needing invasive mechanical ventilation. Those patients showed a high mortality (87.5%) which was associated with right ventricular dysfunction (62.5% vs. 7.7%;p = 0.014), arrhythmias (50.0% vs. none;p = 0.012), and thromboembolic events (50.0% vs. none;p = 0.012). Elevated high-sensitivity cardiac troponin T- and N-terminal prohormone of brain natriuretic peptide were significantly associated with the severe form of COVID-19 (p = 0.017 andp < 0.001, respectively). Conclusion Severe course of COVID-19 was frequent in heart transplanted patients. High mortality was associated with right ventricular dysfunction, arrhythmias, thromboembolic events, and markedly elevated cardiac biomarkers