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

Correcting for Selection Bias and Missing Response in Regression using Privileged Information

When estimating a regression model, we might have data where some labels are missing, or our data might be biased by a selection mechanism. When the response or selection mechanism is ignorable (i.e., independent of the response variable given the features) one can use off-the-shelf regression methods; in the nonignorable case one typically has to adjust for bias. We observe that privileged data (i.e. data that is only available during training) might render a nonignorable selection mechanism ignorable, and we refer to this scenario as Privilegedly Missing at Random (PMAR). We propose a novel imputation-based regression method, named repeated regression, that is suitable for PMAR. We also consider an importance weighted regression method, and a doubly robust combination of the two. The proposed methods are easy to implement with most popular out-of-the-box regression algorithms. We empirically assess the performance of the proposed methods with extensive simulated experiments and on a synthetically augmented real-world dataset. We conclude that repeated regression can appropriately correct for bias, and can have considerable advantage over weighted regression, especially when extrapolating to regions of the feature space where response is never observed

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