Distributed Adaptive Huber Regression

Distributed data naturally arise in scenarios involving multiple sources of observations, each stored at a different location. Directly pooling all the data together is often prohibited due to limited bandwidth and storage, or due to privacy protocols. This paper introduces a new robust distributed algorithm for fitting linear regressions when data are subject to heavy-tailed and/or asymmetric errors with finite second moments. The algorithm only communicates gradient information at each iteration and therefore is communication-efficient. Statistically, the resulting estimator achieves the centralized nonasymptotic error bound as if all the data were pooled together and came from a distribution with sub-Gaussian tails. Under a finite $(2+\delta)$-th moment condition, we derive a Berry-Esseen bound for the distributed estimator, based on which we construct robust confidence intervals. Numerical studies further confirm that compared with extant distributed methods, the proposed methods achieve near-optimal accuracy with low variability and better coverage with tighter confidence width.Comment: 29 page

Doubly Robust Estimation under Possibly Misspecified Marginal Structural Cox Model

In this paper we address the challenges posed by non-proportional hazards and informative censoring, offering a path toward more meaningful causal inference conclusions. We start from the marginal structural Cox model, which has been widely used for analyzing observational studies with survival outcomes, and typically relies on the inverse probability weighting method. The latter hinges upon a propensity score model for the treatment assignment, and a censoring model which incorporates both the treatment and the covariates. In such settings, model misspecification can occur quite effortlessly, and the Cox regression model's non-collapsibility has historically posed challenges when striving to guard against model misspecification through augmentation. We introduce an augmented inverse probability weighted estimator which, enriched with doubly robust properties, paves the way for integrating machine learning and a plethora of nonparametric methods, effectively overcoming the challenges of non-collapsibility. The estimator extends naturally to estimating a time-average treatment effect when the proportional hazards assumption fails. We closely examine its theoretical and practical performance, showing that it satisfies both the assumption-lean and the well-specification criteria discussed in the recent literature. Finally, its application to a dataset reveals insights into the impact of mid-life alcohol consumption on mortality in later life

Evidence of Kitaev interaction in the monolayer 1T-CrTe2_2

The two-dimensional 1T-CrTe$_2$ has been an attractive room-temperature van der Waals magnet which has a potential application in spintronic devices. Although it was recognized as a ferromagnetism in the past, the monolayer 1T-CrTe$_2$ was recently found to exhibit zigzag antiferromagnetism with the easy axis oriented at $70^\circ$ to the perpendicular direction of the plane. Therefore, the origin of the intricate anisotropic magnetic behavior therein is well worthy of thorough exploration. Here, by applying density functional theory with spin spiral method, we demonstrate that the Kitaev interaction, together with the single-ion anisotropy and other off-diagonal exchanges, is amenable to explain the magnetic orientation in the metallic 1T-CrTe$_2$. Moreover, the Ruderman-Kittle-Kasuya-Yosida interaction can also be extracted from the dispersion calculations, which explains the metallic behavior of 1T-CrTe$_2$. Our results demonstrate that 1T-CrTe$_2$ is potentially a rare metallic Kitaev material

Change in Albuminuria and GFR Slope as Joint Surrogate End Points for Kidney Failure:Implications for Phase 2 Clinical Trials in CKD

Significance Statement: Changes in albuminuria and GFR slope are individually used as surrogate end points in clinical trials of CKD progression, and studies have demonstrated that each is associated with treatment effects on clinical end points. In this study, the authors sought to develop a conceptual framework that combines both surrogate end points to better predict treatment effects on clinical end points in Phase 2 trials. The results demonstrate that information from the combined treatment effects on albuminuria and GFR slope improves the prediction of treatment effects on the clinical end point for Phase 2 trials with sample sizes between 100 and 200 patients and duration of follow-up ranging from 1 to 2 years. These findings may help inform design of clinical trials for interventions aimed at slowing CKD progression.Background Changes in log urinary albumin-To-creatinine ratio (UACR) and GFR slope are individually used as surrogate end points in clinical trials of CKD progression. Whether combining these surrogate end points might strengthen inferences about clinical benefit is unknown.Methods Using Bayesian meta-regressions across 41 randomized trials of CKD progression, we characterized the combined relationship between the treatment effects on the clinical end point (sustained doubling of serum creatinine, GFR &lt;15 ml/min per 1.73 m2, or kidney failure) and treatment effects on UACR change and chronic GFR slope after 3 months. We applied the results to the design of Phase 2 trials on the basis of UACR change and chronic GFR slope in combination.Results Treatment effects on the clinical end point were strongly associated with the combination of treatment effects on UACR change and chronic slope. The posterior median meta-regression coefficients for treatment effects were-0.41 (95% Bayesian Credible Interval,-0.64 to-0.17) per 1 ml/min per 1.73 m2per year for the treatment effect on GFR slope and-0.06 (95% Bayesian Credible Interval,-0.90 to 0.77) for the treatment effect on UACR change. The predicted probability of clinical benefit when considering both surrogates was determined primarily by estimated treatment effects on UACR when sample size was small (approximately 60 patients per treatment arm) and follow-up brief (approximately 1 year), with the importance of GFR slope increasing for larger sample sizes and longer follow-up.Conclusions In Phase 2 trials of CKD with sample sizes of 100-200 patients per arm and follow-up between 1 and 2 years, combining information from treatment effects on UACR change and GFR slope improved the prediction of treatment effects on clinical end points.</p

Protective Effect of Tetrahydroxystilbene Glucoside on 6-OHDA-Induced Apoptosis in PC12 Cells through the ROS-NO Pathway

Oxidative stress plays an important role in the pathogenesis of neurodegenerative diseases, such as Parkinson's disease. The molecule, 2,3,5,4′-tetrahydr- oxystilbene-2-O-β-D-glucoside (TSG), is a potent antioxidant derived from the Chinese herb, Polygonum multiflorum Thunb. In this study, we investigated the protective effect of TSG against 6-hydroxydopamine-induced apoptosis in rat adrenal pheochromocytoma PC12 cells and the possible mechanisms. Our data demonstrated that TSG significantly reversed the 6-hydroxydopamine-induced decrease in cell viability, prevented 6-hydroxydopamine-induced changes in condensed nuclei and decreased the percentage of apoptotic cells in a dose-dependent manner. In addition, TSG slowed the accumulation of intracellular reactive oxygen species and nitric oxide, counteracted the overexpression of inducible nitric oxide syntheses as well as neuronal nitric oxide syntheses, and also reduced the level of protein-bound 3-nitrotyrosine. These results demonstrate that the protective effects of TSG on rat adrenal pheochromocytoma PC12 cells are mediated, at least in part, by the ROS-NO pathway. Our results indicate that TSG may be effective in providing protection against neurodegenerative diseases associated with oxidative stress

Statistical Robustness - Distributed Linear Regression, Informative Censoring, Causal Inference, and Non-Proportional Hazards

Robustness broadly refers to the property of the statistical method being valid even when some of the model assumptions are violated. We investigate 4 types of statistical robustness under 4 different problem setups. Firstly, we consider linear regression under the distributed setting where data are stored in separate machines. When errors are subject to heavy-tailed and/or asymmetric errors, we develop a tail-robust distributed estimator that achieves a sub-Gaussian-type deviation bound without pooling all the data together and without assuming Gaussian errors. Moreover, the algorithm only transfers gradient in each step and is hence communication efficient. Secondly, we explore the two-group Cox proportional hazards (PH) model in a randomized study. When the non-informative censoring assumption no longer holds, the inverse probability of censoring weighting (IPCW) estimator helps correct the censoring bias by modeling the nuisance function for conditional censoring survival. To protect against the misspecification of the nuisance function, we propose an augmented IPCW (AIPCW) estimator which also models conditional failure survival. The AIPCW estimator is model double robust (DR) in that the estimator will be consistent and asymptotically normal (CAN) even when one of the root-n nuisance estimators is wrong. The estimator is also CAN if both nuisance functions are consistently estimated with their product error rate being faster than root-n. This so-called rate DR property allows us to make use of machine learning (ML) methods, which directly address the non-collapsibility of the Cox model. Thirdly, we extend the problem to observational data with the two-group survival following the marginal structural Cox model. In addition to the missingness due to censoring, we also need to deal with missingness coming from partial observations of the potential outcomes. By extending the AIPCW estimator to include the nuisance propensity score function, we develop an augmented IPW (AIPW) estimator that is again DR with respect to the models for failure time and for missing mechanisms. Lastly, we consider the scenario when the PH assumption fails and propose a causal estimand that is a weighted average of the time-varying log hazards ratio. We show that this estimand enjoys several desirable properties and can be estimated using the same AIPW estimator we proposed for the marginal structural Cox model. A method for plotting the time-varying log hazard ratio under observational data is also proposed