Identifying Causal Effects Using Instrumental Variables from the Auxiliary Population

Instrumental variable approaches have gained popularity for estimating causal effects in the presence of unmeasured confounding. However, the availability of instrumental variables in the primary population is often challenged due to stringent and untestable assumptions. This paper presents a novel method to identify and estimate causal effects in the primary population by utilizing instrumental variables from the auxiliary population, incorporating a structural equation model, even in scenarios with nonlinear treatment effects. Our approach involves using two datasets: one from the primary population with joint observations of treatment and outcome, and another from the auxiliary population providing information about the instrument and treatment. Our strategy differs from most existing methods by not depending on the simultaneous measurements of instrument and outcome. The central idea for identifying causal effects is to establish a valid substitute through the auxiliary population, addressing unmeasured confounding. This is achieved by developing a control function and projecting it onto the function space spanned by the treatment variable. We then propose a three-step estimator for estimating causal effects and derive its asymptotic results. We illustrate the proposed estimator through simulation studies, and the results demonstrate favorable performance. We also conduct a real data analysis to evaluate the causal effect between vitamin D status and BMI.Comment: 19 page

Identification and Estimation of Causal Effects Using non-Gaussianity and Auxiliary Covariates

Assessing causal effects in the presence of unmeasured confounding is a challenging problem. Although auxiliary variables, such as instrumental variables, are commonly used to identify causal effects, they are often unavailable in practice due to stringent and untestable conditions. To address this issue, previous researches have utilized linear structural equation models to show that the causal effect can be identifiable when noise variables of the treatment and outcome are both non-Gaussian. In this paper, we investigate the problem of identifying the causal effect using auxiliary covariates and non-Gaussianity from the treatment. Our key idea is to characterize the impact of unmeasured confounders using an observed covariate, assuming they are all Gaussian. The auxiliary covariate can be an invalid instrument or an invalid proxy variable. We demonstrate that the causal effect can be identified using this measured covariate, even when the only source of non-Gaussianity comes from the treatment. We then extend the identification results to the multi-treatment setting and provide sufficient conditions for identification. Based on our identification results, we propose a simple and efficient procedure for calculating causal effects and show the $\sqrt{n}$-consistency of the proposed estimator. Finally, we evaluate the performance of our estimator through simulation studies and an application.Comment: 16 papges, 7 Figure

(R)-[1-(2-Chloro­phen­yl)-2-meth­oxy-2-oxoeth­yl][2-(thio­phen-2-yl)eth­yl]ammonium (+)-camphor-10-sulfonate acetone monosolvate

The title compound, C15H17ClNO2S+·C10H15O4S−·C3H6O, was synthesized by N-alkyl­ation of α-amino-(2-chloro­phen­yl)acetate with 2-thienylethyl p-toluene­sulfonate, followed by reaction with (+)-camphor-10-sulfonic acid. In the crystal, the cations and anions are linked through N—H⋯O hydrogen bonds. The thio­phene ring of the cation was found to be disordered over two sites, with refined occupancies of 0.798 (4) and 0.202 (4)

Optimization calculation of stope structure parameters based on Mathews stabilization graph method

Mathews stability graphic method, based on the rock classification system, measures the stability of the ore roof area of a relatively simple calculation method and provides a theoretical basis for mine rational design stope structure size parameters. In this study, we used a large-scale tungsten mine in Jiangxi Province as the engineering background and performed on-site engineering geological surveys and indoor ore rock mechanics tests in the middle section of mine 417 to obtain multiple engineering quality indicators for the mines and surrounding rocks. The Mathews stability map method and Barton limit span theory were used. The reasonable size range of the exposed face of the stope was calculated by performing theoretical analysis on the ultimate span. Then, FLAC3D calculation and analysis software were used for the simulation of the stope structure, and the most reasonable design of the exposed surface dimension was selected and used as reference for ensuring the safe production of the mine

Effect of Al alloying on cavitation erosion behavior of TaSi2 nanocrystalline coatings

To broaden the scope of non-aerospace applications for titanium-based alloys, both hexagonal C40 binary TaSi2 and ternary Al alloyed TaSi2 nanocrystalline coatings were exploited to enhance the cavitation erosion resistance of Ti-6Al-4V alloy in acidic environments. To begin with, the roles of Al addition in influencing the structural stability and mechanical properties of hexagonal C40 Ta(Si1-xAlx)2 compounds were modelled using first-principles calculations. The calculated key parameters, such as Pugh\u27s index (B/G ratio), Poisson\u27s ratio, and Cauchy pressures, indicated that there was a threshold value for Al addition, below which the increase of Al content would render the Ta(Si1-xAlx)2 compounds more ductile, but above which no obvious change would occur. Subsequently, the TaSi2 and Ta(Si0.875Al0.125)2 coatings were prepared and their microstructure and phase composition were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Both the two coatings exhibited a uniform thickness of 15 μm and a densely packed structure mainly composed of spherically shaped nanocrystallites with an average diameter of about 5 nm. Nanoindentation measurements revealed that Al alloying reduced the hardness (H) and elastic modulus (E) values of the TaSi2 coating. Ultrasonic cavitation erosion tests were carried out by immersing coated and uncoated samples in a 0.5 M HCl solution. The cavitation-erosion analysis of the tested samples was investigated by various electrochemical techniques, mass loss weight and SEM observation. The results suggested that both coated samples provided a better protection for Ti-6Al-4V against the cavitation-erosion damage in acidic environments, but the addition of Al further improved the cavitation-erosion resistance of the TaSi2 coating