CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regression

In causal inference about two treatments, Conditional Average Treatment Effects (CATEs) play an important role as a quantity representing an individualized causal effect, defined as a difference between the expected outcomes of the two treatments conditioned on covariates. This study assumes two linear regression models between a potential outcome and covariates of the two treatments and defines CATEs as a difference between the linear regression models. Then, we propose a method for consistently estimating CATEs even under high-dimensional and non-sparse parameters. In our study, we demonstrate that desirable theoretical properties, such as consistency, remain attainable even without assuming sparsity explicitly if we assume a weaker assumption called implicit sparsity originating from the definition of CATEs. In this assumption, we suppose that parameters of linear models in potential outcomes can be divided into treatment-specific and common parameters, where the treatment-specific parameters take difference values between each linear regression model, while the common parameters remain identical. Thus, in a difference between two linear regression models, the common parameters disappear, leaving only differences in the treatment-specific parameters. Consequently, the non-zero parameters in CATEs correspond to the differences in the treatment-specific parameters. Leveraging this assumption, we develop a Lasso regression method specialized for CATE estimation and present that the estimator is consistent. Finally, we confirm the soundness of the proposed method by simulation studies

Synthetic Control Methods by Density Matching under Implicit Endogeneity

Synthetic control methods (SCMs) have become a crucial tool for causal inference in comparative case studies. The fundamental idea of SCMs is to estimate counterfactual outcomes for a treated unit by using a weighted sum of observed outcomes from untreated units. The accuracy of the synthetic control (SC) is critical for estimating the causal effect, and hence, the estimation of SC weights has been the focus of much research. In this paper, we first point out that existing SCMs suffer from an implicit endogeneity problem, which is the correlation between the outcomes of untreated units and the error term in the model of a counterfactual outcome. We show that this problem yields a bias in the causal effect estimator. We then propose a novel SCM based on density matching, assuming that the density of outcomes of the treated unit can be approximated by a weighted average of the densities of untreated units (i.e., a mixture model). Based on this assumption, we estimate SC weights by matching moments of treated outcomes and the weighted sum of moments of untreated outcomes. Our proposed method has three advantages over existing methods. First, our estimator is asymptotically unbiased under the assumption of the mixture model. Second, due to the asymptotic unbiasedness, we can reduce the mean squared error for counterfactual prediction. Third, our method generates full densities of the treatment effect, not only expected values, which broadens the applicability of SCMs. We provide experimental results to demonstrate the effectiveness of our proposed method

2,7-Bis(4-acetyl­phen­oxy)naphthalene

The title compound, C26H20O4, has an asymmetrical conformation at 193 K. The 4-acetyl­phenyl groups are twisted away from the the naphthalene ring system, with one benzene ring turned towards the 1-position of the naphthalene ring and the other benzene ring turned towards the 6-position. The inter­planar angles between the mean planes of the benzene rings and the naphthalene ring system are 68.71 (6) and 74.01 (6)°. The structure displays C—H⋯O hydrogen bonding and π–π stacking inter­actions [centroid–centroid and interplanar distances are 3.5938 (9) and 3.517 Å, respectively]

Adenomyoepithelioma of the Breast A with an Immunohistochemical Study

Adenomyoepithelioma is a rare primary tumor of the breast in women. It is characterized by a bicellular pattern consisting of both ductal and myoepithelial elements. We report here an additional case of adenomyoepithelioma in a 57-year-old woman. The aspiration cytology revealed atypical cell clusters, and the simple mastectomy was performed under the diagnosis of ductal carcinoma. Macroscopically, the tumor presented as a well-defined mass. Histologically, the tumor demonstrated the characteristic bicellular growth pattern consisting of ducts and a periductal proliferation of mainly polygonal neoplastic cells. Immunohistochemically, epithelial cells lining the glandular structures were strongly positive for cytokeratin and epithelial membrane antigen (EMA). Polygonal myoepithelial cells gave negative reactions with cytokeratin and EMA. Most polygonal myoepithelial cells were positive for ﾎｱ-smooth muscle actin (SMA) and S-100 protein. Our case was a representative example of a typical adenomyoepithelioma, but the cytological diagnosis needs a deep attention to avoid overdiagnosis

2-(4-Chloro­benzo­yl)-3,6-dimethoxy­naphthalene

In the title compound, C19H15ClO3, the inter­planar angle between the naphthalene and benzene ring systems is 62.67 (6)°. The carbonyl group is twisted from both ring planes, with torsion angles of −44.9 (2)° with respect to the naphthalene ring and −26.7 (2)° with respect to the phenyl­ene ring. There is an inter­molecular hydrogen bond between an H atom of one meth­oxy group and the O atom of the second meth­oxy group, forming chains along the ac diagonal

Small Molecules with Similar Structures Exhibit Agonist, Neutral Antagonist or Inverse Agonist Activity toward Angiotensin II Type 1 Receptor

Small differences in the chemical structures of ligands can be responsible for agonism, neutral antagonism or inverse agonism toward a G-protein-coupled receptor (GPCR). Although each ligand may stabilize the receptor conformation in a different way, little is known about the precise conformational differences. We synthesized the angiotensin II type 1 receptor blocker (ARB) olmesartan, R239470 and R794847, which induced inverse agonism, antagonism and agonism, respectively, and then investigated the ligand-specific changes in the receptor conformation with respect to stabilization around transmembrane (TM)3. The results of substituted cysteine accessibility mapping studies support the novel concept that ligand-induced changes in the conformation of TM3 play a role in stabilizing GPCR. Although the agonist-, neutral antagonist and inverse agonist-binding sites in the AT1 receptor are similar, each ligand induced specific conformational changes in TM3. In addition, all of the experimental data were obtained with functional receptors in a native membrane environment (in situ)

Optimal Best Arm Identification in Two-Armed Bandits with a Fixed Budget under a Small Gap

We consider fixed-budget best arm identification in two-armed bandit problems. One of the longstanding open questions is a tight lower bound on the probability of misidentifying the best arm and a strategy whose upper bound matches the lower bound when the optimal target allocation ratio of arm draws is unknown. We address this problem when the gap between the expected rewards is small. First, we introduce a distribution-dependent lower bound. Then, we propose the ``RS-AIPW'' strategy, which consists of the random sampling (RS) rule using the estimated optimal target allocation ratio and the recommendation rule using the augmented inverse probability weighting (AIPW) estimator. Our proposed strategy is optimal in the sense that the upper bound achieves the lower bound when the budget goes to infinity and the gap goes to zero. In the course of the analysis, we present a novel large deviation bound for martingales

Adenomyoepithelioma of the Breast A with an Immunohistochemical Study

Adenomyoepithelioma is a rare primary tumor of the breast in women. It is characterized by a bicellular pattern consisting of both ductal and myoepithelial elements. We report here an additional case of adenomyoepithelioma in a 57-year-old woman. The aspiration cytology revealed atypical cell clusters, and the simple mastectomy was performed under the diagnosis of ductal carcinoma. Macroscopically, the tumor presented as a well-defined mass. Histologically, the tumor demonstrated the characteristic bicellular growth pattern consisting of ducts and a periductal proliferation of mainly polygonal neoplastic cells. Immunohistochemically, epithelial cells lining the glandular structures were strongly positive for cytokeratin and epithelial membrane antigen (EMA). Polygonal myoepithelial cells gave negative reactions with cytokeratin and EMA. Most polygonal myoepithelial cells were positive for ﾎｱ-smooth muscle actin (SMA) and S-100 protein. Our case was a representative example of a typical adenomyoepithelioma, but the cytological diagnosis needs a deep attention to avoid overdiagnosis