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

Intensive endoscopic resection for downstaging of polyp burden in patients with familial adenomatous polyposis (J-FAPP Study III) : a multicenter prospective interventional study

Background Total colectomy is the standard treatment for familial adenomatous polyposis (FAP). Recently, an increasing number of young patients with FAP have requested the postponement of surgery or have refused to undergo surgery. We aimed to evaluate the effectiveness of intensive endoscopic removal for downstaging of polyp burden (IDP) in FAP. Method A single-arm intervention study was conducted at 22 facilities. Participants were patients with FAP, aged ≥ 16 years, who had not undergone colectomy or who had undergone colectomy but had ≥ 10 cm of large intestine remaining. For IDP, colorectal polyps of ≥ 10 mm were removed, followed by polyps of ≥ 5 mm. The primary end point was the presence/absence of colectomy during a 5-year intervention period. Results 222 patients were eligible, of whom 166 had not undergone colectomy, 46 had undergone subtotal colectomy with ileorectal anastomosis, and 10 had undergone partial resection of the large intestine. During the intervention period, five patients (2.3 %, 95 % confidence interval [CI] 0.74 %–5.18 %) underwent colectomy, and three patients died. Completion of the 5-year intervention period without colectomy was confirmed in 150 /166 patients who had not undergone colectomy (90.4 %, 95 %CI 84.8 %–94.4 %) and in 47 /56 patients who had previously undergone colectomy (83.9 %, 95 %CI 71.7 %–92.4 %). Conclusion IDP in patients with mild-to-moderate FAP could have the potential to be a useful means of preventing colorectal cancer without implementing colectomy. However, if the IDP protocol was proposed during a much longer term, it may not preclude the possibility that a large proportion of colectomies may still need to be performed

Necessary optimality conditions for robust nonsmooth multiobjective optimization problems

This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly robust efficient solutions of the considered problem. These optimality conditions are presented in terms of Karush-Kuhn-Tucker multipliers and convexificators of the related functions. Examples illustrating our findings are also given

Optimality conditions for MPECs in terms of directional upper convexifactors

In this paper, we investigate necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. For this goal, we introduce an appropriate type of MPEC regularity condition and a stationary concept given in terms of directional upper convexificators and directional upper semi-regular convexificators. The appearing functions are not necessarily smooth/locally Lipschitz/convex/continuous, and the continuity directions’ sets are not assumed to be compact or convex. Finally, notions of directional pseudoconvexity and directional quasiconvexity are used to establish sufficient optimality conditions for MPECs

On interval-valued bilevel optimization problems using upper convexificators

In this paper, we investigate a bilevel interval valued optimization problem. Reducing the problem into a one-level nonlinear and nonsmooth program, necessary optimality conditions are developed in terms of upper convexificators. Our approach consists of using an Abadie’s constraint qualification together with an appropriate optimal value reformulation. Later on, using an upper estimate for upper convexificators of the optimal value function, we give a more detailed result in terms of the initial data. The appearing functions are not necessarily Lipschitz continuous, and neither the objective function nor the constraint functions of the lower-level optimization problem are assumed to be convex. There are additional examples highlighting both our results and the limitations of certain past studies

Rectal Foreign Body of Eggplant Treated Successfully by Endoscopic Transanal Removal

Transanal rectal foreign body implies that a foreign body has been inserted transanally due to sexual orientation or other reasons and cannot be removed. Such cases require emergency measures because foreign bodies often present difficulties in manual removal or endoscopic removal and may even require surgery when peritonitis due to gastrointestinal perforation occurs. We report a patient in our hospital who had a rectal foreign body inserted into the deep part of the proctosigmoid that could be removed endoscopically. A 66-year-old man visited our hospital because of an eggplant which had been inserted into his rectum by his friend and could not be removed. Since plain abdominal computed tomography showed a foreign body thought to be an eggplant in the proctosigmoid, the foreign body was captured and removed with a snare under lower gastrointestinal endoscope guidance