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The K-means clustering algorithm has had successful application in sufficient dimension reduction. Unfortunately, the algorithm does have reproducibility and nestness, which will be discussed in this paper. These are clear deficits for the K-means clustering algorithm; however, the hierarchical clustering algorithm has both reproducibility and nestness, but intensive comparison between K-means and hierarchical clustering algorithm has not yet been done in a sufficient dimension reduction context. In this paper, we rigorously study the two clustering algorithms for two popular sufficient dimension reduction methodology of inverse mean and clustering mean methods throughout intensive numerical studies. Simulation studies and two real data examples confirm that the use of hierarchical clustering algorithm has a potential advantage over the K-means algorithm.

Recently, Yoo (Statistics 50:1086–1099, 2016) newly defines an informative predictor subspace to contain the central subspace. The method to estimate the informative predictor subspace does not require any of the conditions assumed to hold in usual sufficient dimension reduction methodologies. However, like sliced inverse regression (Li in J Am Stat Assoc 86:316–342, 1991) and sliced average variance estimation (Cook and Weisberg in J Am Stat Assoc 86:328–332, 1991), its non-asymptotic behavior in the estimation is sensitive to the choices of the categorization of the predictors and response. The paper develops an estimation approach that is robust to the categorization choices. For this, sample kernel matrices are combined in two ways. Numerical studies and real data analysis are presented to confirm the potential usefulness of the proposed approach in practice.

Background Although tramadol is an effective weak opioid analgesic, careful monitoring of potential central nervous system adverse reactions in older adults is needed, especially when used with concomitant medications which may trigger the adverse effects. We aimed to characterize tramadol users with potentially inappropriate co-medications in older adults using a latent class analysis (LCA). Method Patients aged 65 years or older using tramadol and receiving potentially inappropriate co-medications were included from a nationwide healthcare claims database. We defined antidepressants, first-generation antihistamines, and anxiolytics as potentially inappropriate co-medications. We applied an LCA for grouping tramadol users based on the common characteristics of medication use and healthcare utilization, and each patient was probabilistically assigned to a class. Patients’ characteristics in different latent classes were compared. Potential adverse drug reactions (ADRs) was defined as the any visits for emergency department after the occurrence of potentially inappropriate co-medications. Logistic regression analysis was used to examine the association between latent classes and potential ADRs. Results We identified four distinct latent classes of tramadol users representing different patterns of co-medications: multiple potential drug-drug interaction (pDDI) combination users, antihistamines-tramadol users, antidepressants-tramadol users, and anxiolytics-tramadol users. Multiple pDDI combination users showed high proportion of regular tramadol use, tended to visit more medical institutions, and had a high Charlson comorbidity score. The duration of use of potentially inappropriate co-medications with tramadol was the longest in multiple pDDI combination users and the shortest in antihistamines-tramadol users. When compared with antihistamines-tramadol users, increased potential ADR risk was observed in multiple pDDI combination users (adjusted odds ratio (OR), 1.81; 95% confidence interval (CI), 1.75–1.88), antidepressants-tramadol users (1.24; 1.19–1.29), and anxiolytics-tramadol users (1.04; 1.00–1.08). Conclusions Four distinct classes were identified among older adults using tramadol and potentially inappropriate co-medications. Differences in potential ADR risk were observed between these classes. These findings may help to identify patients at a high risk for ADRs owing to potentially inappropriate co-medications with tramadol.

Summary Objectives An outbreak of joint and cutaneous infections among patients who had been injected at a single clinic in South Korea was investigated. Methods In this retrospective case–control study, 61 cases were diagnosed based on symptoms and signs of septic arthritis or cutaneous infection that developed after injections at the clinic between April and September 2012; 64 controls were investigated by administering questionnaires on risk factors and analyzing the clinic medical records. An environmental investigation was performed, and clinical specimens of the cases were analyzed by pulsed-field gel electrophoresis. Results All cases were injected with triamcinolone. A greater number of triamcinolone injections (adjusted odds ratio 4.3, 95% confidence interval 1.5–12.1 for six or more visits, compared with one or two visits) was associated with the development of an infection. In the clinic, only the triamcinolone injection was prepared by mixing with lidocaine and normal saline, and an alcohol swab was prepared using boiled tap water by members of the clinic staff. Although injected medications and environmental cultures were not found to be responsible, a single strain of Mycobacterium massiliense was isolated from the affected sites of 16 cases. Conclusions Repeated injection of triamcinolone contaminated with NTM from the clinic environment may have caused this post-injection outbreak.

High-dimensional data analysis often suffers the so-called curse of dimensionality, and various data reduction methods are adopted in order to avoid it in practice. Consequently, in multivariate regression, high-dimensional predictors should be reduced to lower-dimensional ones without the loss of information, following a notion of sufficient dimension reduction. In this paper, a fused clustered seeded reduction approach is proposed for multivariate regression. The proposed method utilizes two types of information: supervised learning between the responses and the predictors, and unsupervised learning of the predictors alone. Fusing all the information has a potential advantage in the accuracy of the reduction of predictors. Numerical studies and a real data analysis confirm the practical usefulness of the proposed approach over existing methods.