There are two notoriously hard problems in cluster analysis, estimating the number of clusters, and checking whether the population to be clustered is not actually homogeneous. Given a dataset, a clustering method and a cluster validation index, this paper proposes to set up null models that capture structural features of the data that cannot be interpreted as indicating clustering. Artificial datasets are sampled from the null model with parameters estimated from the original dataset. This can be used for testing the null hypothesis of a homogeneous population against a clustering alternative. It can also be used to calibrate the validation index for estimating the number of clusters, by taking into account the expected distribution of the index under the null model for any given number of clusters. The approach is illustrated by three examples, involving various different clustering techniques (partitioning around medoids, hierarchical methods, a Gaussian mixture model), validation indexes (average silhouette width, prediction strength and BIC), and issues such as mixed-type data, temporal and spatial autocorrelation.

Summary The risk of cancer among adults with metabolically healthy obesity (MHO) has not yet been established. We systematically searched from inception to 15 March 2020. We included prospective cohort studies that compared participants with MHO and participants with metabolically healthy non‐obesity (MHNO) for incidence of any type of cancer. Benign tumors, cancer mortality or cancer prognosis were not in the scope of our analysis. The Newcastle–Ottawa Scale was used for quality assessment. Ultimately, eight studies with a total of 12 542 390 participants were included. The pooled meta‐analysis using random effect model showed participants with MHO demonstrated a significantly increased risk of developing cancer (odds ratio [OR], 1.14; 95% confidence interval [CI], 1.05 to 1.23; and I2 = 39%) than those with MHNO. The subgroup analysis revealed a higher pooled estimate (OR, 1.17; 95% CI, 1.01–1.35; and I2 = 56%) in comparison with metabolically healthy normal weight. No evidence of effect modification by age, sex, ethnicity, smoking, sample size or length of follow‐up was found. In conclusion, the present study reports a positive association between MHO and cancer incidence. All individuals with obesity, even in the absence of metabolic dysfunction, should be encouraged to lose weight.

We investigated the association among metabolically healthy obesity (MHO), cardiovascular disease (CVD)risk, and all-cause mortality in the Asian population. We searched databases from inception to 16 November, 2019 and pooled data using a random-effects model. Subgroup analysis was conducted according to the following comparison groups: MHNW (without overweight or underweight participants) and MHNO (non-obese, including overweight and underweight participants). Nineteen studies were included. The mean Newcastle–Ottawa Scale score was 7.8. Participants with MHO had a significantly higher CVD risk (odds ratio (OR) = 1.36, 95% confidence interval (CI) = 1.13–1.63) and significantly lower risk of all-cause mortality (OR = 0.88, 95% CI = 0.78–1.00) than the comparison group. Subgroup analyses revealed participants with MHO had a significantly higher CVD risk than MHNW participants (OR = 1.61; 95% CI = 1.24–2.08; I2 = 73%), but there was no significant difference compared with MHNO participants (OR, 1.04; 95% CI, 0.80–1.36; I2 = 68%). Participants with MHO had a significantly lower risk of all-cause mortality (OR = 0.83; 95% CI = 0.78–0.88; I2 = 9%) than MHNO participants, but a borderline significantly higher risk of all-cause mortality than MHNW participants (OR = 1.30; 95% CI = 0.99–1.72; I2 = 0%). The CVD risk and all-cause mortality of the MHO group changed depending on the control group. Thus, future studies should select control groups carefully.

In this study, the authors demonstrate the preventive effect of continuous intrathecal minocycline on the development of nociceptive behaviors induced by L5/6 spinal-nerve ligation in rats. Further studies are required to examine if continuous intrathecal minocycline could be used safely in the clinical setting.

Prenatal anxiety is extremely common and may result in adverse effects on both the mother and the baby. Music interventions have been used to reduce anxiety in various medical patients and in pregnant women during childbirth. This study aims to assess the clinical efficacy of music interventions in women during pregnancy rather than during labor. Seven databases were searched from inception to September 2019 without language restrictions. We included only randomized controlled trials that compared music intervention and control groups for anxiety reduction in pregnant women. We used the revised Cochrane risk-of-bias tool (RoB 2.0) for quality assessment. Finally, 11 studies with 1482 participants were included. The pooled meta-analysis results showed that music interventions significantly decreased anxiety levels (standardized mean difference (SMD), −0.42; 95% confidence interval (CI), −0.83 to −0.02; I2 = 91%). Moreover, subgroup analysis showed that listening to music at home had significant anxiolytic benefits (SMD, −0.28; 95% CI, −0.47 to −0.08; I2 = 0%). However, meta-regression revealed a nonsignificant trend for increase in the anxiety-reducing effects of music interventions with increasing maternal age. In conclusion, music interventions may be beneficial in reducing anxiety and may be applied in pregnant women.

In many phase II trials in solid tumours, patients are assessed using endpoints based on the Response Evaluation Criteria in Solid Tumours (RECIST) scale. Often, analyses are based on the response rate. This is the proportion of patients who have an observed tumour shrinkage above a predefined level and no new tumour lesions. The augmented binary method has been proposed to improve the precision of the estimator of the response rate. The method involves modelling the tumour shrinkage to avoid dichotomising it. However, in many trials the best observed response is used as the primary outcome. In such trials, patients are followed until progression, and their best observed RECIST outcome is used as the primary endpoint. In this paper, we propose a method that extends the augmented binary method so that it can be used when the outcome is best observed response. We show through simulated data and data from a real phase II cancer trial that this method improves power in both single‐arm and randomised trials. The average gain in power compared to the traditional analysis is equivalent to approximately a 35% increase in sample size. A modified version of the method is proposed to reduce the computational effort required. We show this modified method maintains much of the efficiency advantages.

Background Pneumonia is a leading cause of hospitalization and death worldwide. However, studies focusing on risk factors of community-acquired pneumonia (CAP) in the home health care (HHC) population remain scarce. Aims This study aimed to evaluate risk factors associated with hospitalization for CAP among HHC patients in Taiwan. Methods This retrospective cross-sectional study extracted data from patients' electronic medical records between 1 January 2017 and 31 December 2017. Multiple logistic regression analyses were performed to explore factors associated with hospitalization for CAP. Results In total, 598 patients (men/women: 236/362) were included. One hundred ninety-nine patients (33.28%) were hospitalized for pneumonia. Inpatients showed a higher proportion of the following: male sex, functional impairment, hypoalbuminemia, anemia, nasogastric tube use, excessive polypharmacy, stroke, dementia, heart failure, chronic respiratory disease, and chronic liver disease. Furthermore, nasogastric tube use (odds ratio [OR] 3.01, 95% confidence interval [

Photonic crystals (PCs) are a novel optical nanostructure with periodic refractive-index modulation. They can give rise to a photonic band gap within which the propagation and emission of light are prohibited. The band gap can be tuned by geometric parameters such as the lattice constant or filling ratio to alter the transmission spectra or the dispersion of light propagating through the PC structure. 2D PCs, [1][2][3][4] which can manipulate the propagation of in-plane light at telecommunication wavelengths, [1,3] have received much attention recently.Such a device consists of a 2D array of air holes embedded in a high-dielectric-constant slab constructed on top of a lowdielectric-constant substrate and can be made using presentday semiconductor fabrication technologies. However 2D PCs suffer from difficulties arising from unwanted coupling to free-space modes in the substrate. This coupling breaks translation symmetry and has to be avoided by carefully designing the crystal parameters. One of the common approaches to eliminating this coupling is to suspend the slabs using a SiO 2 sacrificial layer, forming a quasi-3D PC structure. Silicon-oninsulator (SOI)-based suspended 2D PCs [5] are a good example, in which the incident light is confined in the third dimension. But full confinement of photons can only be achieved in 3D PCs, in which a photonic band gap is present in all three directions and complete control of light propagation and emission is possible. Early work on 3D PCs utilized techniques such as self-assembly, [6] 3D interference lithography, [7,8] direct laser writing, [9,10] glancing-angle deposition, [11] and electron-beam lithography (EBL) with wafer fusion. [12] However unsolved issues in these techniques still exist. For example, EBL with wafer fusion has layer-to-layer alignment problems, and both glancing-angle deposition and self-assembly techniques present difficulties for making defect modes such as waveguides or microcavities.A polymer-based PC with a photonic band gap is a candidate for optical integrated circuits because of its low propagation loss at telecommunication wavelengths and compatibility with optical fibers.[13] The photonic-band-structure calculation [14] has shown a complete band gap for transverse-electric (TE)-like modes. Furthermore, conjugated polymer [15][16] has been shown to exhibit excellent performance in luminescence and lasing, and is thus an ideal building block for active optical components. In this paper, we demonstrate a simple new method to fabricate polymer-based suspended quasi-3D photonic slabs and 3D PCs. Polymethylmethacrylate (PMMA) is a widely used polymer material because it is a standard resist for EBL and it can also be used in nanoimprint lithography [17] owing to its low glasstransition temperature (T g = 105°C). For PC applications, the PMMA layer should have good verticality, large aspect ratio, and high dimensional accuracy. In view of this, high-energy EBL is the most suitable technique because it has several advantages such as: 1) a long pene...