Star-shaped distributions and their generalizations

Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured densities to “star-shaped distributions” with concentric star-shaped contours and show that many results in the former case continue to hold in the more general case. We develop a general theory in the framework of abstract group invariance so that the results can be applied to other cases as well, especially those involving random matrices.     

Bayesian longitudinal paired comparison model and its application to sports data using weighted likelihood bootstrap

This article describes a procedure for Bayesian longitudinal paired comparison data analysis to rank stimuli. The proposed model is developed by combining the Bradley–Terry model and a nonlinear model that utilizes an exponential distribution to describe longitudinal changes in scale values. The weighted likelihood bootstrap method (WLB) is used to obtain samples from posterior distributions of parameters. WLB is an effective tool because neither diagnosing parameter convergence nor specifying proposal distributions is required, which decreases both the preparation necessary and the time involved. The proposed model is a simple one with few parameters, so WLB can be effectively accommodated. An actual example using sports data from sumo wrestling is presented to verify the efficacy of the proposed method.     

新农村建设中少数民族地方行政组织的改革及其问题

进行社会主义新农村建设,应注意农村综合改革中地方行政组织的改革,而在少数民族地区进行地方行政组织的改革更是一个艰巨任务。在采取社会学的文献调查、实地调查和向地方政府问卷调查等方法基础上,在阐明中国农村行政体制改革的内容及其存在问题的同时,着重分析内蒙古少数民族农村牧区基层行政组织改革的目标和任务。     

Bayesian response adaptive randomization using longitudinal outcomes

The response adaptive randomization (RAR) method is used to increase the number of patients assigned to more efficacious treatment arms in clinical trials. In many trials evaluating longitudinal patient outcomes, RAR methods based only on the final measurement may not benefit significantly from RAR because of its delayed initiation. We propose a Bayesian RAR method to improve RAR performance by accounting for longitudinal patient outcomes (longitudinal RAR). We use a Bayesian linear mixed effects model to analyze longitudinal continuous patient outcomes for calculating a patient allocation probability. In addition, we aim to mitigate the loss of statistical power because of large patient allocation imbalances by embedding adjusters into the patient allocation probability calculation. Using extensive simulation we compared the operating characteristics of our proposed longitudinal RAR method with those of the RAR method based only on the final measurement and with an equal randomization method. Simulation results showed that our proposed longitudinal RAR method assigned more patients to the presumably superior treatment arm compared with the other two methods. In addition, the embedded adjuster effectively worked to prevent extreme patient allocation imbalances. However, our proposed method may not function adequately when the treatment effect difference is moderate or less, and still needs to be modified to deal with unexpectedly large departures from the presumed longitudinal data model. Copyright © 2015 John Wiley & Sons, Ltd.     

Implications of urbanism for the use of local news media: effects of population concentration on types of news acquisition in Japan

The Internet, a global computer network enabling people to send and receive information anywhere in the world, also functions as a local medium of communication. This study focuses on the role of the Internet in transmitting local news and examines the effects of community population concentrations as socio-ecological environments on the use of local news media consumed online and offline. Data from 1367 respondents across 156 Japanese communities were used to analyze the relationships between type of community and type of news source. The findings suggest that people who live in highly populated communities tend more often to use the Internet to access local news, whereas those in less populated communities tend to use more traditional mass media. However, the results of this study did not show a relationship between population concentrations within communities and the acquisition of international news, nor did the social features of residents adequately explain the effects of population concentration on the acquisition of local news. These results are consistent with theoretical predictions based on network externalities, urbanism, and collective action. The findings indicate that local news consumption is embedded in local social contexts in a way that international news is not, reinforcing the importance of urbanism in the information age.     

Replacement policies for age and working numbers with random life cycle

It has been modeled for several replacement policies in literatures that the whole life cycle or operating interval of an operating unit should be finite rather than infinite as is done with the traditional method. However, it is more natural to consider the case in which the finite life cycle is a fluctuated parameter that could be used to estimate replacement times, which will be taken up in this article. For this, we first formulate a general model in which the unit is replaced at random age U, random time Y for the first working number, random life cycle S, or at failure X, whichever occurs first. The following models included in the general model, such that replacement done at age T when variable U is a degenerate distribution, and replacement done at working numbers N summed by number N of variable Y, are optimized. We obtain the total expected cost until replacement and the expected replacement cost rate for each model. Optimal age T, working number N, and a pair of (T, N) are discussed analytically and computed numerically.     

The evaluation of general non-centred orthant probabilities

Summary. The evaluation of the cumulative distribution function of a multivariate normal distribution is considered. The multivariate normal distribution can have any positive definite correlation matrix and any mean vector. The approach taken has two stages. In the first stage, it is shown how non-centred orthoscheme probabilities can be evaluated by using a recursive integration method. In the second stage, some ideas of Schläfli and Abrahamson are extended to show that any non-centred orthant probability can be expressed as differences between at most ( m −1)! non-centred orthoscheme probabilities. This approach allows an accurate evaluation of many multivariate normal probabilities which have important applications in statistical practice.     

Bayesian adaptive patient enrollment restriction to identify a sensitive subpopulation using a continuous biomarker in a randomized phase 2 trial

With the development of molecular targeted drugs, predictive biomarkers have played an increasingly important role in identifying patients who are likely to receive clinically meaningful benefits from experimental drugs (i.e., sensitive subpopulation) even in early clinical trials. For continuous biomarkers, such as mRNA levels, it is challenging to determine cutoff value for the sensitive subpopulation, and widely accepted study designs and statistical approaches are not currently available. In this paper, we propose the Bayesian adaptive patient enrollment restriction (BAPER) approach to identify the sensitive subpopulation while restricting enrollment of patients from the insensitive subpopulation based on the results of interim analyses, in a randomized phase 2 trial with time‐to‐endpoint outcome and a single biomarker. Applying a four‐parameter change‐point model to the relationship between the biomarker and hazard ratio, we calculate the posterior distribution of the cutoff value that exhibits the target hazard ratio and use it for the restriction of the enrollment and the identification of the sensitive subpopulation. We also consider interim monitoring rules for termination because of futility or efficacy. Extensive simulations demonstrated that our proposed approach reduced the number of enrolled patients from the insensitive subpopulation, relative to an approach with no enrollment restriction, without reducing the likelihood of a correct decision for next trial (no‐go, go with entire population, or go with sensitive subpopulation) or correct identification of the sensitive subpopulation. Additionally, the four‐parameter change‐point model had a better performance over a wide range of simulation scenarios than a commonly used dichotomization approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Dependence structures and asymptotic properties of Baker's distributions with fixed marginals

We investigate the properties of Baker's (2008) bivariate distributions with fixed marginals and their multivariate extensions. The properties include the weak convergence to the Fréchet–Hoeffding upper bound, the product-moment convergence, as well as the dependence structures TP₂ (totally positive of order 2), or MTP₂ (multivariate TP₂). In proving the weak convergence, a generalized local limit theorem for binomial distribution is provided.