Optimal nonparametric estimator of the area under ROC curve based on clustered data

Abstract

In diagnostic trials, clustered data are obtained when several subunits of the same patient are observed. Intracluster correlations need to be taken into account when analyzing such clustered data. A nonparametric method has been proposed by Obuchowski (1997 Obuchowski, N. A. 1997. Nonparametric analysis of clustered ROC curve data. Biometrics 53 (2):567–78.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) to estimate the Receiver Operating Characteristic curve area (AUC) for such clustered data. However, Obuchowski’s estimator is not efficient as it gives equal weight to all pairwise rankings within and between cluster. In this paper, we propose a more efficient nonparametric AUC estimator with two sets of optimal weights. Simulation results show that the loss of efficiency of Obuchowski’s estimator for a single AUC or the AUC difference can be substantial when there is a moderate intracluster test correlation and the cluster size is large. The efficiency gain of our weighted AUC estimator for a single AUC or the AUC difference is further illustrated using the data from a study of screening tests for neonatal hearing.     

中国能源消费的组合预测

组合预测理论及建模技术对于信息不完备的复杂经济系统具有一定的实用性。鉴于能源消费系统的复杂性及非线性的特征,可利用中国能源消费量的历史数据,分别采用指数回归模型、多元回归模型及灰色模型建立中国能源消费系统的单项预测模型。之后,可采用标准差法进行非负权重分配,建立中国能源消费量的组合预测模型。分析结果表明,组合预测模型的精度高于单项预测模型。进而可应用该模型对中国未来10年的能源消费量进行预测。     

基于区间数的PROMETHEE Ⅱ方法中权重确定

本文引入一种新的区间数距离测度,扩展了可直接处理特征空间为区间数的PROMETHEE Ⅱ多属性决策方法。并在分析属性加权向量ω与最终综合优先序值之间关系的同时,提出了一种基于区间数的PROMETHEE Ⅱ方法的属性权重ω确定原理。应用实例表明了该方法的可行性和有效性,具有推广应用价值。     

Bayesian weighted inference from surveys

Data from large surveys are often supplemented with sampling weights that are designed to reflect unequal probabilities of response and selection inherent in complex survey sampling methods. We propose two methods for Bayesian estimation of parametric models in a setting where the survey data and the weights are available, but where information on how the weights were constructed is unavailable. The first approach is to simply replace the likelihood with the pseudo likelihood in the formulation of Bayes theorem. This is proven to lead to a consistent estimator but also leads to credible intervals that suffer from systematic undercoverage. Our second approach involves using the weights to generate a representative sample which is integrated into a Markov chain Monte Carlo (MCMC) or other simulation algorithms designed to estimate the parameters of the model. In the extensive simulation studies, the latter methodology is shown to achieve performance comparable to the standard frequentist solution of pseudo maximum likelihood, with the added advantage of being applicable to models that require inference via MCMC. The methodology is demonstrated further by fitting a mixture of gamma densities to a sample of Australian household income.     

Minimax weights for generalised M‐estimation in biased regression models

The authors consider the construction of weights for Generalised M‐estimation. Such weights, when combined with appropriate score functions, afford protection from biases arising through incorrectly specified response functions, as well as from natural variation. The authors obtain minimax fixed weights of the Mallows type under the assumption that the density of the independent variables is correctly specified, and they obtain adaptive weights when this assumption is relaxed. A simulation study indicates that one can expect appreciable gains in precision when the latter weights are used and the various sources of model uncertainty are present.     

热天平法水合石灰脱硫实验研究

利用热天平进行水合石灰脱硫实验研究。结果表明：对于不同水合石灰作为吸收剂，石灰中杂质虽然能提高吸收剂活性，但其中氧化钙的含量对于脱硫率起决定作用；吸收剂对于CO2的吸收规律与SO2的不同，吸收剂中水固比越大，吸收剂吸收CO2的量先增加然后不变甚至降低；而对于SO2水固比越大，吸收剂吸收SO2的量越大，所以水固比对于脱硫率有一定的影响；当烟气中含有CO2时，吸收剂转化率提高，脱硫率降低。     

Enriched biplots for canonical correlation analysis

This paper discusses biplots of the between-set correlation matrix obtained by canonical correlation analysis. It is shown that these biplots can be enriched with the representation of the cases of the original data matrices. A representation of the cases that is optimal in the generalized least squares sense is obtained by the superposition of a scatterplot of the canonical variates on the biplot of the between-set correlation matrix. Goodness of fit statistics for all correlation and data matrices involved in canonical correlation analysis are discussed. It is shown that adequacy and redundancy coefficients are in fact statistics that express the goodness of fit of the original data matrices in the biplot. The within-set correlation matrix that is represented in standard coordinates always has a better goodness of fit than the within-set correlation matrix that is represented in principal coordinates. Given certain scalings, the scalar products between variable vectors approximate correlations better than the cosines of angles between variable vectors. Several data sets are used to illustrate the results.     

综合评价模型权重确定方法研究

目前,众多学者对信息化、城市化、项目选优等进行评价时习惯上采用单一的主观赋权或客观赋权方法,主观赋权和客观赋权结合评价无疑将会提高评价结果的可靠性。实践表明在对煤炭资源型城市城市化评价时,采用局部权重法取得了良好的评价结果。     

一类振荡奇异积分算子的加权模不等式

本文考虑一类振荡奇异积分算子在L~p(R~n)上的加权模不等式,得到几个结果.     

中部六省雾霾压力动态综合评价模型与实证

为了验证动态综合评价模型在雾霾压力综合评价中的适用性,利用中部六省2005—2013年的相关数据,考察其雾霾压力状况及影响因素。结果发现:中部六省的雾霾压力指数呈现动态上升趋势,且呈现不同的动态演变特征,湖北和山西两省体现为"先改善、再恶化、再改善"的特征,安徽和河南两省为"先恶化、再改善",而湖南和江西两省呈现"波浪式上升"波动特征。资源因素、治理因素、城市化因素和工业化因素对雾霾的影响依次递减。根据评价结果,提出了改善雾霾的建议。