Modal non‐linear regression in the presence of Laplace measurement error

In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error. Starting with the modal regression procedure developed for the measurement error‐free case, a non‐trivial modification is made so that the modified version can effectively correct the potential bias caused by measurement error. Large sample properties of the proposed estimate, such as the convergence rate and the asymptotic normality, are thoroughly investigated. A simulation study and real data application are conducted to illustrate the satisfying finite sample performance of the proposed estimation procedure.     

Bayesian inference for zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables

Abstract

In the fields of internet financial transactions and reliability engineering, there could be more zero and one observations simultaneously. In this paper, considering that it is beyond the range where the conventional model can fit, zero-and-one-inflated geometric distribution regression model is proposed. Ingeniously introducing Pólya-Gamma latent variables in the Bayesian inference, posterior sampling with high-dimensional parameters is converted to latent variables sampling and posterior sampling with lower-dimensional parameters, respectively. Circumventing the need for Metropolis-Hastings sampling, the sample with higher sampling efficiency is obtained. A simulation study is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, a doctoral dissertation data set is analyzed to illustrate the practicability of the proposed method, research shows that zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables can achieve better fitting results.     

中国粮食增产的主要因素贡献分解与实证估算

已有测算中国粮食增产要素贡献率的方法存在虚增或低估某要素贡献率的缺陷,文章通过改进粮食增产贡献率测算方法实证估计了2003—2016年期间单产、播种面积和结构调整对中国粮食增产的贡献。结果表明,中国粮食实现“十二连增”的巨大成就主要是单产增长贡献,年均贡献率50%以上,播种面积和作物内部结构调整也是不可忽视的重要力量,年均贡献率分别为30%与10%以上。然而,未来中国粮食增产依靠播种面积扩大和结构调整的空间变窄,需要探索新的增产路径。     

A win ratio approach to comparing continuous non‐normal outcomes in clinical trials

Clinical trials are often designed to compare continuous non‐normal outcomes. The conventional statistical method for such a comparison is a non‐parametric Mann–Whitney test, which provides a P‐value for testing the hypothesis that the distributions of both treatment groups are identical, but does not provide a simple and straightforward estimate of treatment effect. For that, Hodges and Lehmann proposed estimating the shift parameter between two populations and its confidence interval (CI). However, such a shift parameter does not have a straightforward interpretation, and its CI contains zero in some cases when Mann–Whitney test produces a significant result. To overcome the aforementioned problems, we introduce the use of the win ratio for analysing such data. Patients in the new and control treatment are formed into all possible pairs. For each pair, the new treatment patient is labelled a ‘winner’ or a ‘loser’ if it is known who had the more favourable outcome. The win ratio is the total number of winners divided by the total numbers of losers. A 95% CI for the win ratio can be obtained using the bootstrap method. Statistical properties of the win ratio statistic are investigated using two real trial data sets and six simulation studies. Results show that the win ratio method has about the same power as the Mann–Whitney method. We recommend the use of the win ratio method for estimating the treatment effect (and CI) and the Mann–Whitney method for calculating the P‐value for comparing continuous non‐Normal outcomes when the amount of tied pairs is small. Copyright © 2016 John Wiley & Sons, Ltd.     

Modelling PK/QT relationships from Phase I dose‐escalation trials for drug combinations and developing quantitative risk assessments of clinically relevant QT prolongations

In current industry practice, it is difficult to assess QT effects at potential therapeutic doses based on Phase I dose‐escalation trials in oncology due to data scarcity, particularly in combinations trials. In this paper, we propose to use dose‐concentration and concentration‐QT models jointly to model the exposures and effects of multiple drugs in combination. The fitted models then can be used to make early predictions for QT prolongation to aid choosing recommended dose combinations for further investigation. The models consider potential correlation between concentrations of test drugs and potential drug–drug interactions at PK and QT levels. In addition, this approach allows for the assessment of the probability of QT prolongation exceeding given thresholds of clinical significance. The performance of this approach was examined via simulation under practical scenarios for dose‐escalation trials for a combination of two drugs. The simulation results show that invaluable information of QT effects at therapeutic dose combinations can be gained by the proposed approaches. Early detection of dose combinations with substantial QT prolongation is evaluated effectively through the CIs of the predicted peak QT prolongation at each dose combination. Furthermore, the probability of QT prolongation exceeding a certain threshold is also computed to support early detection of safety signals while accounting for uncertainty associated with data from Phase I studies. While the prediction of QT effects is sensitive to the dose escalation process, the sensitivity and limited sample size should be considered when providing support to the decision‐making process for further developing certain dose combinations. Copyright © 2016 John Wiley & Sons, Ltd.     

A search of maximum generalized resolution quaternary-code designs via integer linear programming

Quaternary-code (QC) designs, an attractive class of nonregular fractional factorial designs, have received much attention due to their theoretical elegance and practical applicability. Some recent works of QC designs revealed their good properties over their regular counterparts under commonly used criteria. We develop an optimization tool that can maximize the generalized resolution of a QC design of a given size. The problem can be recast as an integer linear programming (ILP) problem through a linear simplification that combines the \(k\)- and \(a\)-equations, even though the generalized resolution does not linearly depend on the aliasing indexes. The ILP surprisingly improves a class of \((1/16)\)th-fraction QC designs with higher generalized resolutions. It also applies to obtain some \((1/64)\)th-fraction QC designs with maximum generalized resolutions, and these QC designs generally have higher generalized resolutions than the regular designs of the same size.     

Functional Partial Linear Single‐index Model

This paper deals with the problem of predicting the real‐valued response variable using explanatory variables containing both multivariate random variable and random curve. The proposed functional partial linear single‐index model treats the multivariate random variable as linear part and the random curve as functional single‐index part, respectively. To estimate the non‐parametric link function, the functional single‐index and the parameters in the linear part, a two‐stage estimation procedure is proposed. Compared with existing semi‐parametric methods, the proposed approach requires no initial estimation and iteration. Asymptotical properties are established for both the parameters in the linear part and the functional single‐index. The convergence rate for the non‐parametric link function is also given. In addition, asymptotical normality of the error variance is obtained that facilitates the construction of confidence region and hypothesis testing for the unknown parameter. Numerical experiments including simulation studies and a real‐data analysis are conducted to evaluate the empirical performance of the proposed method.     

特征AHP在高校教师教学质量评定中的应用

本文针对高校教师教学质量的评定提出了一种特征层次分析法。首先通过分析教学质量的影响因素,建立三层层次分析模型。在其基础上引入特征法,选取特征群并确定特征群中个体的权重,利用反算法根据组合权重及方案层权重,求取准则层评定指标权重,避免了不同质指标间对比的不确定性,摒除了专家直接给出评定指标对比矩阵的主观性,减少了对教师评定过程的不一致性和不完备性。