On the α-risks for shewhart control charts

The performance of the usual Shewhart control charts for monitoring process means and variation can be greatly affected by nonnormal data or subgroups that are correlated. Define the α_k-risk for a Shewhart chart to be the probability that at least one “out-of-control” subgroup occurs in k subgroups when the control limits are calculated from the k subgroups. Simulation results show that the α_k-risks can be quite large even for a process with normally distributed, independent subgroups. When the data are nonnormal, it is shown that the α_k-risk increases dramatically. A method is also developed for simulating an “in-control” process with correlated subgroups from an autoregressive model. Simulations with this model indicate marked changes in the α_k-risks for the Shewhart charts utilizing this type of correlated process data. Therefore, in practice a process should be investigated thoroughly regarding whether or not it is generating normal, independent data before out-of-control points on the control charts are interpreted to be due to some real assignable cause.     

数量化Ⅱ类弓形效应修正方法及应用

对应分析在对定性数据进行数量化处理过程中出现了“弓形效应”，关于对应分析的“弓形效应”的修正方法已经有了丰富的研究成果，避免了可能错误的分析结果，对理论界和应用领域都有重要意义。数量化Ⅱ类是关于定性数据的一种判别分析方法，在国内外已被广泛应用。本文通过大量模拟数据研究发现，数量化Ⅱ类在对定性数据进行数量化过程中出现了“弓形效应”，降低了正判别率，同时不能正确再现原始数据信息，得出与原始数据信息不符的错误分析结果，为修正“弓形效应”，提出了二阶段判别分析法，并从正判别率和对原始数据再现程度两个方面对数量化Ⅱ类与二阶段判别分析法进行了比较，同时将二阶段判别分析法运用到个人信用评级中，发现二阶段判别分析法的判别性能优于数量化Ⅱ类。     

“What If” analysis: Benefits of utilizing a “What If” analysis in excel

The “What If” analysis is applicablein research and heuristic situations that utilize statistical significance testing. One utility for the “What If” is in a pedagogical perspective; the “What If” analysis provides professors an interactive tool that visually represents examples of what statistical significance testing entails and the variables that affect the commonly misinterpreted p_CALCULATED value. In order to develop a strong understanding of what affects the p_CALCULATED value, the students tangibly manipulate data within the Excel sheet to create a visualize representation that explicitly demonstrates how variables affect the p_CALCULATED value. The second utility is primarily applicable to researchers. “What If” analysis contributes to research in two ways: (1) a “What If” analysis can be run a priori to estimate the sample size a researcher may wish to use for his study; and (2) a “What If” analysis can be run a posteriori to aid in the interpretation of results. If used, the “What If” analysis provides researchers with another utility that enables them to conduct high-quality research and disseminate their results in an accurate manner.     

Estimand framework: Are we asking the right questions? A case study in the solid tumor setting

The estimand framework requires a precise definition of the clinical question of interest (the estimand) as different ways of accounting for “intercurrent” events post randomization may result in different scientific questions. The initiation of subsequent therapy is common in oncology clinical trials and is considered an intercurrent event if the start of such therapy occurs prior to a recurrence or progression event. Three possible ways to account for this intercurrent event in the analysis are to censor at initiation, consider recurrence or progression events (including death) that occur before and after the initiation of subsequent therapy, or consider the start of subsequent therapy as an event in and of itself. The new estimand framework clarifies that these analyses address different questions (“does the drug delay recurrence if no patient had received subsequent therapy?” vs “does the drug delay recurrence with or without subsequent therapy?” vs “does the drug delay recurrence or start of subsequent therapy?”). The framework facilitates discussions during clinical trial planning and design to ensure alignment between the key question of interest, the analysis, and interpretation. This article is a result of a cross-industry collaboration to connect the International Council for Harmonisation E9 addendum concepts to applications. Data from previously reported randomized phase 3 studies in the renal cell carcinoma setting are used to consider common intercurrent events in solid tumor studies, and to illustrate different scientific questions and the consequences of the estimand choice for study design, data collection, analysis, and interpretation.     

On Galton's Change From “Reversion” to “Regression”

Galton's first work on regression probably led him to think of it as a unidirectional, genetic process, which he called “reversion.” A subsequent experiment on family heights made him realize that the phenomenon was symmetric and nongenetic. Galton then abandoned “reversion” in favor of “regression.” Final confirmation was provided through Dickson's mathematical analysis and Galton's examination of height data on brothers.     

Depth functions as measures of representativeness

Data depth provides a natural means to rank multivariate vectors with respect to an underlying multivariate distribution. Most existing depth functions emphasize a centre-outward ordering of data points, which may not provide a useful geometric representation of certain distributional features, such as multimodality, of concern to some statistical applications. Such inadequacy motivates us to develop a device for ranking data points according to their “representativeness” rather than “centrality” with respect to an underlying distribution of interest. Derived essentially from a choice of goodness-of-fit test statistic, our device calls for a new interpretation of “depth” more akin to the concept of density than location. It copes particularly well with multivariate data exhibiting multimodality. In addition to providing depth values for individual data points, depth functions derived from goodness-of-fit tests also extend naturally to provide depth values for subsets of data points, a concept new to the data-depth literature.     

基于非线性主成分和聚类分析的综合评价方法

针对传统主成分在处理非线性问题上的不足，阐述了传统方法在数据无量纲化中“中心标准化”的缺点和处理“线性”数据时的缺陷，给出了数据无量纲化和处理“非线性”数据时的改进方法，并建立了一种基于“对数中心化”的非线性主成分分析和聚类分析的新的综合评价方法。实验表明，该方法能有效地处理非线性数据。     

Comparing first hitting time and proportional hazards regression models

Cox's widely used semi-parametric proportional hazards (PH) regression model places restrictions on the possible shapes of the hazard function. Models based on the first hitting time (FHT) of a stochastic process are among the alternatives and have the attractive feature of being based on a model of the underlying process. We review and compare the PH model and an FHT model based on a Wiener process which leads to an inverse Gaussian (IG) regression model. This particular model can also represent a “cured fraction” or long-term survivors. A case study of survival after coronary artery bypass grafting is used to examine the interpretation of the IG model, especially in relation to covariates that affect both of its parameters.     

A Multivariate Group Runs Control Chart for Process Dispersion

In this article, control charts for bivariate as well as for multivariate normal data are proposed to detect a shift in the process variability. Methods of obtaining design parameters and procedures of implementing the proposed charts are discussed. Performance of the proposed charts is compared with some existing control charts. It is verified that the proposed charts significantly reduce the out of control “average run length” (ARL) as compared to other charts considered in the study. Also, when the process variability decreases (process improvement), it is verified that the ARL of the proposed multivariate control chart increases as compared to other charts considered in the study.     

Estimation of Some Nonlinear Panel Data Models With Both Time-Varying and Time-Invariant Explanatory Variables

The so-called “fixed effects” approach to the estimation of panel data models suffers from the limitation that it is not possible to estimate the coefficients on explanatory variables that are time-invariant. This is in contrast to a “random effects” approach, which achieves this by making much stronger assumptions on the relationship between the explanatory variables and the individual-specific effect. In a linear model, it is possible to obtain the best of both worlds by making random effects-type assumptions on the time-invariant explanatory variables while maintaining the flexibility of a fixed effects approach when it comes to the time-varying covariates. This article attempts to do the same for some popular nonlinear models.     

On derivaton and application of aic as a data-based criterion for histograms

In this paper a derivation of the Akaike's Information Criterion (AIC) is presented to select the number of bins of a histogram given only the data, showing that AIC strikes a balance between the “bias” and “variance” of the histogram estimate. Consistency of the criterion is discussed, an asymptotically optimal histogram bin width for the criterion is derived and its relationship to penalized likelihood methods is shown. A formula relating the optimal number of bins for a sample and a sub-sample obtained from it is derived. A number of numerical examples are presented.     

Bayesian break-point forecasting in parallel time series,with application to university admissions

A regular supply of applicants to Queen's University in Kingston, Ontario is provided by 65 high schools. Each high school can be characterized by a series of grading standards which change from year to year. To aid admissions decisions, it is desirable to forecast the current year's grading standards for all 65 high schools using grading standards estimated from past year's data. We develop and apply a Bayesian break-point time-series model that generates forecasts which involve smoothing across time for each school and smoothing across schools. “Break point” refers to a point in time which divides the past into the “old past” and the “recent past” where the yearly observations in the recent past are exchangeable with the observations in the year to be forecast. We show that this model works fairly well when applied to 11 years of Queen's University data. The model can be applied to other data sets with the parallel time-series structure and short history, and can be extended in several ways to more complicated structures.     

Computational precision in statistics: variances and covariances †

“Precision” may be thought of either as the closeness with which a reported value approximates a “true” value, or as the number of digits carried in computations, depending on context. With suitable formal definitions, it is shown that the precision of a reported value is the difference between the precision with which computations are performed and the “loss” in precision due to the computations. Loss in precision is a function of the quantity computed and of the algorithm used to compute it; in the case of the usual “computing formula” for variances and covariances, it is shown that the loss of precision is expected to be log k _i k _j where k _i , the reciprocal of the coefficient of variation, is the ratio of the mean to the standard deviation of the ith variable. When the precision of a reported value, the precision of computations, and the loss of precision due to the computations are expressed to the same base, all three quantities have the units of significant digits in the corresponding number system. Using this metric for “precision,” the expected precision of a computed (co)variance may be estimated in advance of the computation; for data reported in the paper, the estimates agree closely with observed precision. Implications are drawn for the programming of general-purpose statistical programs, as well as for users of existing programs, in order to minimize the loss of precision resulting from characteristics of the data, A nomograph is provided to facilitate the estimation of precision in binary, decimal, and hexadecimal digits.     

论统计指标的构造过程

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Who Forecasts Better?

This article suggests that the emphasis on forecast evaluations should be redirected from searching for “best” forecasters to finding those who are “better.” A new methodology is developed, and the results indicate that it is possible to identify “better” forecasters.     

环境“二维化”视角下的居民幸福感量化研究：来自中国CGSS数据的新证据

幸福不仅是影响人们行为的重要因素,更是人们生活追求的最终目标。本文基于中国综合社会调查（CGSS）数据,创新性地从环境“二维化”这一研究视角,将环境因素划分为两个维度,即客观存在的环境污染因素与居民主观的环境行为,采用优化的两阶段有序Probit回归模型,沿着“客观存在的环境污染因素——居民幸福感”和“居民幸福感——居民主观的环境行为”两条研究思路展开实证分析,在实证过程中引入控制变量及工具变量,同时对经济因素及地区因素可能导致的组群差异进行考量和比较。结果显示,无论是环境污染对居民幸福感,还是居民幸福感对居民环境行为,其影响均是显著的,且具有异质性;环境污染通过影响居民的身体健康、生活质量和社会活动对居民幸福感产生影响,而居民环境行为则因个体收入和居民幸福感程度的不同产生差异。本文对环境与居民幸福感之间的作用机制展开深入分析,为政府出台环境政策的制定、提升居民幸福感及居民环境行为贡献度奠定理论基础。     

Inference and Decision Making for 21st-Century Drug Development and Approval

ABSTRACT

The cost and time of pharmaceutical drug development continue to grow at rates that many say are unsustainable. These trends have enormous impact on what treatments get to patients, when they get them and how they are used. The statistical framework for supporting decisions in regulated clinical development of new medicines has followed a traditional path of frequentist methodology. Trials using hypothesis tests of “no treatment effect” are done routinely, and the p-value < 0.05 is often the determinant of what constitutes a “successful” trial. Many drugs fail in clinical development, adding to the cost of new medicines, and some evidence points blame at the deficiencies of the frequentist paradigm. An unknown number effective medicines may have been abandoned because trials were declared “unsuccessful” due to a p-value exceeding 0.05. Recently, the Bayesian paradigm has shown utility in the clinical drug development process for its probability-based inference. We argue for a Bayesian approach that employs data from other trials as a “prior” for Phase 3 trials so that synthesized evidence across trials can be utilized to compute probability statements that are valuable for understanding the magnitude of treatment effect. Such a Bayesian paradigm provides a promising framework for improving statistical inference and regulatory decision making.     

Statistical learning theory for fitting multimodal distribution to rainfall data: an application

The promising methodology of the “Statistical Learning Theory” for the estimation of multimodal distribution is thoroughly studied. The “tail” is estimated through Hill's, UH and moment methods. The threshold value is determined by nonparametric bootstrap and the minimum mean square error criterion. Further, the “body” is estimated by the nonparametric structural risk minimization method of the empirical distribution function under the regression set-up. As an illustration, rainfall data for the meteorological subdivision of Orissa, India during the period 1871–2006 are used. It is shown that Hill's method has performed the best for tail density. Finally, the combined estimated “body” and “tail” of the multimodal distribution is shown to capture the multimodality present in the data.     

A computer program for the design of group testing experiments

This paper describes a computer program GTEST for designing group testing experiments for classifying each member of a population of items as “good” or “defective”. The outcome of a test on a group of items is either “negative” (if all items in the group are good) or “positive” (if at least one of the items is defective, but it is not known which). GTEST is based on a Bayesian approach. At each stage, it attempts to maximize (nearly) the expected reduction in the “entropy”, which is a quantitative measure of the amount of uncertainty about the state of the items. The user controls the procedure through specification of the prior probabilities of being defective, restrictions on the construction of the test group, and priorities that are assigned to the items. The nominal prior probabilities can be modified adaptively, to reduce the sensitivity of the procedure to the proportion of defectives in the population.