On implementing Jeffreys' substitution likelihood for Bayesian inference concerning the medians of unknown distributions

When statisticians are uncertain as to which parametric statistical model to use to analyse experimental data, they will often resort to a non-parametric approach. The purpose of this paper is to provide insight into a simple approach to take when it is unclear as to the appropriate parametric model and plan to conduct a Bayesian analysis. I introduce an approximate, or substitution likelihood, first proposed by Harold Jeffreys in 1939 and show how to implement the approach combined with both a non-informative and an informative prior to provide a random sample from the posterior distribution of the median of the unknown distribution. The first example I use to demonstrate the approach is a within-patient bioequivalence design and then show how to extend the approach to a parallel group design.     

Optimal adaptive designs for acute oral toxicity assessment

Acute oral toxicity studies are used to assess the toxicity to experimental animals of a single dose of the substance under investigation, assigning the substance to one of a number of classes. Animal welfare concerns have led to the development of three adaptive designs as alternatives to the traditional fixed sample design. These lead to reductions in the number of animals required in total and in the number exposed to lethal doses. In this paper, we show how designs can be constructed to optimise utility functions combining the need to classify correctly with the desire to use a small number of animals. Constrained optimal designs are also obtained in which no animal is exposed to a dose higher than that at which a death has been observed. The optimal designs lead to the correct classification with high probability whilst reducing the expected number of animal deaths relative to existing adaptive designs.     

Estimation and Testing of Learning Curves

This article describes a new approach to learning curve estimation. Our approach is to formulate statistical procedures that conform to alternative learning curve theories. This leads to the development of nonlinear statistical models of the learning curves. For the three data sets analyzed, autocorrelation seems to be an important problem. Parameter estimates were derived using the maximum likelihood principle in the presence of first-order autocorrelation. Nonnested tests were used to select the appropriate formulation of the learning curve. Research conclusions are to use unit data when estimating a learning curve and to be prepared to treat autocorrelation if present.     

A modified two-stage randomized response model for estimating the proportion of stigmatized attribute

The survey related to stigmatized characteristics leads to the non-response problem if it is conducted according to classical (direct) methods, especially, developed for non-sensitive issues; therefore, it needs to be applied appropriate survey methodology to get a reliable response from respondents in incriminating issues. Randomized response model is one of the most recent methods which is attracting the attention of survey practitioners to deal with the problems of non-response because it protects the privacy of individuals in order to acquire the truthful response. The present work proposes a new two-stage randomized response model to get rid of misleading response or non-response due to the stigmatized nature of attribute under the study. The proposed randomized response model results in the unbiased estimator of population proportion possessing the sensitive attribute. The properties of the resultant estimator have been studied and empirical comparisons are performed to show its dominance over existing estimators. Suitable recommendations have been put forward to the survey practitioners.     

Replenishing the pipeline: A quantitative approach to optimising the sourcing of new projects

Large pharmaceutical companies maintain a portfolio of assets, some of which are projects under development while others are on the market and generating revenue. The budget allocated to R&D may not always be sufficient to fund all the available projects for development. Much attention has been paid to the selection of optimal subsets of available projects to fit within the available budget. In this paper, we argue the need for a forward-looking approach to portfolio decision-making. We develop a quantitative model that allows the portfolio management to evaluate the need for future inflow of new projects to achieve revenue at desired levels, often aspiring to a certain annual revenue growth. Optimisation methods are developed for the presented model, allowing an optimal choice of number, timing and type of projects to be added to the portfolio. The proposed methodology allows for a proactive approach to portfolio management, prioritisation, and optimisation. It provides a quantitatively based support for strategic decisions regarding the efforts needed to secure the future development pipeline and revenue stream of the company.     

中国教育收益率的长期变动趋势分析

本研究采用中国健康与营养调查1989-2009年的追踪数据,使用多层线性交互分类模型估计了全国教育收益率的总体变化趋势,并通过引入宏观经济发展指标来考察教育收益率变化的影响因素.结果表明,21世纪以来全国教育收益率并没有延续以往快速稳定增长的势头,中国市场转型过程中的制度变革和经济结构变化对教育收益率的变动都有显著影响.由于我国城乡分割的二元经济结构,本研究还比较了城镇和农村地区教育收益率变动趋势的差异,农村地区教育收益率先高后低反映了我国先农村后城市的改革开放进程.     

非均衡发展战略与中国城乡收入差距的关系——来自省级面板数据的经验分析

运用非均衡发展战略理论构建中国城乡收入差距成因的理论框架。利用2005—2008年中国省级的数据资料,建立了panel data模型,实证研究中国偏向城市的财政政策、金融政策、就业政策、贸易政策以及偏向城市的社会保障制度和公共产品供给制度对中国城乡收入差距的影响,研究表明：非均衡发展战略所衍生的一系列偏向城市的制度和政策是导致城乡收入差距的原因,逐步改革户籍制度,打破城乡二元体制,统筹城乡发展是缩小城乡收入差距的基础。     

Estimating age-specific incidence of dementia using prevalent cohort data

In prospective cohort studies individuals are usually recruited according to a certain cross-sectional sampling criterion. The prevalent cohort is defined as a group of individuals who are alive but possibly with disease at the beginning of the study. It is appealing to incorporate the prevalent cases to estimate the incidence rate of disease before the enrollment. The method of back calculation of incidence rate has been used to estimate the incubation time from HIV infection to AIDS. The time origin is defined as the time of HIV infection. In aging cohort studies, the primary time scale is age of disease onset, subjects have to survive certain years to be enrolled into the study, thus creating left truncation (delay entry). The current methods usually assume that either the disease incidence is rare or the excess mortality due to disease is small compared to the healthy subjects. By far the validity of the results based on these assumptions has not been examined. In this paper, a simple alternative method is proposed to estimate dementia incidence rate before enrollment using prevalent cohort data with left truncation. Furthermore simulations are used to examine the performance of the estimation of disease incidence under different assumptions of disease incidence rates and excess mortality hazards due to disease. As application, the method is applied to the prevalent cases of dementia from the Honolulu Asia Aging Study to estimate dementia incidence rate and to assess the effect of hypertension, Apoe 4 and education on dementia onset.     

R&D补贴、寻租与全要素生产率提升

R&D补贴一方面可以弥补研发活动外部性所产生的市场失灵,另一方面容易诱发寻租行为而削弱补贴效率,关于R&D补贴能否促进TFP提升尚未达成一致。本文从政府和企业互动视角着手构建两阶段动态博弈模型,演绎R&D补贴机制。研究发现,当R&D补贴强度高于某阈值后,容易诱使企业在创新策略选择中发送虚假信号,降低政府R&D补贴效率。进而利用中国省域面板数据检验不同强度R&D补贴对TFP的异质性影响,并探析寻租在R&D补贴与TFP之间的影响路径。实证结果表明,R&D补贴总体上对TFP具有负向影响,且补贴强度越高,负向作用越强;寻租是高额度R&D补贴抑制TFP提升的一个重要渠道。据此,创新政策实施过程中要及时调整对不同创新类型企业的补贴额度,防止长期高强度补贴引发寻租活动,确保企业所获取补贴与其实际需求相一致,有效促进全要素生产率提升。     

Hypothesis testing for the dispersion parameter of the hyper-Poisson regression model

The Poisson distribution is widely used to deal with count data, however, it is unable to capture the dispersion problems. The hyper-Poisson distribution is a particular case of the extended Conway–Maxwell distribution which takes into account the dispersion phenomena of the count data. The main motivation to consider this model is the possibility to link the mean to the regressor variables in very natural way to solve testing problems. So, this paper will be focalized in the gradient statistics to detect dispersions and to compare with the classical likelihood ratio statistic. Two illustrative applications are considered.     

How many ways can you look at a proportion?: cross-community vote transfers in Northern Ireland after the Belfast Agreement

Summary.  The single transferable vote is a method of election that allows voters to mark candidates in order of preference. Votes that are not required to elect a candidate are passed to the next candidate in the voter's order of preference. Results of this kind of election give us data about the degree to which voters of a given persuasion are willing to pass their vote to a candidate of a different persuasion. Measures of voters' willingness to pass a vote to a candidate of a different persuasion are of particular interest in places such as Northern Ireland, where communities differ by religion and national aspiration, and agreed new political institutions are based on cross-community power-sharing. How we quantify this voting data may depend on the questions that we want to answer, of course. But, to understand changes in how the voter orders her or his preference, one may need to ask several questions, and to quantify the results of the election in more than one way.     

Bayesian Analysis for a Redundant Repairable System with Imperfect Coverage

System characteristics of a redundant repairable system with two primary units and one standby are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor is the same for an operating unit failure as that for a standby unit failure. Times to failure and times to repair of the operating and standby units are assumed to follow exponential distributions. When times to failure and times to repair with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.     

城市基本公共服务面向农民工开放度测量研究

2016年1月起实施的《居住证暂行条例》从根本上摒弃了农民工享有城市基本公共服务的制度桎梏，但农民工实际所能享有的水平尚取决于城市政府开放其公共服务的程度，包括“承诺”服务的领域多少和所设置的约束“条件”高低。本文以各城市居住证管理制度文件为依据，运用全国流动人口调查数据，测量城市基本公共服务面向农民工群体的开放度。结果显示：（1）城市基本公共服务全部领域超过一半面向农民工开放，开放度0.5076。即便在排他性服务领域，也超过1/3面向农民工开放，开放度达到0.3569，农民工开始实质性享有城市基本公共服务，但离平等权利仍有距离；（2）开放度在区域间的分布表现为东部城市低于中部城市更低于西部城市、直辖市低于省会城市更低于其他地级市，珠三角、长三角和京津冀城市低于三大经济圈外城市。相对发达的城市开放度更低，反映出开放度高低主要取决于城市政府的开放意愿而非提供服务的能力；（3）开放限制主要来源于“条件”约束，城市政府在排他性服务领域的承诺度0.7703，承诺服务的领域超过3/4。但约束度达0.4502，城市政府只向其中54.98%能满足约束条件的农民工开放所承诺的服务，源自约束条件的限制占到开放限制的60%以上。城市政府遵循居住证制度规范面向外来人口统一“承诺”服务，但通过“条件”约束选择性地限制了农民工获得城市基本公共服务的机会，农民工平等权利的最终实现尚需要政策制度的系统性配套改革。     

The use of finite mixture models to estimate the distribution of the health utilities index in the presence of a ceiling effect

Finite mixture models are flexible parametric models that allow one to describe complex probability distributions as a mixture of a small number of simple probability distributions. Measures of health status are often used to reflect a person's overall health. Such measures may be subject to a ceiling effect, in that the measure is unable to discern gradations in health status above the ceiling. The purpose of this paper is to illustrate the use of finite mixture models to describe the probability distribution of the Health Utilities Index, under the assumption that the HUI is subject to a ceiling effect. Mixture models with two through six components are fit to the HUI. Bayes factors were used to compare the evidence that the Canadian population of non-institutionalized residents is composed of four distinct subpopulations, and that a mixture of six Normal components is required to describe these four subpopulations.     

Restricted mean survival time as a summary measure of time‐to‐event outcome

Many clinical research studies evaluate a time‐to‐event outcome, illustrate survival functions, and conventionally report estimated hazard ratios to express the magnitude of the treatment effect when comparing between groups. However, it may not be straightforward to interpret the hazard ratio clinically and statistically when the proportional hazards assumption is invalid. In some recent papers published in clinical journals, the use of restricted mean survival time (RMST) or τ ‐year mean survival time is discussed as one of the alternative summary measures for the time‐to‐event outcome. The RMST is defined as the expected value of time to event limited to a specific time point corresponding to the area under the survival curve up to the specific time point. This article summarizes the necessary information to conduct statistical analysis using the RMST, including the definition and statistical properties of the RMST, adjusted analysis methods, sample size calculation, information fraction for the RMST difference, and clinical and statistical meaning and interpretation. Additionally, we discuss how to set the specific time point to define the RMST from two main points of view. We also provide developed SAS codes to determine the sample size required to detect an expected RMST difference with appropriate power and reconstruct individual survival data to estimate an RMST reference value from a reported survival curve.     

A Bayesian model for estimating the malaria transition probabilities considering individuals lost to follow-up

It is known that patients may cease participating in a longitudinal study and become lost to follow-up. The objective of this article is to present a Bayesian model to estimate the malaria transition probabilities considering individuals lost to follow-up. We consider a homogeneous population, and it is assumed that the considered period of time is small enough to avoid two or more transitions from one state of health to another. The proposed model is based on a Gibbs sampling algorithm that uses information of lost to follow-up at the end of the longitudinal study. To simulate the unknown number of individuals with positive and negative states of malaria at the end of the study and lost to follow-up, two latent variables were introduced in the model. We used a real data set and a simulated data to illustrate the application of the methodology. The proposed model showed a good fit to these data sets, and the algorithm did not show problems of convergence or lack of identifiability. We conclude that the proposed model is a good alternative to estimate probabilities of transitions from one state of health to the other in studies with low adherence to follow-up.     

Responsive design for household surveys: tools for actively controlling survey errors and costs

Summary.  Over the past few years surveys have expanded to new populations, have incorporated measurement of new and more complex substantive issues and have adopted new data collection tools. At the same time there has been a growing reluctance among many household populations to participate in surveys. These factors have combined to present survey designers and survey researchers with increased uncertainty about the performance of any given survey design at any particular point in time. This uncertainty has, in turn, challenged the survey practitioner's ability to control the cost of data collection and quality of resulting statistics. The development of computer-assisted methods for data collection has provided survey researchers with tools to capture a variety of process data ('paradata') that can be used to inform cost–quality trade-off decisions in realtime. The ability to monitor continually the streams of process data and survey data creates the opportunity to alter the design during the course of data collection to improve survey cost efficiency and to achieve more precise, less biased estimates. We label such surveys as 'responsive designs'. The paper defines responsive design and uses examples to illustrate the responsive use of paradata to guide mid-survey decisions affecting the non-response, measurement and sampling variance properties of resulting statistics.     

行政记录整合的贝叶斯分层记录链接模型及应用

记录链接的技术问题与统计理论密切相关,尤其是在建立记录链接分类规则时需要构建统计模型,识别关键变量以完成数据匹配。在贝叶斯框架下构建分层模型整合行政记录,通过多元回归可以实现匹配错误率的估计,而且一对一限制下的记录链接允许通过模块反映记录信息的来源变化,基于MCMC模拟的后验分布计算方便,有助于提高数据整合效率。     

Modifying a central composite design to model the process mean and variance when there are hard-to-change factors

Summary.  An important question within industrial statistics is how to find operating conditions that achieve some goal for the mean of a characteristic of interest while simultaneously minimizing the characteristic's process variance. Often, people refer to this kind of situation as the robust parameter design problem. The robust parameter design literature is rich with ways to create separate models for the mean and variance from this type of experiment. Many times time and/or cost constraints force certain factors of interest to be much more difficult to change than others. An appropriate approach to such an experiment restricts the randomization, which leads to a split-plot structure. The paper modifies the central composite design to allow the estimation of separate models for the characteristic's mean and variances under a split-plot structure. The paper goes on to discuss an appropriate analysis of the experimental results. It illustrates the methodology with an industrial experiment involving a chemical vapour deposition process for the manufacture of silicon wafers. The methodology was used to achieve a silicon layer thickness value of 485 Å while minimizing the process variation.     

Prediction for generalized linear models

Regression models are often used to make predictions. All the information needed is contained in the predictive distribution. However, this cannot be evaluated explicitly for most generalized linear models. We construct two approximations to this distribution and demonstrate their use on two sets of survival data, corresponding to the outcome of patients admitted to intensive care units and the survival times of leukaemia patients.Regression models are often used to make predictions. All the information needed is contained in the predictive distribution. However, this cannot be evaluated explicitly for most generalized linear models. We construct two approximations to this distribution and demonstrate their use on two sets of survival data, corresponding to the outcome of patients admitted to intensive care units and the survival times of leukaemia patients.Regression models are often used to make predictions. All the information needed is contained in the predictive distribution. However, this cannot be evaluated explicitly for most generalized linear models. We construct two approximations to this distribution and demonstrate their use on two sets of survival data, corresponding to the outcome of patients admitted to intensive care units and the survival times of leukaemia patients.Regression models are often used to make predictions. All the information needed is contained in the predictive distribution. However, this cannot be evaluated explicitly for most generalized linear models. We construct two approximations to this distribution and demonstrate their use on two sets of survival data, corresponding to the outcome of patients admitted to intensive care units and the survival times of leukaemia patients.