CUSUM Hypothesis Tests and Alternative Response Probabilities for Finite Poisson Trials

This article develops a new cumulative sum statistic to identify aberrant behavior in a sequentially administered multiple-choice standardized examination. The examination responses can be described as finite Poisson trials, and the statistic can be used for other applications which fit this framework. The standardized examination setting uses a maximum likelihood estimate of examinee ability and an item response theory model. Aberrant and non aberrant probabilities are computed by an odds ratio analogous to risk adjusted CUSUM schemes. The significance level of a hypothesis test, where the null hypothesis is non-aberrant examinee behavior, is computed with Markov chains. A smoothing process is used to spread probabilities across the Markov states. The practicality of the approach to detect aberrant examinee behavior is demonstrated with results from both simulated and empirical data.     

Normal mixture method for stock daily returns over different sub-periods

In this paper, the normal mixture model, as an alternative distribution, is utilized to represent the characteristics of stock daily returns over different bull and bear markets. Firstly, we conduct the normality test for the return data and compare the Kolmogorov-Smirnov statistics of normal mixture models with different components. Secondly, we analyze the likely reasons why parameters change over different sub-periods. Our empirical examination proves that majority of the data series reject the normality assumption and mixture models with three components can model the behavior of daily returns more appropriately and steadily. This result has both statistical and economic significance.     

Multivariate multilevel analyses of examination results

Summary. In the study of examination results much interest centres on comparisons of curriculum subjects entered and the correlation between these at individual and institution level based on data where not every individual takes all subjects. Such `missing' data are not missing at random because individuals deliberately select subjects that they wish to study according to criteria that will be associated with their performance. In this paper we propose multivariate multilevel models for the analysis of such data, adjusting for such subject selection effects as well as for prior achievement. This then enables more appropriate institutional comparisons and correlation estimates. We analyse A- and AS-level results in different mathematics papers of 52 587 students from 2592 institutions in England in 1997. Although this paper is concerned largely with methodology, substantive findings emerge on the effects of gender, age, intakes of General Certificate of Education pupils, examination board and establishment type for A- and AS-level mathematics.     

On the analysis of unbalanced two-level supersaturated designs via generalized linear models

Supersaturated designs (SSDs) are factorial designs in which the number of experimental runs is smaller than the number of parameters to be estimated in the model. While most of the literature on SSDs has focused on balanced designs, the construction and analysis of unbalanced designs has not been developed to a great extent. Recent studies discuss the possible advantages of relaxing the balance requirement in construction or data analysis of SSDs, and that unbalanced designs compare favorably to balanced designs for several optimality criteria and for the way in which the data are analyzed. Moreover, the effect analysis framework of unbalanced SSDs until now is restricted to the central assumption that experimental data come from a linear model. In this article, we consider unbalanced SSDs for data analysis under the assumption of generalized linear models (GLMs), revealing that unbalanced SSDs perform well despite the unbalance property. The examination of Type I and Type II error rates through an extensive simulation study indicates that the proposed method works satisfactorily.     

A new process for modeling heartbeat signals during exhaustive run with an adaptive estimator of its fractal parameters

This paper is devoted to a new study of the fractal behavior of heartbeats during a marathon. Such a case is interesting since it allows the examination of heart behavior during a very long exercise in order to reach reliable conclusions on the long-term properties of heartbeats. Three points of this study can be highlighted. First, the whole race heartbeats of each runner are automatically divided into several stages where the signal is nearly stationary and these stages are detected with an adaptive change points detection method. Secondly, a new process called the locally fractional Gaussian noise (LFGN) is proposed to fit such data. Finally, a wavelet-based method using a specific mother wavelet provides an adaptive procedure for estimating low frequency and high frequency fractal parameters as well as the corresponding frequency bandwidths. Such an estimator is theoretically proved to converge in the case of LFGNs, and simulations confirm this consistency. Moreover, an adaptive chi-squared goodness-of-fit test is also built, using this wavelet-based estimator. The application of this method to marathon heartbeat series indicates that the LFGN fits well data at each stage and that the low frequency fractal parameter increases during the race. A detection of a too large low frequency fractal parameter during the race could help prevent the too frequent heart failures occurring during marathons.     

ROBUST NON-PARAMETRIC ESTIMATION OF GENOTYPE–PHENOTYPE RELATIONSHIPS IN HUMAN PEDIGREES

Non‐parametric estimation of functional relationships is an important part of data analysis, particularly in the exploratory stages. This paper considers non‐parametric estimation of the mean functions in family studies using weighted robust estimating equations while retaining a fully parametric model for the covariance structure. The proposed procedure allows an exploratory examination of complex pedigree data that is an invaluable aid in determining appropriate models. This is illustrated by an examination of the relationship between IQ and the level of a particular protein in individuals collected as part of a large family study.     

A statistical algorithm for detecting cognitive plateaus in Alzheimer’s disease

Repeated neuropsychological measurements, such as mini-mental state examination (MMSE) scores, are frequently used in Alzheimer’s disease (AD) research to study change in cognitive function of AD patients. A question of interest among dementia researchers is whether some AD patients exhibit transient “plateaus” of cognitive function in the course of the disease. We consider a statistical approach to this question, based on irregularly spaced repeated MMSE scores. We propose an algorithm that formalizes the measurement of an apparent cognitive plateau, and a procedure to evaluate the evidence of plateaus in AD using this algorithm based on applying the algorithm to the observed data and to data sets simulated from a linear mixed model. We apply these methods to repeated MMSE data from the Michigan Alzheimer’s Disease Research Center, finding a high rate of apparent plateaus and also a high rate of false discovery. Simulation studies are also conducted to assess the performance of the algorithm. In general, the false discovery rate of the algorithm is high unless the rate of decline is high compared with the measurement error of the cognitive test. It is argued that the results are not a problem of the specific algorithm chosen, but reflect a lack of information concerning the presence of plateaus in the data.     

关于综合运用Benford 法则和面板模型检测统计数据质量的研究

 本文介绍了如何利用Benford 法则来检测统计数据质量的一般方法。在此基础上,进一步探讨了如何将其与面板模型相结合从而找出可能存在质量问题的具体地区和时间序列数据的方法。并利用上述方法对我国多个国家级开发区的主要经济指标的数据质量进行了实证分析。     

有序响应变量的贝叶斯模型选择及其在COPD疾病防治中的应用

慢性阻塞性肺病(COPD)是一种发病率、死亡率都非常高的疾病，且COPD的诊断和严重程度分级依赖于肺功能的检查，但是由于肺功能检查仪器价格昂贵，使得这项检查在很多经济欠发达地区尤其是农村基层医院并没有普及。本文基于有序响应变量模型致力于研究一种便于基层和社区使用的可以初步判别COPD病情的模型，以期提高我国基层和社区的COPD 防治水平。利用贝叶斯变量选择方法和数据增强的潜变量策略得到了易于实施的Gibbs后验抽样算法。数值模拟分析进一步说明了本文提出的有序响应变量贝叶斯模型选择方法的有效性，实例分析得到了易于判别COPD严重程度的稀疏模型。     

On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process

Data envelopment analysis (DEA) is a deterministic econometric model for calculating efficiency by using data from an observed set of decision-making units (DMUs). We propose a method for calculating the distribution of efficiency scores. Our framework relies on estimating data from an unobserved set of DMUs. The model provides posterior predictive data for the unobserved DMUs to augment the frontier in the DEA that provides a posterior predictive distribution for the efficiency scores. We explore the method on a multiple-input and multiple-output DEA model. The data for the example are from a comprehensive examination of how nursing homes complete a standardized mandatory assessment of residents.     

A class of linear transformation models for interval censored data with a cured proportion

Interval-censored data arise due to a sequence random examination such that the failure time of interest occurs in an interval. In some medical studies, there exist long-term survivors who can be considered as permanently cured. We consider a mixed model for the uncured group coming from linear transformation models and cured group coming from a logistic regression model. For the inference of parameters, an EM algorithm is developed for a full likelihood approach. To investigate finite sample properties of the proposed method, simulation studies are conducted. The approach is applied to the National Aeronautics and Space Administration’s hypobaric decompression sickness data.     

Use of a historical control group in a noninferiority trial assessing a new antibacterial treatment: A case study and discussion of practical implementation aspects

When recruitment into a clinical trial is limited due to rarity of the disease of interest, or when recruitment to the control arm is limited due to ethical reasons (eg, pediatric studies or important unmet medical need), exploiting historical controls to augment the prospectively collected database can be an attractive option. Statistical methods for combining historical data with randomized data, while accounting for the incompatibility between the two, have been recently proposed and remain an active field of research. The current literature is lacking a rigorous comparison between methods but also guidelines about their use in practice. In this paper, we compare the existing methods based on a confirmatory phase III study design exercise done for a new antibacterial therapy with a binary endpoint and a single historical dataset. A procedure to assess the relative performance of the different methods for borrowing information from historical control data is proposed, and practical questions related to the selection and implementation of methods are discussed. Based on our examination, we found that the methods have a comparable performance, but we recommend the robust mixture prior for its ease of implementation.     

How Often Likelihood Ratios are Misleading in Sequential Trials

How often would investigators be misled if they took advantage of the likelihood principle and used likelihood ratios—which need not be adjusted for multiple looks at the data—to frequently examine accumulating data? The answer, perhaps surprisingly, is not often. As expected, the probability of observing misleading evidence does increase with each additional examination. However, the amount by which this probability increases converges to zero as the sample size grows. As a result, the probability of observing misleading evidence remains bounded—and therefore controllable—even with an infinite number of looks at the data. Here we use boundary crossing results to detail how often misleading likelihood ratios arise in sequential designs. We find that the probability of observing a misleading likelihood ratio is often much less than its universal bound. Additionally, we find that in the presence of fixed-dimensional nuisance parameters, profile likelihoods are to be preferred over estimated likelihoods which result from replacing the nuisance parameters by their global maximum likelihood estimates.     

Holistic trajectories: a study of combined employment, housing and family careers by using multiple-sequence analysis

Summary.  Social science applications of sequence analysis have thus far involved the development of a typology on the basis of an analysis of one or two variables which have had a relatively low number of different states. There is a yet unexplored potential for sequence analysis to be applied to a greater number of variables and thereby a much larger state space. The development of a typology of employment experiences, for example, without reference to data on changes in housing, marital and family status is arguably inadequate. The paper demonstrates the use of sequence analysis in the examination of multivariable combinations of status as they change over time and shows that this method can provide insights that are difficult to achieve through other analytic methods. The data that are examined here provide support to intuitive understandings of clusters of common experiences which are both life course specific and related to socio-economic factors. Housing tenure is found to be of key importance in understanding the holistic trajectories that are examined. This suggests that life course trajectories are sharply differentiated by experience of social housing.     

Analysis of Irish third-level college applications data

Summary.  The Irish college admissions system involves prospective students listing up to 10 courses in order of preference on their application. Places in third-level educational institutions are subsequently offered to the applicants on the basis of both their preferences and their final second-level examination results. The college applications system is a large area of public debate in Ireland. Detractors suggest that the process creates artificial demand for 'high profile' courses, causing applicants to ignore their vocational callings. Supporters argue that the system is impartial and transparent. The Irish college degree applications data from the year 2000 are analysed by using mixture models based on ranked data models to investigate the types of application behaviour that are exhibited by college applicants. The results of this analysis show that applicants form groups according to both the discipline and the geographical location of their course choices. In addition, there is evidence of the suggested 'points race' for high profile courses. Finally, gender emerges as an influential factor when studying course choice behaviour.     

A Critical Look at Some Analyses of Major League Baseball Salaries

At a data analysis exposition sponsored by the Section on Statistical Graphics of the ASA in 1988, 15 groups of statisticians analyzed the same data about salaries of major league baseball players. By examining what they did, what worked, and what failed, we can begin to learn about the relative strengths and weaknesses of different approaches to analyzing data. The data are rich in difficulties. They require reexpression, contain errors and outliers, and exhibit nonlinear relationships. They thus pose a realistic challenge to the variety of data analysis techniques used. The analysis groups chose a wide range of model-fitting methods, including regression, principal components, factor analysis, time series, and CART. We thus have an effective framework for comparing these approaches so that we can learn more about them. Our examination shows that approaches commonly identified with Exploratory Data Analysis are substantially more effective at revealing the underlying patterns in the data and at building parsimonious, understandable models that fit the data well. We also find that common data displays, when applied carefully, are often sufficient for even complex analyses such as this.     

A marginalized diffusion model for estimating age at first lower endoscopy use from current status data

Summary.  We propose an approach for estimating the age at first lower endoscopy examination from current status data that were collected via two series of cross-sectional surveys. To model the national probability of ever having a lower endoscopy examination, we incorporate birth cohort effects into a mixed influence diffusion model. We link a state-specific model to the national level diffusion model by using a marginalized modelling approach. In future research, results from our model will be used as microsimulation model inputs to estimate the contribution of endoscopy examinations to observed changes in colorectal cancer incidence and mortality.     

Measuring Usage: A Comprehensive Analysis of a Social Work Journal Collection

Abstract

This study examines what can be learned about a library’s electronic social work journal collection from usage statistics, survey data, faculty publications, and an examination of open access (OA) availability. A collections analysis was completed using data from two sources: a custom report by 1Science and results of a faculty survey on top journals for teaching. After creating a list of journals important to social work, top journals were identified by article downloads, faculty-authored publications, and references to faculty-authored papers. A publications analysis using faculty websites and author searches in Web of Science was also completed, to provide local, contextual data. SHERPA/RoMEO was used to determine the journals’ OA level and archiving policy. Library coverage for the journals was also included in the analysis. Results show that the McGill University Library has access to almost all of the journals identified as important to social work. Nearly one-third of publications authored by the McGill University School of Social Work since 2006 are OA, and more than half of the faculty in the school have at least one article published in an OA journal. While this is a good start for librarians who want to help faculty and students understand OA publishing and access, there is room for outreach in this area. While these results will aid librarians supporting faculty, students, and practitioners in the field of social work, a secondary aim of the study is to demonstrate a method that can be used by librarians undertaking similar analyses in other fields.     

Regression Modeling with Recurrent Events and Time-Dependent Interval-Censored Marker Data

In life history studies involving patients with chronic diseases it is often of interest to study the relationship between a marker process and a more clinically relevant response process. This interest may arise from a desire to gain a better understanding of the underlying pathophysiology, a need to evaluate the utility of the marker as a potential surrogate outcome, or a plan to conduct inferences based on joint models. We consider data from a trial of breast cancer patients with bone metastases. In this setting, the marker process is a point process which records the onset times and cumulative number of bone lesions which reflects the extent of metastatic bone involvement. The response is also a point process, which records the times patients experience skeletal complications resulting from these bone lesions. Interest lies in assessing how the development of new bone lesions affects the incidence of skeletal complications. By considering the marker as an internal time-dependent covariate in the point process model for skeletal complications we develop and apply methods which allow one to express the association via regression. A complicating feature of this study is that new bone lesions are only detected upon periodic radiographic examination, which makes the marker processes subject to interval-censoring. A modified EM algorithm is used to deal with this incomplete data problem.     

A comparison of statistical methods for animal oncology studies

In pre-clinical oncology studies, tumor-bearing animals are treated and observed over a period of time in order to measure and compare the efficacy of one or more cancer-intervention therapies along with a placebo/standard of care group. A data analysis is typically carried out by modeling and comparing tumor volumes, functions of tumor volumes, or survival. Data analysis on tumor volumes is complicated because animals under observation may be euthanized prior to the end of the study for one or more reasons, such as when an animal's tumor volume exceeds an upper threshold. In such a case, the tumor volume is missing not-at-random for the time remaining in the study. To work around the non-random missingness issue, several statistical methods have been proposed in the literature, including the rate of change in log tumor volume and partial area under the curve. In this work, an examination and comparison of the test size and statistical power of these and other popular methods for the analysis of tumor volume data is performed through realistic Monte Carlo computer simulations. The performance, advantages, and drawbacks of popular statistical methods for animal oncology studies are reported. The recommended methods are applied to a real data set.