Sample Size Requirements and Study Duration for Testing Main Effects and Interactions in Completely Randomized Factorial Designs When Time to Event is the Outcome

In this paper, we develop the methodology for designing clinical trials with any factorial arrangement when the primary outcome is time to event. We provide a matrix formulation for calculating the sample size and study duration necessary to test any effect with a prespecified type I error rate and power. Assuming that a time to event follows an exponential distribution, we describe the relationships between the effect size, the power, and the sample size. We present examples for illustration purposes. We provide a simulation study to verify the numerical calculations of the expected number of events and the duration of the trial. The change in the power produced by a reduced number of observations or by accruing no patients to certain factorial combinations is also described.     

Real-Time Prediction With U.K. Monetary Aggregates in the Presence of Model Uncertainty

A popular account for the demise of the U.K.’s monetary targeting regime in the 1980s blames the fluctuating predictive relationships between broad money and inflation and real output growth. Yet ex post policy analysis based on heavily revised data suggests no fluctuations in the predictive content of money. In this paper, we investigate the predictive relationships for inflation and output growth using both real-time and heavily revised data. We consider a large set of recursively estimated vector autoregressive (VAR) and vector error correction models (VECM). These models differ in terms of lag length and the number of cointegrating relationships. We use Bayesian model averaging (BMA) to demonstrate that real-time monetary policymakers faced considerable model uncertainty. The in-sample predictive content of money fluctuated during the 1980s as a result of data revisions in the presence of model uncertainty. This feature is only apparent with real-time data as heavily revised data obscure these fluctuations. Out-of-sample predictive evaluations rarely suggest that money matters for either inflation or real output. We conclude that both data revisions and model uncertainty contributed to the demise of the U.K.’s monetary targeting regime.     

Bayesian networks for imputation

Summary.  Bayesian networks are particularly useful for dealing with high dimensional statistical problems. They allow a reduction in the complexity of the phenomenon under study by representing joint relationships between a set of variables through conditional relationships between subsets of these variables. Following Thibaudeau and Winkler we use Bayesian networks for imputing missing values. This method is introduced to deal with the problem of the consistency of imputed values: preservation of statistical relationships between variables ( statistical consistency ) and preservation of logical constraints in data ( logical consistency ). We perform some experiments on a subset of anonymous individual records from the 1991 UK population census.     

Distance-Based Measures of Association with Applications in Relating Hyperspectral Images

We propose a distance-based method to relate two data sets. We define and study some measures of multivariate association based on distances between observations. The proposed approach can be used to deal with general data sets (e.g., observations on continuous, categorical or mixed variables). An application, using Hellinger distance, provides the relationships between two regions of hyperspectral images.     

BAYESIAN BETA REGRESSION: APPLICATIONS TO HOUSEHOLD EXPENDITURE DATA AND GENETIC DISTANCE BETWEEN FOOT-AND-MOUTH DISEASE VIRUSES

There is considerable interest in understanding how factors such as time and geographic distance between isolates might influence the evolutionary direction of foot‐and‐mouth disease. Genetic differences between viruses can be measured as the proportion of nucleotides that differ for a given sequence or gene. We present a Bayesian hierarchical regression model for the statistical analysis of continuous data with sample space restricted to the interval (0, 1). The data are modelled using beta distributions with means that depend on covariates through a link function. We discuss methodology for: (i) the incorporation of informative prior information into an analysis; (ii) fitting the model using Markov chain Monte Carlo sampling; (iii) model selection using Bayes factors; and (iv) semiparametric beta regression using penalized splines. The model was applied to two different datasets.     

Bayes methods in the ecological fallacy cntext:estimation of individual correlation from aggregate data

The ecological fallacy is related to Simpson's paradox (1951) where relationships among group means may be counterintuitive and substantially different from relationships within groups, where the groups are usually geographic entities such as census tracts. We consider the problem of estimating the correlation between two jointly normal random variables where only ecological data (group means) are available. Two empirical Bayes estimators and one fully Bayesian estimator are derived and compared with the usual ecological estimator, which is simply the Pearson correlation coefficient of the group sample means. We simulate the bias and mean squared error performance of these estimators, and also give an example employing a dataset where the individual level data are available for model checking. The results indicate superiority of the empirical Bayes estimators in a variety of practical situations where, though we lack individual level data, other relevant prior information is available.     

Adaptive modelling of dose–response relationships using smoothing splines

We consider the use of smoothing splines for the adaptive modelling of dose–response relationships. A smoothing spline is a nonparametric estimator of a function that is a compromise between the fit to the data and the degree of smoothness and thus provides a flexible way of modelling dose–response data. In conjunction with decision rules for which doses to continue with after an interim analysis, it can be used to give an adaptive way of modelling the relationship between dose and response. We fit smoothing splines using the generalized cross‐validation criterion for deciding on the degree of smoothness and we use estimated bootstrap percentiles of the predicted values for each dose to decide upon which doses to continue with after an interim analysis. We compare this approach with a corresponding adaptive analysis of variance approach based upon new simulations of the scenarios previously used by the PhRMA Working Group on Adaptive Dose‐Ranging Studies. The results obtained for the adaptive modelling of dose–response data using smoothing splines are mostly comparable with those previously obtained by the PhRMA Working Group for the Bayesian Normal Dynamic Linear model (GADA) procedure. These methods may be useful for carrying out adaptations, detecting dose–response relationships and identifying clinically relevant doses. Copyright © 2009 John Wiley & Sons, Ltd.     

Extended pairwise local alignment of wild card DNA/RNA sequences using dynamic programming

Optimal string alignment is used to discover evolutionary relationships or mutations in DNA/RNA or protein sequences. Errors, missing parts or uncertainty in such a sequence can be covered with wild cards, so-called wild bases. This makes an alignment possible even when the data are corrupted or incomplete. The extended pairwise local alignment of wild card DNA/RNA sequences requires additional calculations in the dynamic programming algorithm and necessitates a subsequent best- and worst-case analysis for the wild card positions. In this paper, we propose an algorithm which solves the problem of input data wild cards, offers a highly flexible set of parameters and displays a detailed alignment output and a compact representation of the mutated positions of the alignment. An implementation of the algorithm can be obtained at https://github.com/sysbio-bioinf/swat+ and http://sysbio.uni-ulm.de/?Software:Swat+.     

Spatial modelling of the two‐party preferred vote in Australian federal elections: 2001–2016

We examine the relationships between electoral socio‐demographic characteristics and two‐party preferences in the six Australian federal elections held between 2001 and 2016. Socio‐demographic information is derived from the Australian Census which occurs every 5 years. Since a census is not directly available for each election, an imputation method is employed to estimate census data for the electorates at the time of each election. This accounts for both spatial and temporal changes in electoral characteristics between censuses. To capture any spatial heterogeneity, a spatial error model is estimated for each election, which incorporates a spatially structured random effect vector. Over time, the impact of most socio‐demographic characteristics that affect electoral two‐party preference do not vary, with age distribution, industry of work, incomes, household mobility and relationships having strong effects in each of the six elections. Education and unemployment are among those that have varying effects. All data featured in this study have been contributed to the eechidna R package (available on CRAN).     

市场化程度、政府治理、制度安排与反腐败关系——基于2000—2013年宏观面板数据的分析

腐败治理是一项复杂的社会工程。目前,中国进入全面深化改革的新时期,如何处理好反腐败与市场经济改革、政府治理、制度安排之间的关系,成为当前改革的重点与难点。利用中国2000—2013年宏观面板数据,系统分析了市场化程度、政府治理和制度安排因素对反腐败的影响机制。研究发现:市场化程度提升能够起到消减腐败的作用。政府治理对反腐败影响较为复杂,政府规模表现为规模越大,治理能力越完善,越有助于减少腐败,但子指标公职人员相对工资水平与反腐败相关性较为模糊,需要理性看待现阶段"高薪养廉"的作用。制度安排特别是法治化和信息化水平的提升起到了显著减少腐败的作用,佐证了全面推进依法治国和加强信息化建设对反腐倡廉的必要性。     

Relationships Between Full and Layer Models with Applications to Level Merging

Analysis of a large dimensional contingency table is quite involved. Models corresponding to layers of a contingency table are easier to analyze than the full model. Relationships between the interaction parameters of the full log-linear model and that of its corresponding layer models are obtained. These relationships are not only useful to reduce the analysis but also useful to interpret various hierarchical models. We obtain these relationships for layers of one variable, and extend the results for the case when layers of more than one variable are considered. We also establish, under conditional independence, relationships between the interaction parameters of the full model and that of the corresponding marginal models. We discuss the concept of merging of factor levels based on these interaction parameters. Finally, we use the relationships between layer models and full model to obtain conditions for level merging based on layer interaction parameters. Several examples are discussed to illustrate the results.     

Model determination for categorical data with factor level merging

Summary.  We deal with contingency table data that are used to examine the relationships between a set of categorical variables or factors. We assume that such relationships can be adequately described by the cond`itional independence structure that is imposed by an undirected graphical model. If the contingency table is large, a desirable simplified interpretation can be achieved by combining some categories, or levels, of the factors. We introduce conditions under which such an operation does not alter the Markov properties of the graph. Implementation of these conditions leads to Bayesian model uncertainty procedures based on reversible jump Markov chain Monte Carlo methods. The methodology is illustrated on a 2×3×4 and up to a 4×5×5×2×2 contingency table.     

Resolution dependence of the maximal information coefficient for noiseless relationship

Reshef et al. (Science 334:1518–1523, 2011) introduce the maximal information coefficient, or MIC, which captures a wide range of relationships between pairs of variables. We derive a useful property which can be employed either to substantially reduce the computer time to determine MIC, or to obtain a series of MIC values for different resolutions. Through studying the dependence of the MIC scores on the maximal resolution, employed to partition the data, we show that relationships of different natures can be discerned more clearly. We also provide an iterative greedy algorithm, as an alternative to the ApproxMaxMI proposed by Reshef et al., to determine the value of MIC through iterative optimization, which can be conducted parallelly.     

Human immunodeficiency virus, DNA and statistics

Understanding the causes and consequences of genetic variation in human immunodeficiency virus (HIV) is one of the most important tasks facing medical and evolutionary biologists alike. A powerful analytical tool which is available to those working in this field is the phylogenetic tree, which describes the evolutionary relationships of the sequences in a sample and the history of the mutational events which separate them. Although phylogenetic trees of HIV are becoming commonplace, their use can be improved by tailoring the underlying statistical models to the idiosyncrasies of viral biology. The design and refinement of phylogenetic analyses consequently represents an important practical use of statistical methods in HIV research.     

Weighted nonparametric regression

In the fixed design regression model, additional weights are considered for the Nad a ray a-Watson and Gasser-Miiller kernel estimators. We study their asymptotic behavior and the relationships between new and classical estimators. For a simple family of weights, and considering the AIMSEAS global loss criterion, we show some possible theoretical advantages. An empirical study illustrates the performance of the weighted kernel estimators in theoretical ideal situations and in simulated data sets. Also some results concerning the use of weights for local polynomial estimators are given.     

A Discrete Variable Chain Graph for Applicants for Credit

A bank offering unsecured personal loans may be interested in several related outcome variables, including defaulting on the repayments, early repayment or failing to take up an offered loan. Current predictive models used by banks typically consider such variables individually. However, the fact that they are related to each other, and to many interrelated potential predictor variables, suggests that graphical models may provide an attractive alternative solution. We developed such a model for a data set of 15 variables measured on a set of 14 000 applications for unsecured personal loans. The resulting global model of behaviour enabled us to identify several previously unsuspected relationships of considerable interest to the bank. For example, we discovered important but obscure relationships between taking out insurance, prior delinquency with a credit card and delinquency with the loan.     

Regression for non-Euclidean data using distance matrices

Regression methods for common data types such as measured, count and categorical variables are well understood but increasingly statisticians need ways to model relationships between variable types such as shapes, curves, trees, correlation matrices and images that do not fit into the standard framework. Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the responses can be developed using standard methods. We call scoring as the transformation from a new observation to a score, whereas backscoring is a method to represent a score as an observation in the data space. Both methods are essential for prediction and explanation. We illustrate the methodology for shape data, unregistered curve data and correlation matrices using motion capture data from an experiment to study the motion of children with cleft lip.     

论经营者激励机制与企业技术创新

研究经营者激励机制对企业技术创新的影响是现代企业管理的重要内容。以中国2004—2007年372家上市公司的数据为样本,探讨经营者激励机制与技术创新之间的关系并对其进行了实证研究。研究发现：由于国有企业的所有权和经营权的分离程度较高,技术创新代理行为的影响要甚于民营企业,因此经营者持股极少,较高的技术创新动力只能来自于边际激励效应。通过采用White—Heteroskedasticity方法对模型进行异方差检验,结果表明：经营者拥有剩余索取权有利于企业的技术创新;国有企业经营者拥有剩余索取权对企业技术创新的影响程度要高于民营企业。     

A segmented regression model for event history data: an application to the fertility patterns in Italy

We propose a segmented discrete-time model for the analysis of event history data in demographic research. Through a unified regression framework, the model provides estimates of the effects of explanatory variables and jointly accommodates flexibly non-proportional differences via segmented relationships. The main appeal relies on ready availability of parameters, changepoints, and slopes, which may provide meaningful and intuitive information on the topic. Furthermore, specific linear constraints on the slopes may also be set to investigate particular patterns. We investigate the intervals between cohabitation and first childbirth and from first to second childbirth using individual data for Italian women from the Second National Survey on Fertility. The model provides insights into dramatic decrease of fertility experienced in Italy, in that it detects a ‘common’ tendency in delaying the onset of childbearing for the more recent cohorts and a ‘specific’ postponement strictly depending on the educational level and age at cohabitation.     

A Bayesian nonparametric Markovian model for non-stationary time series

Stationary time series models built from parametric distributions are, in general, limited in scope due to the assumptions imposed on the residual distribution and autoregression relationship. We present a modeling approach for univariate time series data, which makes no assumptions of stationarity, and can accommodate complex dynamics and capture non-standard distributions. The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals. This results in a flexible autoregressive form for the conditional transition density, defining a time-homogeneous, non-stationary Markovian model for real-valued data indexed in discrete time. To obtain a computationally tractable algorithm for posterior inference, we utilize a square-root-free Cholesky decomposition of the mixture kernel covariance matrix. Results from simulated data suggest that the model is able to recover challenging transition densities and non-linear dynamic relationships. We also illustrate the model on time intervals between eruptions of the Old Faithful geyser. Extensions to accommodate higher order structure and to develop a state-space model are also discussed.