Exact tests for matched pairs:studies with covariates

In prospective or retrospective studies with matched pairs one often wishes to control for covariates other than those used in the matching process.Large sample procedures assuming a logistic model are available for this problem.The present paper presents some exact permutation tests which are uniformly most powerful unbiased within a large class of tests.     

Three-Factor Cartographic Representation

Statistics and statisticians have contributed to industry. Attention has been given to the appropriate training of statisticians for careers in industry. Statistics is used with benefit to industry in quality control, experimental design in research and development, and management decisions. Statistics can benefit from industry's assistance, the subject of this article. Five premises are set forth, three of them suggesting problems for statistics and industry. They relate to public understanding of statistics, the recruitment of students to statistics, the recruitment of statisticians to industry, and the relevance of research in statistics to the needs of industry. Thirteen recommendations are made on what industry can do for statistics and suggestions are made on how the American Statistical Association and the American Society for Quality Control can provide leadership in meeting the problems posed with the help of industry.     

On the advantages of the non-concave penalized likelihood model selection method with minimum prediction errors in large-scale medical studies

Variable and model selection problems are fundamental to high-dimensional statistical modeling in diverse fields of sciences. Especially in health studies, many potential factors are usually introduced to determine an outcome variable. This paper deals with the problem of high-dimensional statistical modeling through the analysis of the trauma annual data in Greece for 2005. The data set is divided into the experiment and control sets and consists of 6334 observations and 112 factors that include demographic, transport and intrahospital data used to detect possible risk factors of death. In our study, different model selection techniques are applied to the experiment set and the notion of deviance is used on the control set to assess the fit of the overall selected model. The statistical methods employed in this work were the non-concave penalized likelihood methods, smoothly clipped absolute deviation, least absolute shrinkage and selection operator, and Hard, the generalized linear logistic regression, and the best subset variable selection.The way of identifying the significant variables in large medical data sets along with the performance and the pros and cons of the various statistical techniques used are discussed. The performed analysis reveals the distinct advantages of the non-concave penalized likelihood methods over the traditional model selection techniques.     

Measuring the complexity of generalized linear hierarchical models

Measuring a statistical model's complexity is important for model criticism and comparison. However, it is unclear how to do this for hierarchical models due to uncertainty about how to count the random effects. The authors develop a complexity measure for generalized linear hierarchical models based on linear model theory. They demonstrate the new measure for binomial and Poisson observables modeled using various hierarchical structures, including a longitudinal model and an areal‐data model having both spatial clustering and pure heterogeneity random effects. They compare their new measure to a Bayesian index of model complexity, the effective number p_D of parameters (Spiegelhalter, Best, Carlin & van der Linde 2002); the comparisons are made in the binomial and Poisson cases via simulation and two real data examples. The two measures are usually close, but differ markedly in some instances where p_D is arguably inappropriate. Finally, the authors show how the new measure can be used to approach the difficult task of specifying prior distributions for variance components, and in the process cast further doubt on the commonly‐used vague inverse gamma prior.     

SIMULATIONS AND DERIVED APPROXIMATIONS FOR THE MEANS AND STANDARD DEVIATIONS OF THE CHARACTERISTIC ROOTS OF A WISHART MATRIX

Monte Carlo simulations were done to estimate the means and standard deviations of the characteristic roots of a Wishart matrix which can be used in computing tests of hypotheses concerning multiplicative terms in balanced linear-bilinear (multiplicative) models for an m × n table of data. In this report we extend the previous results (Mandel, 1971; Cornelius, 1980) to r ≤ 199, c ≤ 149 or r ≤ 149, c ≤ 199, where r and c are row and column degrees of freedom, respectively, of the two-way array of residuals (with total degrees of freedom rc) after fitting the linear effects. For 187 combinations of r and c at intervals over this domain, we used 5000 simulations to estimate expectations and standard deviations of the Wishart roots. Using weighted linear regression variable selection techniques, symmetric functions of r and c were obtained for approximating the simulated means and standard deviations. Use of these approximating functions will avoid the need for reference to tables for input to computer programs which require these values for tests of significance of sequentially fitted terms in the analyses of balanced linear-bilinear models.     

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.     

Asymptotic theory for the Cox semi-Markov illness-death model

Irreversible illness-death models are used to model disease processes and in cancer studies to model disease recovery. In most applications, a Markov model is assumed for the multistate model. When there are covariates, a Cox (1972, J Roy Stat Soc Ser B 34:187–220) model is used to model the effect of covariates on each transition intensity. Andersen et al. (2000, Stat Med 19:587–599) proposed a Cox semi-Markov model for this problem. In this paper, we study the large sample theory for that model and provide the asymptotic variances of various probabilities of interest. A Monte Carlo study is conducted to investigate the robustness and efficiency of Markov/Semi-Markov estimators. A real data example from the PROVA (1991, Hepatology 14:1016–1024) trial is used to illustrate the theory.     

Model Identification in Dynamic Regression (Distributed Lag) Models

Dynamic regression models (also known as distributed lag models) are widely used in engineering for quality control and in economics for forecasting. In this article I propose a procedure for specifying such models in practice. The proposed procedure requires no prewhitening and can directly handle the nonstationary series. Furthermore, the procedure cross-validates prior beliefs about causal relationships between variables with empirical findings to ensure the suitability of model structure. An illustrative example is given.     

An integrated model for economic design of chi-square control chart and maintenance planning

Considered process in this article is a two-stage dependent process. Each item in this process has two quality characteristics as x and y while x and y are related to the stage 1 and 2, respectively. Each stage has two operational states as the in-control state and out-of-control state and transition time from the in-control state to the out-of-control state follows a general continues distribution function. The process is monitored using a chi-square control chart. An integrated model that coordinates the decisions related to the economic design of the used control chart and maintenance planning is presented. For the evaluation of the integrated model performance, a stand-alone maintenance model is also presented, and the performance of these two models is compared with each other.     

Covariate selection for estimating the causal effect of control plans by using causal diagrams

Summary. Consider a case where cause–effect relationships between variables can be described by a causal path diagram and the corresponding linear structural equation model. The paper proposes a graphical selection criterion for covariates to estimate the causal effect of a control plan. For designing the control plan, it is essential to determine both covariates that are used for control and covariates that are used for identification. The selection of covariates used for control is only constrained by the requirement that the covariates be non-descendants of a treatment variable. However, the selection of covariates used for identification is dependent on the selection of covariates used for control and is not unique. In the paper, the difference between covariates that are used for identification is evaluated on the basis of the asymptotic variance of the estimated causal effect of an effective control plan. Furthermore, the results can be also described in terms of a graph structure.     

林业碳汇经济价值评价及其影响因素分析——基于碳控排企业支付意愿的调查

林业碳汇的经济价值是决定林业碳汇生产和交易的重要指标。基于浙江省温州市碳控排企业调查数据,运用条件价值法(CVM),引入计划行为理论,从碳控排企业支付意愿视角探讨林业碳汇经济价值及其影响因素。结果表明,碳控排企业对林业碳汇的支付意愿是"是否愿意支付"和"愿意支付多少金额"两个决策过程的统一。受访企业负责人个体特征、企业特征、气候变化认知、行为态度、主观规范变量显著正向影响碳控排企业是否愿意为林业碳汇支付;受访企业负责人个体特征、企业特征、林业碳汇认知、行为态度、知觉行为控制、行为经验变量显著正向影响碳控排企业的林业碳汇支付金额,反向行为执行意向则产生显著负向影响,利用PCE模型计算得到其平均支付金额,即林业碳汇经济价值为47.36元/t·CO_2。     

EWMA control charts for monitoring correlated counts with finite range

In this work, we develop and study upper and lower one-sided EWMA control charts for monitoring correlated counts with finite range. Often in practice, data of that kind can be adequately described by a first-order binomial or beta-binomial autoregressive model. Especially, when there is evidence that data demonstrate extra-binomial variation, the latter model is preferable than the former. The proposed charts can be used for detecting upward or downward shifts in process mean level. Practical guidelines concerning the statistical design of the proposed charts are given, while the effect of the extra-binomial variation is investigated as well. Comparisons with existing control charting procedures are also provided. Finally, an illustrative real-data example is also given.     

Bias due to Ignoring the Sample Design in Case–Control Studies

Case–control studies allow efficient estimation of the associations of covariates with a binary response in settings where the probability of a positive response is small. It is well known that covariate–response associations can be consistently estimated using a logistic model by acting as if the case–control (retrospective) data were prospective, and that this result does not hold for other binary regression models. However, in practice an investigator may be interested in fitting a non–logistic link binary regression model and this paper examines the magnitude of the bias resulting from ignoring the case–control sample design with such models. The paper presents an approximation to the magnitude of this bias in terms of the sampling rates of cases and controls, as well as simulation results that show that the bias can be substantial.     

A New Survival Model for the Diffusion Pattern of TV Programs

The study of television audience viewing behavior is very important. The results can provide broadcasters and advertisers useful information to increase the effectiveness of television programming and advertising. Based on hazard rate analysis for survival model, this research develops a new statistical model to fit the diffusion pattern of TV programs, which is a measure of the overall popularity of the program and is used as a criterion to sell the television time. The model helps the decision makers at the networks better understand the acceptance of the show and the underlying behavioral patterns of the viewers. It fits the empirical data in Hong Kong very well and outperforms the existing models. This basic model is then extended to the proportional hazard model to study the covariate effects on the likelihood of an individual watching the program at an earlier stage. Advertisers can benefit from these results in targeting their desired customers.     

Residuals in the Extended Growth Curve Model

Abstract.  The Extended Growth Curve model is considered. It turns out that the estimated mean of the model is the projection of the observations on the space generated by the design matrices which turns out to be the sum of two tensor product spaces. The orthogonal complement of this space is decomposed into four orthogonal spaces and residuals are defined by projecting the observation matrix on the resulting components. The residuals are interpreted and some remarks are given as to why we should not use ordinary residuals, what kind of information our residuals give and how this information might be used to validate model assumptions and detect outliers and influential observations. It is shown that the residuals are symmetrically distributed around zero and are uncorrelated with each other. The covariance between the residuals and the estimated model as well as the dispersion matrices for the residuals are also given.     

A semiparametric modeling approach for analyzing clinical biomarkers restricted to limits of detection

Before biomarkers can be used in clinical trials or patients' management, the laboratory assays that measure their levels have to go through development and analytical validation. One of the most critical performance metrics for validation of any assay is related to the minimum amount of values that can be detected and any value below this limit is referred to as below the limit of detection (LOD). Most of the existing approaches that model such biomarkers, restricted by LOD, are parametric in nature. These parametric models, however, heavily depend on the distributional assumptions, and can result in loss of precision under the model or the distributional misspecifications. Using an example from a prostate cancer clinical trial, we show how a critical relationship between serum androgen biomarker and a prognostic factor of overall survival is completely missed by the widely used parametric Tobit model. Motivated by this example, we implement a semiparametric approach, through a pseudo-value technique, that effectively captures the important relationship between the LOD restricted serum androgen and the prognostic factor. Our simulations show that the pseudo-value based semiparametric model outperforms a commonly used parametric model for modeling below LOD biomarkers by having lower mean square errors of estimation.     

Restricted likelihood ratio lack-of-fit tests using mixed spline models

Summary.  Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non-linearity in the smooth function estimates. This motivates the study of lack-of-fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values. For this one-sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis. Conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies, and finite sample approximations to the asymptotic distribution are provided. Test statistics are studied for simple as well as multiple-regression models.     

The Steady-State Performance of Cumulative Count of a Conforming Control Chart Based On Runs Rules

Cumulative count of conforming control chart is usually used to monitor fraction nonconforming in high-yield processes. In this article, we propose m-of-m control chart based on cumulative count of conforming units for high-yield processes. The steady-state properties of the m-of-m control chart are investigated. We compare performance of the m-of-m control chart with control chart based on cumulative count of conforming units. We present Markov chain model of the m-of-m control chart to evaluate average run length, standard deviation of run length and quartiles.     

The Economic Design of the MSE Control Chart

In this article, an economic design model of the MSE control chart is proposed. The formulated cost function includes the cost incurred in production process and the loss borne by customers because of the shift of means and the drift of variation. The economic bounds where the process is shut down if the search indicates the presence of an assignable cause are also being considered. A program written in Matlab 7.0 is used to determine the optimum parameters including the sample size n, the sample interval h and the width of the control limits k. Finally, an example is given to illustrate the proposed economic design and sensitivity analysis is carried out.     

Investigation of disease-free survival as a surrogate endpoint for survival in cancer clinical trials

A stochastic model wiuh exponential components is used to describe our data collected from a phase III cancer clinical trial. Criteria which guarantee that disease-free survival (DFS) can be used as a surrogate for overall survival are explored under this model. We examine several colorectal adjuvant clinical trials and find that these conditions are not satisfied. The relationship between the hazard ratio of DFS for an active treatment versus a control treatment and the cumulative hazard ratio of survival for the same two treatments is then explored. An almost linear relationship is found such that a hazard ratio for DFS of less than a threshold R corresponds to a non-null treatment effect on survival The threshold value R is determined for our colorectal adjuvant trial data. Based on this relationship, a one-sided test of equal hazard rate of survival is equivalent to a test of hazard ratio of DFS small than R This approach assumes that recurrence information is unbiasedly and accurately assessed; an assumpion which is sometimes difficult to ensure for multicenter clinical trials, particularly for interim analyses.