A Procedure for Clustering Means of Unequal-Sized Samples in ANOVA

The proposed procedure “SECOLICO” is based on the sequential construction of linear contrasts. After an analysis of variance the procedure is able to classify the treatments represented by mean values of unequal-sized samples made at random into distinguishable groups. For the purpose of illustrating the procedure “SECOLICO” a simplified example is given.     

A Parameter-Elimination Method for Nonlinear Regression with Linear Parameters and Autocorrelated Errors

In this study, we are interested in the problem of estimating the parameters in a nonlinear regression model when the error terms are correlated. Throughout this work, we restrict ourselves to the special case when the error terms follow a pth order stationary autoregressive model (AR(p)). Following the idea of LAWTON and SYLVESTRE (1971) and GALLANT and GOEBEL (1976), a parameter-elimination method is proposed, which has the advantages that it is not sensitive to the initial values and convergence of the procedure may be more stable because of the reduced dimension of the problem. The parameter-elimination method is compared with the methods by GALLANT and GOEBEL (1976) and GLASBEY (1980) by Monte Carlo Simulation, and the results of applying the first two methods to the real data obtained from the Environmental Protection Administration of the Executive Yuan of the Republic of China are presented.     

Analysis of Nested Designs with Binomially-Distributed Outcome Variables

A model and methods are presented for the analysis of a nested design with binomially-distributed outcome variables. The proposed method may also be applicable to the analysis of singly-ordered contingency tables.     

Mixed-model of ANOVA for measurement reproducibility in proteomics

This work is a statistical analysis of reproducibility of a MALDI-TOF mass spectrometry experiment. Its aim is to evaluate measurement variability and compare peak intensities from two types of MALDI-TOF platforms. We compared and commented on the abilities of Principal Component Analysis and mixed-model analysis of variance to evaluate the biological variability and the technical variability of peak intensities in different patients. The properties and hypotheses of both methods are summarized and applied to spectra from plasma of patients with Hodgkin lymphoma. Principal Component Analysis checks rapidly the balance between the two variabilities; however, a mixed-model analysis of variance is necessary to quantify the biological and technical components of the experimental variance as well as their interactions and to split the total variance into between-subjects and within-subject components. The latter method helped to assess the reproducibility of measurements from two MALDI-TOF platforms and to decompose the technical variability according to the experimental design.     

Sampling Methods for Estimating Breeding Population and Hunting Mortality of Game Birds

In this paper we will summarize some of the important sampling and non-sampling errors with special reference to the mail surveys on migratory game birds and aerial surveys on breeding birds in North America. Where possible, methods for controlling the errors will be indicated.     

Analysis of Repeated Measurements with Ante-Dependence Covariance Models

This paper considers the use of ante-dependence models in problems with repeated measures through time. These are conditional regression models which reflect the dependence of a measure on some of the previous observations from the same subject. We present maximum likelihood estimators of the covariance matrix and procedures for selecting the order of ante-degendence based on penalized like-lihoods. Extensions to missing data situations are discussed. We propose Wald-type test statistics and apply them in two situations common in experiments with repeated measures: one with pre-study observations and another one with small sample size relative to the number of time periods. In these examples, tests assuming ante-dependence find effects which are not detected using competing procedures.     

Ratio estimation with measurement error in the auxiliary variate

Summary .  With auxiliary information that is well correlated with the primary variable of interest, ratio estimation of the finite population total may be much more efficient than alternative estimators that do not make use of the auxiliary variate. The well-known properties of ratio estimators are perturbed when the auxiliary variate is measured with error. In this contribution we examine the effect of measurement error in the auxiliary variate on the design-based statistical properties of three common ratio estimators. We examine the case of systematic measurement error as well as measurement error that varies according to a fixed distribution. Aside from presenting expressions for the bias and variance of these estimators when they are contaminated with measurement error we provide numerical results based on a specific population. Under systematic measurement error, the biasing effect is asymmetric around zero, and precision may be improved or degraded depending on the magnitude of the error. Under variable measurement error, bias of the conventional ratio-of-means estimator increased slightly with increasing error dispersion, but far less than the increased bias of the conventional mean-of-ratios estimator. In similar fashion, the variance of the mean-of-ratios estimator incurs a greater loss of precision with increasing error dispersion compared with the other estimators we examine. Overall, the ratio-of-means estimator appears to be remarkably resistant to the effects of measurement error in the auxiliary variate.     

Model Building and Analysis for Block Designs with Nested Rows and Columns

The paper deals with two main problems: it gives a unified approach to model building for observations obtained in a block design with nested rows and columns and it provides the analysis of variance for such data. Also, some statistical properties of the design are examined.     

多反应变量重复测量的混合效应模型及其应用

本文给出了多反应变量重复测量的协方差矩阵结构,探讨了用迭代广义最小二乘法来求解其带协变量和不带协变量的混合效应模型中固定效应和随机效应系数,并对１９９１年四川省高血压调查资料进行实例分析,得到其结论符合实际情况．     

Unbalanced Repeated Measures with Random Coefficients

In a random coefficient repeated measures model, the regression coefficients relating the observations to some underlying variable, such as time, are themselves taken to be random distributed over experimental units. In this paper, a general approach to repeated measures analysis is extended to this wider model. In the model three specific error structures for the random regression coefficients have been studied, viz, the random coefficients variance matrix is considered to be (i) diagonal, (ii) proportional to the identity matrix and (iii) completely general. An example will be analyzed to illustrate the procedure.     

Using ANOVA for gene selection from microarray studies of the nervous system

Methods are presented for detecting differential expression using statistical hypothesis testing methods including analysis of variance (ANOVA). Practicalities of experimental design, power, and sample size are discussed. Methods for multiple testing correction and their application are described. Instructions for running typical analyses are given in the R programming environment. R code and the sample data set used to generate the examples are available at http://microarray.cpmc.columbia.edu/pavlidis/pub/aovmethods/.     

Smoothing spline ANOVA frailty model for recurrent event data

Gap time hazard estimation is of particular interest in recurrent event data. This article proposes a fully nonparametric approach for estimating the gap time hazard. Smoothing spline analysis of variance (ANOVA) decompositions are used to model the log gap time hazard as a joint function of gap time and covariates, and general frailty is introduced to account for between-subject heterogeneity and within-subject correlation. We estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the Newton-Raphson procedure, the stochastic approximation algorithm (SAA), and the Markov chain Monte Carlo (MCMC) method. The convergence of the algorithm is guaranteed by decreasing the step size of parameter update and/or increasing the MCMC sample size along iterations. Model selection procedure is also developed to identify negligible components in a functional ANOVA decomposition of the log gap time hazard. We evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data.     

MINQUE and ANOVA Estimator for One-way Classification - a Risk Comparison

For the one-way classification in unbalanced case MINQUEstimator for components of variance are given in a more explicit form than it is done in the paper from C. R. RAO (1971). By means of the risk functions we compare MINQUE and ANOVA estimator. For given n_j-patterns angular ranges in the positive quadrant are given where MINQUE is better than ANOVA estimator. A special n_j-pattern and one parameter δ₀ is found for which MINQUE is uniformly better than ANOVA. Limit values are given for MINQUE for δ₀ = ∞ and δ₀ = 0 and their relations to the ANOVA estimator are considered. The coincidence between MINQUE and ANOVA for balanced case is verified. Extensive numerical studies for real data are carried out which stimulated the search for a fixpoint δ as a point for which the distance to the initial parameter δ₀ is as small as possible.     

糖尿病视网膜病变患者多次住院的影响因素分析

目的:探讨糖尿病视网膜病变(DR)患者多次住院(住院次数≥2)的影响因素。方法:以2型糖尿病(DM)并因糖尿病视网膜病变(DR)相关并发症多次住院(住院次数≥2)的患者为实验组,对照组为非糖尿病多次因眼科相关疾病住院(住院次数≥2)患者。比较两组患者在第二次住院时的发病年龄、空腹血糖(fasting blood glucose,GLU)、糖化血清蛋白(glycated serum protrin,GSP)、丙氨酸氨基转移酶(Alanine aminotransferase,ALT)、天冬氨酸氨基转移酶(aspartate aminotransferase,AST)、肌酐(creatinine,Cr)、尿素(urea)、总胆汁酸(total bile acid,TBA)、血清尿酸(uric acid,UA)、甘油三酯(triglycetide,TG)、胆固醇(cholesterol,Ch)、体质指数(body mass index,BMI)等。结果:单因素分析结果显示入院时血糖、糖化血清蛋白、血清尿酸、甘油三酯、胆固醇与DR患者多次住院(住院次数≥2)显著相关(P均≤0.01)。多因素Logistic回归分析显示:空腹血糖(P=0.038;95%CI:1.101~26.325)、糖化血清蛋白(P=0.003;95%CI:1.017~1.082)、尿酸(P=0.167;95%CI:0.994~1.032)、甘油三脂(P=0.023;95%CI:1.774~2228.179)、胆固醇(P=0.029;95%CI:1.317~166.317)水平是DR患者多次住院(住院次数≥2)的独立危险因素。结论:空腹血糖、糖化血清蛋白、尿酸、甘油三脂和胆固醇是DR患者多次住院(住院次数≥2)的独立危险因素。     

Shape-invariant modeling of circadian rhythms with random effects and smoothing spline ANOVA decompositions

Medical studies often collect physiological and/or psychological measurements over time from multiple subjects, to study dynamics such as circadian rhythms. Under the assumption that the expected response functions of all subjects are the same after shift and scale transformations, shape-invariant models have been applied to analyze this kind of data. The shift and scale parameters provide efficient and interpretable data summaries, while the common shape function is usually modeled nonparametrically, to provide flexibility. However, due to the deterministic nature of the shift and scale parameters, potential correlations within a subject are ignored. Furthermore, the shape of the common function may depend on other factors, such as disease. In this article, we propose shape-invariant mixed effects models. A second-stage model with fixed and random effects is used to model individual shift and scale parameters. A second-stage smoothing spline ANOVA model is used to study potential covariate effects on the common shape function. We apply our methods to a real data set to investigate disease effects on circadian rhythms of cortisol, a hormone that is affected by stress. We find that patients with Cushing's syndrome lost circadian rhythms and their 24-hour means were elevated to very high levels. Patients with major depression had the same circadian shape and phases as normal subjects. However, their 24-hour mean levels were elevated and amplitudes were dampened for some patients.     

Confidence Intervals on Ratios of Variance Components for the Unbalanced Two Factor Nested Model

The model considered in this article is the two-factor nested unbalanced variance component model: for p = 1, 2, …, P; q = 1, 2, …, Q_p; and r = 1, 2, …, R_pq. The random variables Y_pqr are observable. The constant μ is an unknown parameter, and A_p, B_pq and C_pqr are (unobservable) normal and independently distributed random variables with zero means and finite variances σ²_A, σ²_B, and σ²_C, respectively. Approximate confidence intervals on ?_A and ?_B using unweighted means are derived, where The performance of these approximate confidence intervals are evaluated using computer simulation. The simulated results indicate that these proposed confidence intervals perform satisfactorily and can be used in applied problems.     

Generalizing Double and Triple Sampling for Repeated Surveys and Partial Verification

Population composition is often estimated by double sampling in which the value of a covariate is noted on each of a large number of randomly selected units and the value of the covariate and the exact class to which the unit belongs is noted for a smaller sample. The cross‐classified sample can be used to estimate the classification rates and these, in turn, can be used in conjunction with the estimated distribution of the covariate to obtain an improved estimate of the population composition over that obtained by direct observation of the identity of the individuals in a small sample. There are two approaches to this problem characterized by the way in which the classification rates are defined. The simplest approach uses estimates of the probability P(i | j) that the unit is actually in class i given that the covariate is in class j. The more complicated approach uses estimates of the probability Pi | j) that the covariate falls in class j given that the unit is actually in class i. The latter approach involves estimating more parameters than the former but avoids the necessity for the two samples to be drawn from the same population. We show the two approaches can be combined when there are multiple surveys. For example, one might conduct a disease survey for several years; in each year the accurate and/or error‐prone techniques may be applied to samples. The sensitivities and specificities of the error‐prone test are assumed constant across surveys. Generalizations allow for more than one error‐prone classifier and partial verification (estimation of misclassification rates by application of the accurate technique to fixed subsamples from each error‐prone category). The general approach is illustrated by considering a repeated survey for malaria.