A Simple Procedure for Constructing Experiment Designs with Incomplete Blocks of Sizes 2 and 3

In order to maximize control of heterogeneity within complete blocks, an experimenter could use incomplete blocks of size k = 2 or 3. In certain situations, incomplete blocks of this nature would eliminate the need for such spatial types of analyses as nearest neighbor. The intrablock efficiency factors for such designs are relatively low. However, with recovery of interblock information, FEDERER and SPEED (1987) have presented measures of design efficiency factors which demonstrate that efficiency factors approach unity for certain ratios of the intrablock and interblock variance components. Hence with recovery of interblock information, even incomplete block designs with k = 2 or 3 have relatively high efficiency factors. The reduction in the intrablock error variance over the complete block error variance in many situations will provide designs with high efficiency. A simple procedure for constructing incomplete blocks of sizes 2 and 3 is presented. It is shown how to obtain additional zero-one association confounding arrangements when v = 4 t, t an integer, and for v = pk, k ≤ p. It is indicated how to do the statistical analysis for these designs.     

Randomized Blocks Analysis for the Exponential Distribution

A procedure for analyzing randomized blocks experiments for uncensored exponential random variables is presented. Its small sample behavior is studied in several simulations. Sample size requirements are given.     

Directly modelling population dynamics in the South American Arid Diagonal using 14C dates

Large anthropogenic ¹⁴C datasets are widely used to generate summed probability distributions (SPDs) as a proxy for past human population levels. However, SPDs are a poor proxy when datasets are small, bearing little relationship to true population dynamics. Instead, more robust inferences can be achieved by directly modelling the population and assessing the model likelihood given the data. We introduce the R package ADMUR which uses a continuous piecewise linear (CPL) model of population change, calculates the model likelihood given a ¹⁴C dataset, estimates credible intervals using Markov chain Monte Carlo, applies a goodness-of-fit test, and uses the Schwarz Criterion to compare CPL models. We demonstrate the efficacy of this method using toy data, showing that spurious dynamics are avoided when sample sizes are small, and true population dynamics are recovered as sample sizes increase. Finally, we use an improved ¹⁴C dataset for the South American Arid Diagonal to compare CPL modelling to current simulation methods, and identify three Holocene phases when population trajectory estimates changed from rapid initial growth of 4.15% per generation to a decline of 0.05% per generation between 10 821 and 7055 yr BP, then gently grew at 0.58% per generation until 2500 yr BP.This article is part of the theme issue ‘Cross-disciplinary approaches to prehistoric demography’.     

Bias‐Corrected Diagonal Discriminant Rules for High‐Dimensional Classification

Summary Diagonal discriminant rules have been successfully used for high‐dimensional classification problems, but suffer from the serious drawback of biased discriminant scores. In this article, we propose improved diagonal discriminant rules with bias‐corrected discriminant scores for high‐dimensional classification. We show that the proposed discriminant scores dominate the standard ones under the quadratic loss function. Analytical results on why the bias‐corrected rules can potentially improve the predication accuracy are also provided. Finally, we demonstrate the improvement of the proposed rules over the original ones through extensive simulation studies and real case studies.     

Analysis of Partial Diallel Crosses in Incomplete Blocks

With a large number of lines in a diallel cross experiment, the number of crosses becomes unmanageable to be accommodated in homogeneous blocks. To overcome this problem, a sample of crosses, known as partial diallel cross (PDC) is often used. The selection of a PDC is based on the criterion of high efficiency for the estimation of general combining ability (gca) effects. Even with a moderately large number of crosses, the use of incomplete blocks is necessary to obtain homogeneous experimental units. The analysis of data from a general PDC grown in general incomplete block designs is being described. An iterative scheme is being developed for obtaining a generalized inverse of the information matrix used in estimating gca effects. Properties such as connectedness and efficiency of mating designs embedded in environment designs are being examined. The paper also examines the universal optimality of some designs in a class of designs. An illustration of the numerical procedure is also presented.     

采用不同方法制作胸腹水细胞块的效果比较及临床价值研究

目的:比较不同方法制作胸腹水细胞块的效果以优化胸腹水细胞块制作程序,并对其临床价值进行探讨。方法:以2014年3月至2015年3月我科收集的胸腹水标本120例为研究对象,将每样标本平均分成三组,使用三种不同方法(试管包埋法、直接离心法、细胞块试剂盒法)制作胸腹水细胞块。对不同方法制作细胞块的成功率、完整性及细胞切片恶性细胞的检出率进行考察与比较。结果:细胞块试剂盒法成功率最高,为96.67%,试管包埋法次之,成功率为92.50%,二者相比无显著差异(P0.05)。直接离心法制作成功率为80.83%,远远低于试管包埋法及细胞块试剂盒法,差异有统计学意义(P0.05)。细胞块试剂盒法制作的细胞块完整性最高,完整标本所占比例为96.67%,试管包埋法次之,完整率为94.17%,二者相比无显著差异(P0.05)。直接离心法制作完整率为68.33%,远远低于试管包埋法及细胞块试剂盒法,差异有统计学意义(P0.05)。三种方法恶性细胞检出率以细胞块试剂盒最高,与其他两种方法比较差异有统计学意义(P0.05)。结论:细胞块试剂盒法制作胸腹水细胞块具有最高的成功率及完整性,并且可以显著提高恶性细胞检出率,值得广泛使用。     

Testing Multivariate Normality in Series Experiments of Incomplete Blocks by Generalized Shapiro-Wilk Test

In this paper, we verify our assumption about multivariate normality in series experiments of incomplete blocks by the generalized Shapiro-Wilk test. This test utilizes transformations of mean yields of the investigated varieties and the generated random variables according to Durbin's randomization principle.     

A Note on Optimality of Certain Rank Tests for Ordered Alternatives in Randomized Blocks

Nonparametric tests for ordered alternatives in randomised block designs based on within block rankings have been proposed by many authors. This note is concerned with the optimality of the choice of so-called regression constants usually considered in such rank tests. Some examples are discussed.     

MIVQUE and REML Estimators of Variance Components under Proportionality Condition

In this study, a one-way random effect model with unequal cell variances is considered, and the Minimum Variance Quadratic Unbiased Estimator (MIVQUE) and Restricted Maximum Likelihood (REML) estimator of the variance components are studied. The algebraic inversion of the variance matrix of the observation vector is obtained to achieve some computational convenience. Using the proportionality condition described by Talukder (1992) that the cell sizes are proportional to the cell variances, MIVQUE and REML estimators are shown to be the same as the ANOVA estimators.     

The Longest (A+T) and (G+C) Blocks in the Human and Other Genomes

Abstract

We analysed complete or almost complete nucleotide sequences of the human, chimp, mouse, rat, chicken, dog, and other genomes to find that they contain extremely long (A+T) a (G+C) blocks that do not occur at all in the corresponding randomized sequences. The longest is an (A+T) block containing 1040 consecutive AT pairs that occurs in the 16^th human chromosome. The longest human (G+C) block has 261 bp in length. About a half of the longest blocks occur in introns. The (A+T) blocks are discrete units whereas the (G+C) blocks are diffuse. They are embeeded in the genome through connectors longer than 1 kilobase where the (G+C) content gradually decreases to the value of 50%. Remarkably, the (A+T) as well as (G+C) blocks are substantially shorter in the chimp genome. Chicken is characteristic by very long (G+C) blocks that are even longer than in the human genome. Though much shorter, long (G+C) and especially (A+T) blocks occur in lower organisms as well, which means that AT and GC pair clustering is an ancient property that has evolved into large scales in higher eukaryote genomes and the human genome in particular. Very long (A+T) and (G+C) blocks confer specific biophysical properties on DNA that are likely to influence genome folding in cell nuclei and its functional properties.     

Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem

Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally.     

应用多层次结构的功能反应模型比较捕食螨对不同猎物的捕食行为

在害虫生物防治研究中,选择适合的天敌种类或类型是能否有效控制害虫的关键.虽然传统的功能反应试验能够为评价天敌的捕食行为与猎物(或寄主)密度的关系提供有益的依据,但不能根据这些结果对天敌捕食能力进行统计比较.本文在Michaelis-Menten模型的基础上,提出多级层次结构的功能反应模型,使试验习子(如天敌类型、猎物种类等)对捕食行为的影响,表达为模型参数的改变.并根据Ibralim和Rahman(1997)发表的12组功能反应试验结果,应用这一多层次结构模型统计比较不同天敌类型的捕食行为、及猎物种类、猎物生长期对试验结果的影响.取得如下结论:1.根据模型预测值与试验观测结果的吻合程度及模型误差的分布,说明以Michaelis-Menton为基础的多层次结构的功能反应模型能够用于统计比较捕食螨种类间的捕食行为,以及猎物类型、猎物生长阶段和其它环境因子对天敌捕食行为的影响作用.2.这一模型的分析结果不仅从统计角度证实了Ibahim和Rahman(1997)的推测,即红色叶螨是更适于这种捕食螨的猎物.同时为捕食螨种类的选择及田间释放技术提供统计依据.     

Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values

Several theorems on estimation and verification of linear hypotheses in some Zyskind-Martin (ZM) models are given. The assumptions are as follows. Let y = Xβ + e or (y, Xβ, σ²V) be a fixed model where y is a vector of n observations, X is a known matrix nXp with rank r(X) = r ≦ p < n, where p is a number of coordinates of the unknown parameter vector β, e is a random vector of errors with covariance matrix σ²V, where σ² is unknown scalar parameter, V is a known non-negative definite matrix such that R(X) ? R(V). Symbol R(A) denotes a vector space generated by columns of matrix A. The expected value of y is Xβ. In this paper four following Zyskind-Martin (ZM) models are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector y y₁ y₂ involves a vector y₁ of m missing values and a vector y₂ with (n — m) observed values. A special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind-Martin models with missing values (cf. theorem 2.2) test functions F are given in (2.11)) are presented. The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, Xβ, σ²I) to ZM model. Estimation of vector y₁ (cf. 3.3) of vector β (cf. th. 3.2) and of scalar σ² (cf. th. 3.4) in actual ZMa model and in diagonal quasi-ZM model (ZMqd) are presented. Relation between y? ₁ and β is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.     

Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture

Shared random effects joint models are becoming increasingly popular for investigating the relationship between longitudinal and time‐to‐event data. Although appealing, such complex models are computationally intensive, and quick, approximate methods may provide a reasonable alternative. In this paper, we first compare the shared random effects model with two approximate approaches: a naïve proportional hazards model with time‐dependent covariate and a two‐stage joint model, which uses plug‐in estimates of the fitted values from a longitudinal analysis as covariates in a survival model. We show that the approximate approaches should be avoided since they can severely underestimate any association between the current underlying longitudinal value and the event hazard. We present classical and Bayesian implementations of the shared random effects model and highlight the advantages of the latter for making predictions. We then apply the models described to a study of abdominal aortic aneurysms (AAA) to investigate the association between AAA diameter and the hazard of AAA rupture. Out‐of‐sample predictions of future AAA growth and hazard of rupture are derived from Bayesian posterior predictive distributions, which are easily calculated within an MCMC framework. Finally, using a multivariate survival sub‐model we show that underlying diameter rather than the rate of growth is the most important predictor of AAA rupture.     

多水平贝叶斯模型预测森林土壤全氮

多水平贝叶斯方法阐明了预测中观测值、模型和参数的不确定性,被越来越多的生态学家所使用.应用多水平贝叶斯方法建立了北京八达岭地区森林土壤全氮模型,分析了模型参数及其不确定性,并对该区不同土壤层(A、B、C)全氮含量进行了预测.得到如下结论:(1)该区森林土壤全氮多水平贝叶斯模型为yi～N(β0j[i],k[j]+β1j[i],k[j]xi,σ2y).(2)对模型参数和其曲线不确定性分析表明,该模型能够很好的预测该区土壤全氮含量.(3)模型预测表明:土壤A层,随着海拔的增加,全氮含量递增.土壤B层,随着海拔的升高,植被类型0、1、2、3土壤全氮含量递增,而植被类型4土壤全氮含量出现递减现象.土壤C层,随着海拔的增加,植被类型0土壤全氮含量递增,而植被类型1、2、3、4土壤全氮含量均表现为递减.各植被类型土壤全氮含量都随着土层的深度而减少.     

A new species of Silene (Caryophyllaceae) from South Anatolia, Turkey

Silene doganii A.Duran & Y.Menemen sp. nov. from the Amanos Mountains (C6: Osmaniye-Turkey) is described and illustrated. It is closely related to S. caramanica Boiss. & Heldr., from which it differs mainly in its habit, hairiness, leaf and floral features.  © 2003 The Linnean Society of London, Botanical Journal of the Linnean Society , 2003, 143 , 109−113.     

Surrogate marker evaluation from an information theory perspective

The last 20 years have seen lots of work in the area of surrogate marker validation, partly devoted to frame the evaluation in a multitrial framework, leading to definitions in terms of the quality of trial- and individual-level association between a potential surrogate and a true endpoint (Buyse et al., 2000, Biostatistics 1, 49-67). A drawback is that different settings have led to different measures at the individual level. Here, we use information theory to create a unified framework, leading to a definition of surrogacy with an intuitive interpretation, offering interpretational advantages, and applicable in a wide range of situations. Our method provides a better insight into the chances of finding a good surrogate endpoint in a given situation. We further show that some of the previous proposals follow as special cases of our method. We illustrate our methodology using data from a clinical study in psychiatry.     

Just-identified versus overidentified two-level hierarchical linear models with missing data

The development of model-based methods for incomplete data has been a seminal contribution to statistical practice. Under the assumption of ignorable missingness, one estimates the joint distribution of the complete data for thetainTheta from the incomplete or observed data y(obs). Many interesting models involve one-to-one transformations of theta. For example, with y(i) approximately N(mu, Sigma) for i= 1, ... , n and theta= (mu, Sigma), an ordinary least squares (OLS) regression model is a one-to-one transformation of theta. Inferences based on such a transformation are equivalent to inferences based on OLS using data multiply imputed from f(y(mis) | y(obs), theta) for missing y(mis). Thus, identification of theta from y(obs) is equivalent to identification of the regression model. In this article, we consider a model for two-level data with continuous outcomes where the observations within each cluster are dependent. The parameters of the hierarchical linear model (HLM) of interest, however, lie in a subspace of Theta in general. This identification of the joint distribution overidentifies the HLM. We show how to characterize the joint distribution so that its parameters are a one-to-one transformation of the parameters of the HLM. This leads to efficient estimation of the HLM from incomplete data using either the transformation method or the method of multiple imputation. The approach allows outcomes and covariates to be missing at either of the two levels, and the HLM of interest can involve the regression of any subset of variables on a disjoint subset of variables conceived as covariates.     

Development of Chiral Building Blocks Having a Bicyclo[3.3.0]Octane Framework Using a Diastereomeric Resolution‐Selective Deprotection

A protocol is presented for an efficient and practical approach to the synthesis of enantiomerically pure bicyclo[3.3.0]octane derivatives from achiral C_s‐symmetric bicyclo[3.3.0]octane‐2,8‐dione using a diastereomeric resolution‐selective deprotection method. This method affords chiral building blocks having bicyclo[3.3.0]octane framework with the same site of diastereotopic carbonyl functional group. Chirality 27:364–369, 2015. © 2015 Wiley Periodicals, Inc.