Levene tests of homogeneity of variance for general block and treatment designs

This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F-distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plots.     

A matrix‐based method of moments for fitting the multivariate random effects model for meta‐analysis and meta‐regression

Multivariate meta‐analysis is becoming more commonly used. Methods for fitting the multivariate random effects model include maximum likelihood, restricted maximum likelihood, Bayesian estimation and multivariate generalisations of the standard univariate method of moments. Here, we provide a new multivariate method of moments for estimating the between‐study covariance matrix with the properties that (1) it allows for either complete or incomplete outcomes and (2) it allows for covariates through meta‐regression. Further, for complete data, it is invariant to linear transformations. Our method reduces to the usual univariate method of moments, proposed by DerSimonian and Laird, in a single dimension. We illustrate our method and compare it with some of the alternatives using a simulation study and a real example.     

Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data

The Mantel test is widely used to test the linear or monotonic independence of the elements in two distance matrices. It is one of the few appropriate tests when the hypothesis under study can only be formulated in terms of distances; this is often the case with genetic data. In particular, the Mantel test has been widely used to test for spatial relationship between genetic data and spatial layout of the sampling locations. We describe the domain of application of the Mantel test and derived forms. Formula development demonstrates that the sum-of-squares (SS) partitioned in Mantel tests and regression on distance matrices differs from the SS partitioned in linear correlation, regression and canonical analysis. Numerical simulations show that in tests of significance of the relationship between simple variables and multivariate data tables, the power of linear correlation, regression and canonical analysis is far greater than that of the Mantel test and derived forms, meaning that the former methods are much more likely than the latter to detect a relationship when one is present in the data. Examples of difference in power are given for the detection of spatial gradients. Furthermore, the Mantel test does not correctly estimate the proportion of the original data variation explained by spatial structures. The Mantel test should not be used as a general method for the investigation of linear relationships or spatial structures in univariate or multivariate data. Its use should be restricted to tests of hypotheses that can only be formulated in terms of distances.     

Tail posterior probability for inference in pairwise and multiclass gene expression data

We consider the problem of identifying differentially expressed genes in microarray data in a Bayesian framework with a noninformative prior distribution on the parameter quantifying differential expression. We introduce a new rule, tail posterior probability, based on the posterior distribution of the standardized difference, to identify genes differentially expressed between two conditions, and we derive a frequentist estimator of the false discovery rate associated with this rule. We compare it to other Bayesian rules in the considered settings. We show how the tail posterior probability can be extended to testing a compound null hypothesis against a class of specific alternatives in multiclass data.     

Calibration of multivariate scatter plots for exploratory analysis of relations within and between sets of variables in genomic research

The scatter plot is a well known and easily applicable graphical tool to explore relationships between two quantitative variables. For the exploration of relations between multiple variables, generalisations of the scatter plot are useful. We present an overview of multivariate scatter plots focussing on the following situations. Firstly, we look at a scatter plot for portraying relations between quantitative variables within one data matrix. Secondly, we discuss a similar plot for the case of qualitative variables. Thirdly, we describe scatter plots for the relationships between two sets of variables where we focus on correlations. Finally, we treat plots of the relationships between multiple response and predictor variables, focussing on the matrix of regression coefficients. We will present both known and new results, where an important original contribution concerns a procedure for the inclusion of scales for the variables in multivariate scatter plots. We provide software for drawing such scales. We illustrate the construction and interpretation of the plots by means of examples on data collected in a genomic research program on taste in tomato.     

基于物质流分析方法的唐山市经济与环境关系的协整检验和分解

利用物质流分析方法(MFA)建立物质流账户,分析唐山市在经济 环境系统运行中物质投入量与产出量的阶段特征及物质投入和产出强度对经济发展的影响程度;使用计量经济学模型,分别对国内生产总值(GDP)、直接物质投入(DMI)和直接废弃物排放(DPO)进行单位根检验、Johansen协整检验、向量误差修正分析、脉冲响应和方差分解分析,探索了各指标之间的双向作用机制和长期关系.结果表明: 1992—2011年,唐山市DMI和DPO 均呈增长趋势,DMI的增幅高于DPO.DMI投入强度呈增长趋势,DPO产出强度呈波动下降趋势.GDP与DMI、DPO之间存在着长期稳定协整关系,指标间的作用关系经历了由波动到逐步平稳的过程.DMI与DPO在短期内会对经济发展起到较强的正向冲击作用,但是经济-环境系统会逐步消化这些影响,并对系统内外指标进行短期的动态调整,最终使系统表现出一种长期的均衡关系;经济发展受到经济规模效应的影响逐步增加.将各指标对GDP的贡献度予以分解,其中,DMI的贡献度上升,GDP的贡献度下降,DPO的贡献度变化不大.总体上,唐山市的经济发展遵循了资源型城市的传统生产轨迹,较大程度上依赖于物质投入,高能源消耗又加剧了环境污染.     

Sensitivity of 70-mer oligonucleotides and cDNAs for microarray analysis of gene expression in Arabidopsis and its related species

Synthetic oligonucleotides (oligos) represent an attractive alternative to cDNA amplicons for spotted microarray analysis in a number of model organisms, including Arabidopsis, C. elegans, Drosophila, human, mouse and yeast. However, little is known about the relative effectiveness of 60-70-mer oligos and cDNAs for detecting gene expression changes. Using 192 pairs of Arabidopsis thaliana cDNAs and corresponding 70-mer oligos, we performed three sets of dye-swap experiments and used analysis of variance (anova) to compare sources of variation and sensitivities for detecting gene expression changes in A. thaliana, A. arenosa and Brassica oleracea. Our major findings were: (1) variation among different RNA preparations from the same tissue was small, but large variation among dye-labellings and slides indicates the need to replicate these factors; (2) sources of variation were similar for experiments with all three species, suggesting these feature types are effective for analysing gene expression in related species; (3) oligo and cDNA features had similar sensitivities for detecting expression changes and they identified a common subset of significant genes, but results from quantitative RT-PCR did not support the use of one over the other. These findings indicate that spotted oligos are at least as effective as cDNAs for microarray analyses of gene expression. We are using oligos designed from approximately 26,000 annotated genes of A. thaliana to study gene expression changes in Arabidopsis and Brassica polyploids.     

Genetic analysis of candidate SNPs for metabolic syndrome in obstructive sleep apnea (OSA)

Obstructive sleep apnea (OSA) is a common disorder characterized by the reduction or complete cessation in airflow resulting from an obstruction of the upper airway. Several studies have observed an increased risk for cardiovascular morbidity and mortality among OSA patients. Metabolic syndrome (MetS), a cluster of cardiovascular risk factors characterized by the presence of insulin resistance, is often found in patients with OSA, but the complex interplay between these two syndromes is not well understood. In this study, we present the results of a genetic association analysis of 373 candidate SNPs for MetS selected in a previous genome wide association analysis (GWAS). The 384 selected SNPs were genotyped using the Illumina VeraCode Technology in 387 subjects retrospectively assessed at the Internal Medicine Unit of the “Virgen de Valme” University Hospital (Seville, Spain). In order to increase the power of this study and to validate our findings in an independent population, we used data from the Framingham Sleep Study which comprises 368 individuals. Only the rs11211631 polymorphism was associated with OSA in both populations, with an estimated OR = 0.57 (0.42–0.79) in the joint analysis (p = 7.21 × 10^− 4). This SNP was selected in the previous GWAS for MetS components using a digenic approach, but was not significant in the monogenic study. We have also identified two SNPs (rs2687855 and rs4299396) with a protective effect from OSA only in the subpopulation with abdominal obesity. As a whole, our study does not support the idea that OSA and MetS share major genetic determinants, although both syndromes share common epidemiological and clinical features.     

Sex different effect of antibiotic and probiotic treatment on intestinal microbiota composition in chemically induced liver injury rats

Differences in the gut microbiota and metabolic processes between males and females may explain differences in the risk of liver injury; however, the sex-specific effects of antibiotics and probiotics on these relationships are not clear. We evaluated differences in the gut microbiota and the risk of liver injury between male and female rats after the oral administration of antibiotics or probiotics followed by a period of diethylnitrosamine treatment to chemically induce liver injuryusing high-throughput sequencing of fecal microbiota combined with histological analyses of liver and colon tissues. Our results suggest that the ratio of gram-positive to gram-negative bacteria in kanamycin-treated rats was significantly higher than that of other groups, and this difference persisted for the duration of the experiment. Antibiotics significantly changed the composition of the gut microbiota of experimental rats. Clindamycin caused more diethylnitrosamine-induced damage to livers of male rats. Probiotics did not influencethe gut microbiota; however, they hadprotective effects against liver injury induced by diethylnitrosamine, especially in female rats. These results strengthen our understanding of sex differences in the indirect effects of antibiotics or probiotics on metabolism and liver injury in hosts via the gut microbiota.