An investigation on performance of Significance Analysis of Microarray (SAM) for the comparisons of several treatments with one control in the presence of small-variance genes

One of multiple testing problems in drug finding experiments is the comparison of several treatments with one control. In this paper we discuss a particular situation of such an experiment, i.e., a microarray setting, where the many-to-one comparisons need to be addressed for thousands of genes simultaneously. For a gene-specific analysis, Dunnett's single step procedure is considered within gene tests, while the FDR controlling procedures such as Significance Analysis of Microarrays (SAM) and Benjamini and Hochberg (BH) False Discovery Rate (FDR) adjustment are applied to control the error rate across genes. The method is applied to a microarray experiment with four treatment groups (three microarrays in each group) and 16,998 genes. Simulation studies are conducted to investigate the performance of the SAM method and the BH-FDR procedure with regard to controlling the FDR, and to investigate the effect of small-variance genes on the FDR in the SAM procedure.     

A renewed approach to the nonparametric analysis of replicated microarray experiments

DNA-microarrays find broad employment in biochemical research. This technology allows the monitoring of the expression levels of thousands of genes at the same time. Often, the goal of a microarray study is to find differentially expressed genes in two different types of tissue, for example normal and cancerous. Multiple hypothesis testing is a useful statistical tool for such studies. One approach using multiple hypothesis testing is nonparametric analysis for replicated microarray experiments. In this paper we present an improved version of this method. We also show how p-values are calculated for all significant genes detected with this testing procedure. All algorithms were implemented in an R-package, and instructions on it's use are included. The package can be downloaded at http://www.statistik.unidortmund.de/de/content/einrichtungen/lehrstuehle/personen/jung.html     

On weighted Hochberg procedures

We consider different ways of constructing weighted Hochberg-typestep-up multiple test procedures including closed proceduresbased on weighted Simes tests and their conservative step-upshort-cuts, and step-up counterparts of two weighted Holm procedures.It is shown that the step-up counterparts have some seriouspitfalls such as lack of familywise error rate control and lackof monotonicity in rejection decisions in terms of p-values.Therefore an exact closed procedure appears to be the best alternative,its only drawback being lack of simple stepwise structure. Aconservative step-up short-cut to the closed procedure may beused instead, but with accompanying loss of power. Simulationsare used to study the familywise error rate and power propertiesof the competing procedures for independent and correlated p-values.Although many of the results of this paper are negative, theyare useful in highlighting the need for caution when procedureswith similar pitfalls may be used.     

具有非齐态生成矩阵罐子模型的渐近性质

研究一种非齐态多臂临床试验的GFU模型,并建立了模型自适应设计.对这种模型,构造了参数的估计量,并获得了相应量的强相合性,收敛速率及其渐近正态性.这些结果对临床试验设计的应用提供了一定的理论依据.     

A unique growth pattern associated with cleistogamy in a tropical legume, Vigna minima (Roxb.) Ohwi & Ohashi (Leguminosae)

Obligate subterranean cleistogamy, observed in a natural population of Vigna minima , is associated with the production of one or two negatively geotropic, leafy shoots and several positively geotropic, highly pigmented, leafless shoots. The latter branch profusely after penetrating the soil and produce much reduced, cleistogamous flowers. The undehisced anthers contain germinated pollen grains. The seeds developing from the cleistogamous flowers differ in size, weight and surface features from those produced by the chasmogamous flowers of other natural populations within the species.     

Properties of adaptive walks on uncorrelated landscapes under strong selection and weak mutation

We examine properties of adaptive walks on uncorrelated (i.e. random) fitness landscapes starting from moderately fit genotypes under strong selection weak mutation. As an extension of Orr's model for a single step in an adaptive walk under these conditions, we show that the fitness rank of the dominant genotype in a population after the fixation of a beneficial mutation is, on average, (i+6)/4, where i is the fitness rank of the starting genotype. This accounts for the change in rank due to acquiring a new set of single-mutation neighbors after fixing a new allele through natural selection. Under this scenario, adaptive walks can be modeled as a simple Markov chain on the space of possible fitness ranks with an absorbing state at i = 1, from which no beneficial mutations are accessible. We find that these walks are typically short and are often completed in a single step when starting from a moderately fit genotype. As in Orr's original model, these results are insensitive to both the distribution of fitness effects and most biological details of the system under consideration.     

A family of Bayes multiple testing procedures

Under the model of independent test statistics, we propose atwo-parameter family of Bayes multiple testing procedures. Thetwo parameters can be viewed as tuning parameters. Using theBenjamini–Hochberg step-up procedure for controlling falsediscovery rate as a baseline for conservativeness, we choosethe tuning parameters to compromise between the operating characteristicsof that procedure and a less conservative procedure that focuseson alternatives that a priori might be considered likely ormeaningful. The Bayes procedures do not have the theoreticaland practical shortcomings of the popular stepwise procedures.In terms of the number of mistakes, simulations for two examplesindicate that over a large segment of the parameter space, theBayes procedure is preferable to the step-up procedure. Anotherdesirable feature of the procedures is that they are computationallyfeasible for any number of hypotheses.