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Results for “Bootstrap resampling”

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PubMed2002

Resampling methods for variance estimation of singular value decomposition analyses from microarray experiments.

Microarray experiments offer the ability to generate gene expression measurements for thousands of genes simultaneously. Work has begun recently on attempting to reconstruct genetic networks based on analyses of microarray experiments in time-course studies. An important tool in these analyses has been the singular value decomposition method. However, little work has been done on assessing the variability associated with singular value decomposition analyses. In this report, we discuss use of the bootstrap as a method of obtaining standard errors for singular value decomposition analyses. We consider use of this method both when there are replicates and when no replicates exist. The proposed methods are illustrated with an application to two datasets: one involving a human foreskin study, the other involving yeast.

Algorithms↗

PubMed1999

Combined molecular phylogenetic analysis of the Orthoptera (Arthropoda, Insecta) and implications for their higher systematics.

A phylogenetic analysis of mitochondrial and nuclear rDNA sequences from species of all the superfamilies of the insect order Orthoptera (grasshoppers, crickets, and relatives) confirmed that although mitochondrial sequences provided good resolution of the youngest superfamilies, nuclear rDNA sequences were necessary to separate the basal groups. To try to reconcile these data sets into a single, fully resolved orthopteran phylogeny, we adopted consensus and combined data strategies. The consensus analysis produced a partially resolved tree that lacked several well-supported features of the individual analyses. However, this lack of resolution was explained by an examination of resampled data sets, which identified the likely source of error as the relatively short length of the individual mitochondrial data partitions. In a subsequent comparison in which the mitochondrial sequences were initially combined, we observed less conflict. We then used two approaches to examine the validity of combining all of the data in a single analysis: comparative analysis of trees recovered from resampled data sets, and the application of a randomization test. Because the results did not point to significant levels of heterogeneity in phylogenetic signal between the mitochondrial and nuclear data sets, we therefore proceeded with a combined analysis. Reconstructing phylogenies under the minimum evolution and maximum likelihood optimality criteria, we examined monophyly of the major orthopteran groups, using nonparametric and parametric bootstrap analysis and Kishino-Hasegawa tests. Our analysis suggests that phylogeny reconstruction under the maximum likelihood criteria is the most discriminating approach for the combined sequences. The results indicate, moreover, that the caeliferan Pneumoroidea and Pamphagoidea, as previously suggested, are polyphyletic. The Acridoidea is redefined to include all pamphagoid families other than the Pyrgomorphidae, which we propose should be accorded superfamily status.

Animals↗

PubMed2006

Assessing performance of prediction rules in machine learning.

INTRODUCTION: An important goal in machine learning is to assess the degree to which prediction rules are robust and replicable, since these rules are used for decision making and for planning follow-up studies. This requires an estimate of a prediction rule's true error rate, a statistic that can be estimated by resampling data. However, there are many possible approaches depending upon whether we draw observations with or without replacement, or sample once, repeatedly, or not at all, and the pros and cons of each are often unclear. This study illustrates and compares different methods for estimating true error with the aim of providing practical guidance to users of machine learning techniques. METHODS: We conducted Monte Carlo simulation studies using four different error estimators: bootstrap, split sample, resubstitution and a direct estimate of true error. Here, 'split sample' refers to a single random partition of the data into a pair of training and test samples, a popular scheme. We used stochastic gradient boosting as a learning algorithm, and considered data from two studies for which the underlying data mechanism was known to be complex: a library of 6000 tripeptide substrates collected for analysis of proteasome inhibition as part of anticancer drug design, and a cardiovascular study involving 600 subjects receiving antiplatelet treatment for acute coronary syndrome. RESULTS: There were important differences in the performance of the various error estimators examined. Error estimators for split sample and resubstitution, while being the most transparent in action and the simplest to apply, did not quantify the performance of prediction rules as accurately as the bootstrap. This was true for both types of study data, despite their highly different nature. CONCLUSIONS: The robustness and reliability of decisions based on analysis of genomics data could, in many cases, be improved by following best practices for prediction error estimation. For this, techniques such as bootstrap should be considered.

Algorithms↗

PubMed1998

[Selective structure of the gene pool. III. Technology of determination from F(ST)-statistics using numerical resampling].

The selection pressure on the ith gene was determined on the basis of the heterogeneity of interpopulation diversity FST(i), assumpting that the significant deviation of FST(i) (observed differentiation of the ith gene) from Fe (selectively neutral differentiation) indicates selection. A selectively neutral variation Fe was estimated from the mean FST, averaged over the total set of genes. Since the validity of the equation FST approximately Fe = (4NeMe + 1)-1 depends on the fulfillment of conditions of the theoretical model as well as on organization of sampling of genes and subpopulations rather than on statistical parameters of the gene sample, an additional correction by boot-strapping is suggested. Simulation of sampling of the gene pool using numerical resampling (10(6) samples from each of the 50 markers) allowed us to characterize the selective structure of the gene pool. This structure consists of the following: one class of selectively neutral genes, NEUTRAL (FST(i) approximately Fe); and two classes of selective genes, LOWER DIFF (FST(i) < Fe) and SUPER DIFF (FST(i) > Fe). Interclass regions N-LOWER and N-SUPER between the classes of neutral and selective genes were defined with the use of bootstrapping. The hypothesis on the presence or absence of selection cannot be formulated with regard to the genes included in the interclass regions. A general trend for all gene pools of the world was revealed: the ratio between the boundary values of selective classes and Fe is constant. On the basis of this, a rapid and simple technique for estimating selective values of genes was developed. The positions of more than 80 immunobiochemical gene markers in the selective structure of six gene pools of the world (Europe, Asia, Africa, Australia, America, and northeastern Eurasia) are presented. The selective structure of five subregions of northeastern Eurasia (Caucasus, Europe, Ural, Siberia, and Central Asia) are characterized as well.

Data Interpretation, Statistical↗

PubMed2006

Genetic typing and prevalence of Border disease virus (BDV) in small ruminant flocks in Spain.

Between 2001 and 2002, samples from 1,413 animals in 21 Spanish small ruminant flocks, most of them with animals showing clinical signs compatible with Border disease (BD), were screened for the presence of Pestivirus antigen and antibodies by an indirect peroxidase monolayer assay (IPMA) and the virus neutralization test (VNT), respectively. Although all flocks harboured seropositive animals, virus could only be isolated from animals in five of the flocks. Between 4 and 11 months later all animals older than 6 months in three of the flocks were resampled. At this time, 51-83% of them had neutralizing antibodies. The prevalence of persistently infected (PI) animals within two of the flocks was 0.3 and 0.6%, respectively. The third flock presumably had eliminated all the PI animals. Fourteen virus isolates were obtained. The 5' untranslated region (5'UTR) was amplified by RT-PCR and directly sequenced. Phylogenetic analyses classified them as a group of Border disease viruses (BDV), separated from BDV-1, but showing a relatively low bootstrap value. Three of the 14 isolates were in the same subgroup as a set of formerly characterised Spanish isolates from the Basque Country, which were allocated to subgroup BDV-C. In addition, they were in the group with an isolate from chamois, which is currently allocated in group BDV-4. Because of its close relation to the chamois isolate, these isolates were tentatively reallocated in a subgroup BDV-4a. The remaining isolates generated a new subgroup, related but not in the same cluster as the chamois isolate, and was therefore tentatively assigned to a new subgroup BDV-4b. Our results show that classification and nomenclature of BDV needs to be harmonised.

5' Untranslated Regions↗

PubMed2004

The benefits of increasing the number of microsatellites utilized in genetic population studies: an empirical perspective.

One of the key issues concerning the application of microsatellite DNA data in evolutionary studies is how the number of loci applied may influence the stability of genetic distances and corresponding phylograms. While computer simulations have suggested that over 30 microsatellites are required for accurate evolutionary inference, we show that a median of only six loci have been generally applied in studies of wild populations. Factors contributing to this contrast include: i) uncertainty regarding the potential benefits that can be gained from a realistic increase in the number of loci used; and ii) the lack of empirical studies assessing the influence of the number of microsatellites on the reliability of genetic distance estimation and phylogeny construction. In order to address these issues, we applied resampling techniques to microsatellite data in widely distributed populations of European grayling (Thymallus thymallus, Salmonidae). In agreement with expectations based on simulated data, we demonstrate empirically that the stability of commonly used genetic distances (DCE, DA and (deltamu)2) and the corresponding neighbor-joining phylograms is positively associated with the number of microsatellites utilized. For instance, increasing the number of loci from six to 17 resulted in a striking 75% increase in the proportion of DCE phylogram nodes supported by a bootstrap estimate of over 70%. Our results demonstrate that even moderately increasing the number of loci can be very beneficial--a finding extremely relevant for studies of natural populations for which optimally high microsatellite numbers are out of reach. Furthermore, the number of loci most commonly used to date may lead to erroneous inference of the evolutionary relationships between populations.

Animals↗

PubMed2004

A simple significance test for quantile regression.

Where OLS regression seeks to model the mean of a random variable as a function of observed variables, quantile regression seeks to model the quantiles of a random variable as functions of observed variables. Tests for the dependence of the quantiles of a random variable upon observed variables have only been developed through the use of computer resampling or based on asymptotic approximations resting on distributional assumptions. We propose an exceedingly simple but heretofore undocumented likelihood ratio test within a logistic regression framework to test the dependence of a quantile of a random variable upon observed variables. Simulated data sets are used to illustrate the rationale, ease, and utility of the hypothesis test. Simulations have been performed over a variety of situations to estimate the type I error rates and statistical power of the procedure. Results from this procedure are compared to (1) previously proposed asymptotic tests for quantile regression and (2) bootstrap techniques commonly used for quantile regression inference. Results show that this less computationally intense method has appropriate type I error control, which is not true for all competing procedures, comparable power to both previously proposed asymptotic tests and bootstrap techniques, and greater computational ease. We illustrate the approach using data from 779 adolescent boys age 12-18 from the Third National Health and Nutrition Examination Survey (NHANES III) to test hypotheses regarding age, ethnicity, and their interaction upon quantiles of waist circumference.

Adolescent↗

PubMed2004

Use of resampling to select among alternative error structure specifications for GLMM analyses of repeated measurements.

Autocorrelated error and missing data due to dropouts have fostered interest in the flexible general linear mixed model (GLMM) procedures for analysis of data from controlled clinical trials. The user of these adaptable statistical tools must, however, choose among alternative structural models to represent the correlated repeated measurements. The fit of the error structure model specification is important for validity of tests for differences in patterns of treatment effects across time, particularly when maximum likelihood procedures are relied upon. Results can be affected significantly by the error specification that is selected, so a principled basis for selecting the specification is important. As no theoretical grounds are usually available to guide this decision, empirical criteria have been developed that focus on mode fit. The current report proposes alternative empirical criteria that focus on bootstrap estimates of actual type I error an power of tests for treatment effects. Results for model selection before and after the blind is broken are compared. Goodness-of-fit statistics also compare favourably for models fitted to the blinded or unblinded data, although the correspondence to actual type I error and power depends on the particular fit statistic that is considered.

Antidepressive Agents↗

PubMed2006

Quantile-function based null distribution in resampling based multiple testing.

Simultaneously testing a collection of null hypotheses about a data generating distribution based on a sample of independent and identically distributed observations is a fundamental and important statistical problem involving many applications. Methods based on marginal null distributions (i.e., marginal p-values) are attractive since the marginal p-values can be based on a user supplied choice of marginal null distributions and they are computationally trivial, but they, by necessity, are known to either be conservative or to rely on assumptions about the dependence structure between the test-statistics. Re-sampling based multiple testing (Westfall and Young, 1993) involves sampling from a joint null distribution of the test-statistics, and controlling (possibly in a, for example, step-down fashion) the user supplied type-I error rate under this joint null distribution for the test-statistics. A generally asymptotically valid null distribution avoiding the need for the subset pivotality condition for the vector of test-statistics was proposed in Pollard, van der Laan (2003) for null hypotheses about general real valued parameters. This null distribution was generalized in Dudoit, vanderLaan, Pollard (2004) to general null hypotheses and test-statistics. In ongoing recent work van der Laan, Hubbard (2005), we propose a new generally asymptotically valid null distribution for the test-statistics and a corresponding bootstrap estimate, whose marginal distributions are user supplied, and can thus be set equal to the (most powerful) marginal null distributions one would use in univariate testing to obtain a p-value. Previous proposed null distributions either relied on a restrictive subset pivotality condition (Westfall and Young) or did not guarantee this latter property (Dudoit, vanderLaan, Pollard, 2004). It is argued and illustrated that the resulting new re-sampling based multiple testing methods provide more accurate control of the wished Type-I error in finite samples and are more powerful. We establish formal results and investigate the practical performance of this methodology in a simulation and data analysis.

Chi-Square Distribution↗