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PubMed2004

Bootstrap white matter tractography (BOOT-TRAC).

White matter tractography is a noninvasive method for estimating and visualizing the white matter connectivity patterns in the human brain using diffusion tensor imaging (DTI) data. Sources of experimental noise may induce errors in the measured fiber directions, which will reduce the accuracy of the estimated white matter trajectories. In this study, a statistical nonparametric bootstrap method is described for estimating the dispersion and other errors in white matter tractography results. Prior studies have derived models of tractography error using the signal-to-noise ratio (SNR) and diffusion anisotropy of the DTI data. Tractography errors measured using bootstrap methods were generally consistent with an analytic model of tractography error except in areas where branching was evident. White matter tractography with bootstrap resampling is also applied to estimate the probabilities of connection between brain regions. The approach was used to generate probabilistic connectivity maps between the cerebral peduncles and specific cortical regions.

Brain↗

PubMed1999

A procedure for generating bootstrap samples for the validation of nonlinear mixed-effects population models.

A method is presented for automated preparation of bootstrap data samples and their presentation to NONMEM for use in the validation of population pharmacokinetic or pharmacodynamic models, which have been developed with relatively small numbers of subjects. The bootstrap sampling procedure involves the use of an MS-DOS batch file and a script file for use with the public-domain text processing program, AWK, which is a single EXE file (48k in size for the version used in this report). A UNIX version of AWK is also available and UNIX users can adapt the process to their needs. Its use obviates the need for expensive, high-end statistical packages and associated script files written using in-built programming languages. The method can easily be adapted to bootstrap sampling requirements in other biomedical modelling applications.

Computer Simulation↗

PubMed1999

Bootstrap prediction and confidence bands: a superior statistical method for analysis of gait data.

Gait analysis studies typically utilize continuous curves of data measured over the gait cycle, or a portion of the gait cycle. Statistical methods which are appropriate for use in studies involving a single point of data are not adequate for analysis of continuous curves of data. This paper determines the operating characteristics for two methods of constructing statistical prediction and confidence bands. The methods are compared, and their performance is evaluated using cross-validation methodology with a data set of the sort commonly evaluated in gait analysis. The methods evaluated are the often-used point-by-point Gaussian theory intervals, and the simultaneous bootstrap intervals of Sutherland et al. The Development of Mature Walking, MacKeith Press, London, 1988 and Olshen et al. Ann. Statist. 17 (1989) 1419-40. The bootstrap bands are shown to provide appropriate coverage for continuous curve gait data (86% coverage for a targeted coverage of 90%). The Gaussian bands are shown to provide inadequate coverage (54% for a targeted coverage of 90%). The deficiency in the Gaussian method can lead to inaccurate conclusions in gait studies. Bootstrap prediction and confidence bands are advocated for use as a standard method for evaluating gait data curves because the method is non-parametric and maintains nominal coverage levels for entire curves of gait data.

Gait↗

PubMed2002

Phylogenetic relationships of the dwarf boas and a comparison of Bayesian and bootstrap measures of phylogenetic support.

Four New World genera of dwarf boas (Exiliboa, Trachyboa, Tropidophis, and Ungaliophis) have been placed by many systematists in a single group (traditionally called Tropidophiidae). However, the monophyly of this group has been questioned in several studies. Moreover, the overall relationships among basal snake lineages, including the placement of the dwarf boas, are poorly understood. We obtained mtDNA sequence data for 12S, 16S, and intervening tRNA-val genes from 23 species of snakes representing most major snake lineages, including all four genera of New World dwarf boas. We then examined the phylogenetic position of these species by estimating the phylogeny of the basal snakes. Our phylogenetic analysis suggests that New World dwarf boas are not monophyletic. Instead, we find Exiliboa and Ungaliophis to be most closely related to sand boas (Erycinae), boas (Boinae), and advanced snakes (Caenophidea), whereas Tropidophis and Trachyboa form an independent clade that separated relatively early in snake radiation. Our estimate of snake phylogeny differs significantly in other ways from some previous estimates of snake phylogeny. For instance, pythons do not cluster with boas and sand boas, but instead show a strong relationship with Loxocemus and Xenopeltis. Additionally, uropeltids cluster strongly with Cylindrophis, and together are embedded in what has previously been considered the macrostomatan radiation. These relationships are supported by both bootstrapping (parametric and nonparametric approaches) and Bayesian analysis, although Bayesian support values are consistently higher than those obtained from nonparametric bootstrapping. Simulations show that Bayesian support values represent much better estimates of phylogenetic accuracy than do nonparametric bootstrap support values, at least under the conditions of our study.

Animals↗

PubMed2000

Components-of-variance models and multiple-bootstrap experiments: an alternative method for random-effects, receiver operating characteristic analysis.

RATIONALE AND OBJECTIVES: The purpose of this study was to develop an alternative approach to random-effects, receiver operating characteristic analysis inspired by a general formulation of components-of-variance models. The alternative approach is a higher-order generalization of the Dorfman, Berbaum, and Metz (DBM) approach that yields additional information on the variance structure of the problem. MATERIALS AND METHODS: Six population experiments were designed to determine the six variance components in the DBM model. For practical problems, in which only a finite set of readers and patients are available, six analogous bootstrap experiments may be substituted for the population experiments to estimate the variance components. Monte Carlo simulations were performed on the population experiments, and those results were compared with the corresponding multiple-bootstrap estimates and those obtained with the DBM approach. Confidence intervals on the difference of ROC parameters for competing diagnostic modalities were estimated, and corresponding comparisons were made. RESULTS: For mean values, the agreement of present estimates of variance structures with population results was excellent and, when suitably weighted and mixed, similar to or closer than that with the DBM method. For many variance structures, the confidence intervals in this study for the difference in ROC area between modalities were comparable to those with the DBM method. When reader variability was large, however, mean confidence intervals from this study were tighter than those with the DBM method and closer to population results. CONCLUSION: The jackknife approach of DBM provides a linear approximation to receiver-operating-characteristic statistics that are intrinsically nonlinear. The multiple-bootstrap technique of this study, however, provides a more general, nonparametric, maximum-likelihood approach. It also yields estimates of the variance structure previously unavailable.

Confidence Intervals↗

PubMed2002

Application of non-parametric bootstrap methods to estimate confidence intervals for QTL location in a beef cattle QTL experimental population.

Empirical confidence intervals (CIs) for the estimated quantitative trait locus (QTL) location from selective and non-selective non-parametric bootstrap resampling methods were compared for a genome scan involving an Angus x Brahman reciprocal fullsib backcross population. Genetic maps, based on 357 microsatellite markers, were constructed for 29 chromosomes using CRI-MAP V2.4. Twelve growth, carcass composition and beef quality traits (n = 527-602) were analysed to detect QTLs utilizing (composite) interval mapping approaches. CIs were investigated for 28 likelihood ratio test statistic (LRT) profiles for the one QTL per chromosome model. The CIs from the non-selective bootstrap method were largest (87 7 cM average or 79-2% coverage of test chromosomes). The Selective II procedure produced the smallest CI size (42.3 cM average). However, CI sizes from the Selective II procedure were more variable than those produced by the two LOD drop method. CI ranges from the Selective II procedure were also asymmetrical (relative to the most likely QTL position) due to the bias caused by the tendency for the estimated QTL position to be at a marker position in the bootstrap samples and due to monotonicity and asymmetry of the LRT curve in the original sample.

Animals↗

PubMed1996

Application of the bootstrap to calibration experiments.

In calibration experiments, a number of samples of known concentration are used to establish the relationship between a measured response and sample concentration; this relationship is then used to estimate the unknown concentration of further samples from their measured responses. In addition to the estimates themselves, it is useful to have available some measure of their precision, usually given in the form of confidence limits. The standard method of inverting prediction limits is found to work well in simple situations, but in nonlinear multivariate calibration it becomes intractable. The bootstrap offers an alternative methodology, but in the calibration framework its application is not obvious. We describe some considerations in bootstrapping calibration data and compare our methods with a previous attempt and with the standard method in linear, nonlinear, and multivariate situations. The bootstrap is found to be a useful tool in those situations where the standard method is difficult to implement.

Calibration↗

PubMed2004

Bootstrap standard error and confidence intervals for the correlation corrected for range restriction: a simulation study.

The standard Pearson correlation coefficient is a biased estimator of the true population correlation, rho, when the predictor and the criterion are range restricted. To correct the bias, the correlation corrected for range restriction, rc, has been recommended, and a standard formula based on asymptotic results for estimating its standard error is also available. In the present study, the bootstrap standard-error estimate is proposed as an alternative. Monte Carlo simulation studies involving both normal and nonnormal data were conducted to examine the empirical performance of the proposed procedure under different levels of rho, selection ratio, sample size, and truncation types. Results indicated that, with normal data, the bootstrap standard-error estimate is more accurate than the traditional estimate, particularly with small sample size. With nonnormal data, performance of both estimates depends critically on the distribution type. Furthermore, the bootstrap bias-corrected and accelerated interval consistently provided the most accurate coverage probability for rho.

Adolescent↗

PubMed2006

Bootstrap model averaging in time series studies of particulate matter air pollution and mortality.

The consensus from time series studies that have investigated the mortality effects of particulate matter air pollution (PM) is that increases in PM are associated with increases in daily mortality. However, recently concerns have been raised that the observed positive association between PM and mortality may be an artefact of model selection due to multiple hypothesis testing. This problem arises when a number of models are investigated, but only the "best" model is reported and all subsequent inference is based on this model, ignoring the model selection process. In this paper, we introduce the use of the bootstrap as a means of addressing the problems of model selection in PM mortality time series studies. Using the bootstrap to perform inference about the effect of PM on mortality is a process based on a set of models rather than on a single model. It is shown that using the bootstrap to overcome the problems of model selection is competitive with the existing methodology of Bayesian model averaging.

Air Pollutants↗

PubMed2005

Estimating misclassification error with small samples via bootstrap cross-validation.

MOTIVATION: Estimation of misclassification error has received increasing attention in clinical diagnosis and bioinformatics studies, especially in small sample studies with microarray data. Current error estimation methods are not satisfactory because they either have large variability (such as leave-one-out cross-validation) or large bias (such as resubstitution and leave-one-out bootstrap). While small sample size remains one of the key features of costly clinical investigations or of microarray studies that have limited resources in funding, time and tissue materials, accurate and easy-to-implement error estimation methods for small samples are desirable and will be beneficial. RESULTS: A bootstrap cross-validation method is studied. It achieves accurate error estimation through a simple procedure with bootstrap resampling and only costs computer CPU time. Simulation studies and applications to microarray data demonstrate that it performs consistently better than its competitors. This method possesses several attractive properties: (1) it is implemented through a simple procedure; (2) it performs well for small samples with sample size, as small as 16; (3) it is not restricted to any particular classification rules and thus applies to many parametric or non-parametric methods.

Algorithms↗

PubMed1998

Empirical nonparametric bootstrap strategies in quantitative trait loci mapping: conditioning on the genetic model.

Several nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL's position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL's position.

Chromosome Mapping↗

PubMedDate not supplied

Nonparametric assessment of toxicologic assay linearity by bootstrap analysis.

An important aspect in the evaluation of toxicologic assay methodology is the assessment of calibration. This paper presents a new approach for validating calibration using bootstrap analysis. The technique is illustrated with a quantitative assay for benzoylecgonine in urine by gas chromatography/mass spectrometry (GC/MS). Because the bootstrap analysis does not rely on parametric assumptions regarding the distribution of errors about the regression line, it can be applied to situations where the parametric distribution of response errors about the regression line is unknown. This application of bootstrap methodology yields a probabilistic measure of confidence on the linearity of the calibration curve.

Calibration↗

PubMed2004

POBO, transcription factor binding site verification with bootstrapping.

Transcription factors can either activate or repress target genes by binding onto short nucleotide sequence motifs in the promoter regions of these genes. Here, we present POBO, a promoter bootstrapping program, for gene expression data. POBO can be used to detect, compare and verify predetermined transcription factor binding site motifs in the promoters of one or two clusters of co-regulated genes. The program calculates the frequencies of the motif in the input promoter sets. A bootstrap analysis detects significantly over- or underrepresented motifs. The output of the program presents bootstrapped results in picture and text formats. The program was tested with published data from transgenic WRKY70 microarray experiments. Intriguingly, motifs recognized by the WRKY transcription factors of plant defense pathways are similarly enriched in both up- and downregulated clusters. POBO analysis suggests slightly modified hypothetical motifs that discriminate between up- and downregulated clusters. In conclusion, POBO allows easy, fast and accurate verification of putative regulatory motifs. The statistical tests implemented in POBO can be useful in eliminating false positives from the results of pattern discovery programs and increasing the reliability of true positives. POBO is freely available from http://ekhidna.biocenter.helsinki.fi:9801/pobo.

Binding Sites↗

PubMed2002

The effects of nucleotide substitution model assumptions on estimates of nonparametric bootstrap support.

The use of parameter-rich substitution models in molecular phylogenetics has been criticized on the basis that these models can cause a reduction both in accuracy and in the ability to discriminate among competing topologies. We have explored the relationship between nucleotide substitution model complexity and nonparametric bootstrap support under maximum likelihood (ML) for six data sets for which the true relationships are known with a high degree of certainty. We also performed equally weighted maximum parsimony analyses in order to assess the effects of ignoring branch length information during tree selection. We observed that maximum parsimony gave the lowest mean estimate of bootstrap support for the correct set of nodes relative to the ML models for every data set except one. For several data sets, we established that the exact distribution used to model among-site rate variation was critical for a successful phylogenetic analysis. Site-specific rate models were shown to perform very poorly relative to gamma and invariable sites models for several of the data sets most likely because of the gross underestimation of branch lengths. The invariable sites model also performed poorly for several data sets where this model had a poor fit to the data, suggesting that addition of the gamma distribution can be critical. Estimates of bootstrap support for the correct nodes often increased under gamma and invariable sites models relative to equal rates models. Our observations are contrary to the prediction that such models cause reduced confidence in phylogenetic hypotheses. Our results raise several issues regarding the process of model selection, and we briefly discuss model selection uncertainty and the role of sensitivity analyses in molecular phylogenetics.

Animals↗

PubMed1996

Bootstrap method of interior-branch test for phylogenetic trees.

Statistical properties of the bootstrap test of interior branch lengths of phylogenetic trees have been studied and compared with those of the standard interior-branch test in computer simulations. Examination of the properties of the tests under the null hypothesis showed that both tests for an interior branch of a predetermined topology are quite reliable when the distribution of the branch length estimate approaches a normal distribution. Unlike the standard interior-branch test, the bootstrap test appears to retain this property even when the substitution rate varies among sites. In this case, the distribution of the branch length estimate deviates from a normal distribution, and the standard interior-branch test gives conservative confidence probability values. A simple correction method was developed for both interior-branch tests to be applied for testing the reliability of tree topologies estimated from sequence data. This correction for the standard interior-branch test appears to be as effective as that obtained in our previous study, though it is much simpler. The bootstrap and standard interior-branch tests for estimated topologies become conservative as the number of sequence groups in a star-like tree increases.

Animals↗

PubMed1999

Bootstrapping: estimating confidence intervals for cost-effectiveness ratios.

Economic evaluations are increasingly being conducted alongside clinical trials of health interventions, with resource consequences being estimated from stochastic data. It is, therefore, important that economic evaluation results, like the clinical results, reflect the underlying variance within the sample data. A statistical methodology, known as bootstrapping, has recently been put forward as a potential method for calculating confidence intervals for cost-effectiveness ratios, yet it is still unusual to see economic evaluations reporting confidence intervals. In this paper we demonstrate the practical application of bootstrapping using real data from clinical trials, and conclude that bootstrapping is easily transferable from theory to practice for the estimation of confidence intervals for cost-effectiveness ratios. We encourage further investigation into its applicability and use.

Confidence Intervals↗

PubMed2001

Bootstrap estimates of chaotic dynamics.

Bootstrap sampling is a nonparametric method for estimating the standard error of a statistic. This paper describes the application of bootstrap sampling to estimate the error in local linear approximations of the dynamics on chaotic attractors reconstructed from time series measurements. We present an algorithm for identifying influential points, i.e., observations with an especially large effect on a least-squares fit, and an algorithm to estimate the standard error of regression coefficients obtained from total least squares. We also consider the application of bootstrap methods to assess the uncertainty in Lyapunov exponent computations from chaotic time series.

Journal Article↗

PubMed2001

Quasisteady high-confinement reversed shear plasma with large bootstrap current fraction under full noninductive current drive condition in JT-60U.

A quasisteady reversed shear plasma with a large bootstrap current fraction ( approximately 80%) has been obtained for the first time in the JT-60U tokamak. The shrinkage of reversed shear region was suppressed by the bootstrap current peaked at the internal transport barrier (ITB) layer and the ITBs at a large radius were sustained, which, by combination with an H-mode edge pedestal, resulted in a high confinement or 2.2 times the H-mode scaling for 6 times energy confinement time or 2.7 s. Furthermore, a full noninductive current drive was obtained by the bootstrap current and the beam driven current.

Journal Article↗