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Results for “Bootstrap resampling”

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PubMed2002

Bump-hunting for the proficiency tester--searching for multimodality.

Kernel density estimation is a method for producing a smooth density approximation to a dataset and avoiding some of the problems associated with histograms. If it is used with a degree of smoothing determined by a fitness for purpose criterion, it can be applied to proficiency test data in order to test for multimodality in the z-scores. The bootstrap is an essential additional technique to determine how rugged the initially estimated kernel density is: the random resampling of the data in the bootstrap simulates a complete blind repeat of the proficiency test. In addition, useful estimates of the standard error of a mode can be thus obtained. It is suggested that a mode and its standard error can be used as an assigned value and its standard uncertainty.

Journal Article↗

PubMed1994

Neural net-bootstrap hybrid methods for prediction of complications in patients implanted with artificial heart valves.

A novel hybrid methodology for prediction of valve related complications in patients with implanted artificial heart valves is discussed. Artificial neural networks provided a mechanism for prediction of postoperative valve-related deaths based on preoperative patient information and valve parameters. Then bootstrap methodology was applied for estimating prediction errors and maximizing prediction accuracy. Data from a clinical trial with 10 years of follow-up on 789 patients implanted with Carpentier-Edwards Pericardial Bioprosthesis were used. A random subset of the data was reserved for validation of the final outcome. The remaining patients' records were repeatedly divided into two groups, using resampling strategy provided by the bootstrap methodology. One of the groups was used for training the neural net and the other one for testing the trained network and determining error rates. Patient information, such as sex, age, NYHA class and anticoagulation therapy, as well as valve parameters, such as size and the date of implant were used as the network inputs. Calculated error rates were then used for assessing the distribution of the error, further optimization of the neural network, and constructing confidence intervals for the error rates. Thus, reliable statistical estimation was obtained on the prediction accuracy. Additionally this new hybrid methodology allowed us to optimize the neural network even further, raising the accuracy of prediction to 78%.

Bioprosthesis↗

PubMed2005

The bootstrap: a technique for data-driven statistics. Using computer-intensive analyses to explore experimental data.

BACKGROUND: The concept of resampling data--more commonly referred to as bootstrapping--has been in use for more than three decades. Bootstrapping has considerable theoretical advantages when it is applied to non-Gaussian data. Most of the published literature is concerned with the mathematical aspects of the bootstrap but increasingly this technique is being utilized in medical and other fields. METHODS: I reviewed the published literature following a 1994 publication assessing the transfer of technology, including the bootstrap, to the biomedical literature. RESULTS: In the ten-year period following that 1994 paper there were 1679 published references to the technique in Medline. In that same time period the following citations were found in the four major medical journals-British Medical Journal (48), JAMA (51), Lancet (52) and the New England Journal of Medicine (45). CONTENT: I introduce the basic theory of the bootstrap, the jackknife, and permutation tests. The bootstrap is used to estimate the accuracy of an estimator such as the standard error, a confidence interval, or the bias of an estimator. The technique may be useful for analysing smallish expensive-to-collect data sets where prior information is sparse, distributional assumptions are unclear, and where further data may be difficult to acquire. Some of the elementary uses of bootstrapping are illustrated by considering the calculation of confidence intervals such as for reference ranges or for experimental data findings, hypothesis testing such as comparing experimental findings, linear regression, and correlation when studying association and prediction of variables, non-linear regression such as used in immunoassay techniques, and ROC curve processing. CONCLUSIONS: These techniques can supplement current nonparametric statistical methods and should be included, where appropriate, in the armamentarium of data processing methodologies.

Computers↗

PubMedDate not supplied

Resampling techniques in the analysis of non-binormal ROC data.

The methods most commonly used for analyzing receiver operating characteristic (ROC) data incorporate "binormal" assumptions about the latent frequency distributions of test results. Although these assumptions have proved robust to a wide variety of actual frequency distributions, some data sets do not "fit" the binormal model. In such cases, resampling techniques such as the jackknife and the bootstrap provide versatile, distribution-independent, and more appropriate methods for hypothesis testing. This article describes the application of resampling techniques to ROC data for which the binormal assumptions are not appropriate, and suggests that the bootstrap may be especially helpful in determining confidence intervals from small data samples. The widespread availability of ever-faster computers has made resampling methods increasingly accessible and convenient tools for data analysis.

Bias↗

PubMed2005

Bootstrap methods for statistical inference from stereological estimates of volume fraction.

We suggest the use of bootstrap methods for inference from stereological estimates of volume fraction. An informal introduction to stereological estimation of volume fraction and to principles of bootstrap techniques is given. The bootstrap method is a robust computer-intensive resampling technique, based on independent random sampling from a data set with replacement. Bootstrap methods were used to estimate confidence intervals for volume fractions, and to test for a significant difference between estimated volume fractions from two samples. Two sampling designs are considered: independent replicated samples (visual fields) from a single object, and estimates of volume fraction from multiple independent objects. The methods are presented as worked examples on real data sets obtained from tumour pathology (mammary cancer, pancreatic cancer). The volume fraction of glandular lumina per total volume of the epithelial phase was chosen as target parameter. It indicates the degree of glandular differentiation in adenocarcinomas and is estimated as a ratio-of-means statistic with variable denominator within cases. The confidence intervals of the volume fraction estimated by the bootstrap method were slightly narrower than the parametrically calculated confidence intervals for all data sets. The outcomes of significance tests based on the bootstrap technique were unchanged as compared with classical tests based on the assumptions of normality and homoscedasticity of the data. Special attention was paid to the reproducibility of the bootstrap technique in replicated trials on the same data.

Breast Neoplasms↗

PubMed2006

Measured FEV1 in the first postoperative day, and not ppoFEV1, is the best predictor of cardio-respiratory morbidity after lung resection.

INTRODUCTION AND OBJECTIVE: There is a low correlation between predicted postoperative FEV1 (ppoFEV1) and FEV1 measured the days after pulmonary resection, when most complications are developed. The hypothesis of this investigation is that ppoFEV1 does not predict postoperative morbidity in patients undergoing lung resection when immediate postoperative FEV1 is considered in the predictive model. METHODS: One hundred ninety-eight consecutive patients undergoing lobectomy or pneumonectomy were included in a prospective, multiinstitutional study. INDEPENDENT VARIABLES: age, body mass index, ppoFEV1, surgical approach (VATS or muscle-sparing thoracotomy), type of analgesia (epidural or intraveous), postoperative visual analogue pain score and FEV1 measured the day after the operation. Target variable: occurrence of postoperative cardio-respiratory complications. Method of analysis: classification tree (CART) dividing the population at random in two subsets and developing a bootstrap set of 100 trees resampling training data. The relative importance of each variable and the accuracy of both initial and committee trees to predict the outcome were presented. RESULTS: One hundred seventy-seven lobectomies and 21 pneumonectomies were included. Overall cardio-respiratory morbidity was 22%. According to CART results, first day FEV1 was the most important variable to classify cases as primary splitter and as a surrogate of each primary splitter (100% importance). Patient age followed (51%) and ppoFEV1 was third (43%) with a score similar to postoperative pain score (42%) and type of analgesia (36%). Sensitivity and specificity of the initial tree were, respectively, 0.5 and 0.7; values for committee tree were 0.5 sensitivity and 0.7 specificity. CONCLUSION: Postoperative cardio-respiratory complications are more related to FEV1 measured in the first postoperative day than to ppoFEV1 value.

Age Factors↗

PubMed2005

Ensembling local learners through multimodal perturbation.

Ensemble learning algorithms train multiple component learners and then combine their predictions. In order to generate a strong ensemble, the component learners should be with high accuracy as well as high diversity. A popularly used scheme in generating accurate but diverse component learners is to perturb the training data with resampling methods, such as the bootstrap sampling used in bagging. However, such a scheme is not very effective on local learners such as nearest-neighbor classifiers because a slight change in training data can hardly result in local learners with big differences. In this paper, a new ensemble algorithm named Filtered Attribute Subspace based Bagging with Injected Randomness (FASBIR) is proposed for building ensembles of local learners, which utilizes multimodal perturbation to help generate accurate but diverse component learners. In detail, FASBIR employs the perturbation on the training data with bootstrap sampling, the perturbation on the input attributes with attribute filtering and attribute subspace selection, and the perturbation on the learning parameters with randomly configured distance metrics. A large empirical study shows that FASBIR is effective in building ensembles of nearest-neighbor classifiers, whose performance is better than that of many other ensemble algorithms.

Algorithms↗

PubMed2006

Selecting immunohistochemical cut-off scores for novel biomarkers of progression and survival in colorectal cancer.

BACKGROUND: Cut-off scores for determining positivity of biomarkers detected by immunohistochemistry are often set arbitrarily and vary between reports. AIMS: To evaluate the performance of receiver operating characteristic (ROC) curve analysis in determining clinically important cut-off scores for a novel tumour marker, the receptor for hyaluronic acid mediated motility (RHAMM), and show the reproducibility of the selected cut-off scores in 1197 mismatch-repair (MMR) proficient colorectal cancers (CRC). METHODS: Immunohistochemistry for RHAMM was performed using a tissue microarray of 1197 MMR-proficient CRC. Immunoreactivity was scored using a semi-quantitative scoring method by evaluating the percentage of positive tumour cells. ROC curve analysis was performed for T stage, N stage, tumour grade, vascular invasion and survival. The score with the shortest distance from the curve to the point with both maximum sensitivity and specificity, i.e. the point (0.0, 1.0), was selected as the cut-off score leading to the greatest number of tumours correctly classified as having or not having the clinical outcome. In order to determine the reliability of the selected cut-off scores, 100 bootstrapped replications were performed to resample the data. RESULTS: The cut-off score for T stage, N stage, tumour grade and vascular invasion was 100% and that for survival 90%. The most frequently selected cut-off score from the 100 resamples was also 100% for T stage, N stage, tumour grade, and vascular invasion and 90% for survival. CONCLUSIONS: ROC curve analysis can be used as an alternative method in the selection and validation of cut-off scores for determining the clinically relevant threshold for immunohistochemical tumour positivity.

Biomarkers, Tumor↗

PubMed2001

A covariance estimator for GEE with improved small-sample properties.

In this paper, we propose an alternative covariance estimator to the robust covariance estimator of generalized estimating equations (GEE). Hypothesis tests using the robust covariance estimator can have inflated size when the number of independent clusters is small. Resampling methods, such as the jackknife and bootstrap, have been suggested for covariance estimation when the number of clusters is small. A drawback of the resampling methods when the response is binary is that the methods can break down when the number of subjects is small due to zero or near-zero cell counts caused by resampling. We propose a bias-corrected covariance estimator that avoids this problem. In a small simulation study, we compare the bias-corrected covariance estimator to the robust and jackknife covariance estimators for binary responses for situations involving 10-40 subjects with equal and unequal cluster sizes of 16-64 observations. The bias-corrected covariance estimator gave tests with sizes close to the nominal level even when the number of subjects was 10 and cluster sizes were unequal, whereas the robust and jackknife covariance estimators gave tests with sizes that could be 2-3 times the nominal level. The methods are illustrated using data from a randomized clinical trial on treatment for bone loss in subjects with periodontal disease.

Alveolar Bone Loss↗

PubMed1989

Bootstrapped confidence intervals for the Cox model using a linear relative risk form.

A linear relative risk form for the Cox model is sometimes more appropriate than the usual exponential form. The usual asymptotic confidence interval may not have the appropriate coverage, however, due to flatness of the likelihood in the neighbourhood of beta. For a single continuous covariate, we derive bootstrapped confidence intervals with use of two resampling methods. The first resamples the original data and yields both one-step and fully iterated estimates of beta. The second resamples the score and information quantities at each failure time to yield a one-step estimate. We computed the bootstrapped confidence intervals by three different methods and compared these intervals to one based on the asymptotic standard error and to a likelihood-based interval. The bootstrapped intervals did not perform well and underestimated the true coverage in most cases.

Computer Simulation↗

PubMed2002

Very fast algorithms for evaluating the stability of ML and Bayesian phylogenetic trees from sequence data.

Evolutionary trees sit at the core of all realistic models describing a set of related sequences, including alignment, homology search, ancestral protein reconstruction and 2D/3D structural change. It is important to assess the stochastic error when estimating a tree, including models using the most realistic likelihood-based optimizations, yet computation times may be many days or weeks. If so, the bootstrap is computationally prohibitive. Here we show that the extremely fast "resampling of estimated log likelihoods" or RELL method behaves well under more general circumstances than previously examined. RELL approximates the bootstrap (BP) proportions of trees better that some bootstrap methods that rely on fast heuristics to search the tree space. The BIC approximation of the Bayesian posterior probability (BPP) of trees is made more accurate by including an additional term related to the determinant of the information matrix (which may also be obtained as a product of gradient or score vectors). Such estimates are shown to be very close to MCMC chain values. Our analysis of mammalian mitochondrial amino acid sequences suggest that when model breakdown occurs, as it typically does for sequences separated by more than a few million years, the BPP values are far too peaked and the real fluctuations in the likelihood of the data are many times larger than expected. Accordingly, several ways to incorporate the bootstrap and other types of direct resampling with MCMC procedures are outlined. Genes evolve by a process which involves some sites following a tree close to, but not identical with, the species tree. It is seen that under such a likelihood model BP (bootstrap proportions) and BPP estimates may still be reasonable estimates of the species tree. Since many of the methods studied are very fast computationally, there is no reason to ignore stochastic error even with the slowest ML or likelihood based methods.

Algorithms↗

PubMed2006

Objective detection of evoked potentials using a bootstrap technique.

Evoked potentials are usually evaluated subjectively, by visual inspection, and considerable differences between interpretations can occur. Objective, automated methods are normally based on calculating one (or more) parameters from the data, but only some of these techniques can provide statistical significance (p-values) for the presence of a response. In this work, we propose a bootstrap technique to provide such p-values, which can be applied to a wide variety of parameters. The bootstrap method is based on randomly resampling (with replacement) the original data and gives an estimate of the probability that the response obtained is due to random variation in the data rather than a physiological response. The method is illustrated using auditory brainstem responses (ABRs) to detecting hearing thresholds. The flexibility of the approach is illustrated, showing how it can be used with different parameters, numbers of stimuli and with user-defined false-positive rates. The bootstrap method provides a new, simple and yet powerful means of detecting evoked potentials, which is very flexible and readily adapted to a wide variety of signal parameters.

Adolescent↗

PubMed2002

Application of resampling techniques to estimate exact significance levels for covariate selection during nonlinear mixed effects model building: some inferences.

PURPOSE: One of the main objectives of the nonlinear mixed effects modeling is to provide rational individualized dosing strategies by explaining the interindividual variability using intrinsic and/or extrinsic factors (covariates). The aim of the current study was to evaluate, using computer simulations and real data, methods for estimating the exact significance level for including or excluding a covariate during model building. METHODS: Original data were simulated using a simple one-compartment pharmacokinetic model with (full model) or without (null model) covariates (one or two). The covariate values in the original data were resampled (using either permutations or parametric bootstrap methods) to generate data under the null hypothesis that there is no covariate effect. The original and permuted data were fitted to null and full models, using first-order and first-order condition estimation (with or without interaction) methods in NONMEM, to compare the asymptotic and conditional p-value. Target log-likelihood ratio cutoffs for assessing covariate effects were derived. RESULTS: The simulations showed that for sparse as well as dense data, the first-order condition estimation methods yielded the best results while the first-order method performs somewhat better for sparse data. Depending on the modeling objective, the appropriate asymptotic p-value can be substituted for the conditional significance level. Target log-likelihood ratio cutoffs should be determined separately for each covariate when exact p-values are important. CONCLUSIONS: Resampling methods can be employed to estimate the exact significance level for including a covariate during nonlinear mixed effects model building. Some reasonable inferences can be drawn for potential application to design future population analyses.

Adolescent↗

PubMed2004

EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis.

We have developed a toolbox and graphic user interface, EEGLAB, running under the crossplatform MATLAB environment (The Mathworks, Inc.) for processing collections of single-trial and/or averaged EEG data of any number of channels. Available functions include EEG data, channel and event information importing, data visualization (scrolling, scalp map and dipole model plotting, plus multi-trial ERP-image plots), preprocessing (including artifact rejection, filtering, epoch selection, and averaging), independent component analysis (ICA) and time/frequency decompositions including channel and component cross-coherence supported by bootstrap statistical methods based on data resampling. EEGLAB functions are organized into three layers. Top-layer functions allow users to interact with the data through the graphic interface without needing to use MATLAB syntax. Menu options allow users to tune the behavior of EEGLAB to available memory. Middle-layer functions allow users to customize data processing using command history and interactive 'pop' functions. Experienced MATLAB users can use EEGLAB data structures and stand-alone signal processing functions to write custom and/or batch analysis scripts. Extensive function help and tutorial information are included. A 'plug-in' facility allows easy incorporation of new EEG modules into the main menu. EEGLAB is freely available (http://www.sccn.ucsd.edu/eeglab/) under the GNU public license for noncommercial use and open source development, together with sample data, user tutorial and extensive documentation.

Computer Simulation↗

PubMed2003

Non-parametric estimators of a monotonic dose-response curve and bootstrap confidence intervals.

In this paper we consider study designs which include a placebo and an active control group as well as several dose groups of a new drug. A monotonically increasing dose-response function is assumed, and the objective is to estimate a dose with equivalent response to the active control group, including a confidence interval for this dose. We present different non-parametric methods to estimate the monotonic dose-response curve. These are derived from the isotonic regression estimator, a non-negative least squares estimator, and a bias adjusted non-negative least squares estimator using linear interpolation. The different confidence intervals are based upon an approach described by Korn, and upon two different bootstrap approaches. One of these bootstrap approaches is standard, and the second ensures that resampling is done from empiric distributions which comply with the order restrictions imposed. In our simulations we did not find any differences between the two bootstrap methods, and both clearly outperform Korn's confidence intervals. The non-negative least squares estimator yields biased results for moderate sample sizes. The bias adjustment for this estimator works well, even for small and moderate sample sizes, and surprisingly outperforms the isotonic regression method in certain situations.

Computer Simulation↗

PubMed1998

Resampling methods in sparse sampling situations in preclinical pharmacokinetic studies.

Toxicokinetic studies often require destructive sampling and the determination of drug concentrations in the various organs. Classically, the corresponding information is summarized in one mean concentration-time profile, which is regarded as representative for the animal population. On the basis of a mean profile, only estimates of the secondary pharmacokinetic parameters (for example AUC, t1/2) but no variability measures may be obtained. In this paper two resampling techniques are contrasted to Bailer's approach. The results obtained show that the resampling techniques can be considered a reliable alternative to Bailer's approach for the estimation of the standard error of the AUC t(k)0 in the case of normally distributed concentration data. They can be extended to the estimation of a variety of other secondary pharmacokinetic parameters and their respective standard deviations. One disadvantage with Bailer's method is its restriction to linear functions of the concentrations. On the other hand, using the population approach, prior knowledge of the underlying pharmacokinetic model is necessary. The resampling techniques discussed here, the "pseudoprofile-based bootstrap" (PpbB) and the "pooled data bootstrap" (PDB), are noncompartmental approaches. They are applicable under nonnormal data constellations and permit the estimation of the usual secondary pharmacokinetic parameters along with their standard deviations, standard errors, and other statistical measures. To assess the accuracy, precision, and robustness of the resampling estimators, theoretical data from three different pharmacokinetic models with different add-on errors (up to 100% variability) were analyzed. Even for the data sets with high variability, the parameters calculated with resampling techniques differ not more than 10% from the true values. Thus, in the case of data that are not normally distributed or when additional secondary pharmacokinetic parameters and their variability are to be estimated, the resampling methods are powerful tools in the safety assessment in preclinical pharmacokinetics and in toxicokinetics where generally sparse data situations are given.

Area Under Curve↗

PubMed2005

Reduction of selection bias in genomewide studies by resampling.

The accuracy of gene localization, the reliability of locus-specific effect estimates, and the ability to replicate initial claims of linkage and/or association have emerged as major methodological concerns in genomewide studies of complex diseases and quantitative traits. To address the issue of multiple comparisons inherent in genomewide studies, the use of stringent criteria for assessing statistical significance has been generally acknowledged as a strategy to control type I error. However, the application of genomewide significance criteria does not take account of the selection bias introduced into parameter estimates, e.g., estimates of locus-specific effect size of disease/trait loci. Some have argued that reliable locus-specific parameter estimates can only be obtained in an independent sample. In this report, we examine statistical resampling techniques, including cross-validation and the bootstrap, applied to the initial sample to improve the estimation of locus-specific effects. We compare them with the naive method in which all data are used for both hypothesis testing and parameter estimation, as well as with the split-sample approach in which part of the data are reserved for estimation. Upward bias of the naive estimator and inadequacy of the split-sample approach are derived analytically under a simple quantitative trait model. Simulation studies of the resampling methods are performed for both the simple model and a more realistic genomewide linkage analysis. Our results suggest that cross-validation and bootstrap methods can substantially reduce the estimation bias, especially when the effect size is small or there is no genetic effect.

Algorithms↗

PubMed2002

Comparing k cumulative incidence functions through resampling methods.

Tests for the equality of k cumulative incidence functions in a competing risks model are proposed. Test statistics are based on a vector of processes related to the cumulative incidence functions. Since their asymptotic distributions appear very complicated and depend on the underlying distribution of the data, two resampling techniques, namely the well-known bootstrap method and the so-called random symmetrization method, are used to approximate the critical values of the tests. Without making any assumptions on the nature of dependence between the risks, the tests allow one to compare k risks simultaneously for k > or = 2 under the random censorship model. Tests against ordered alternatives are also considered. Simulation studies indicate that the proposed tests perform very well with moderate sample size. A real application to cancer mortality data is given.

Animals↗