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ODS_BOOTSTRAP: assessing the statistical reliability of physical maps by bootstrap resampling.

In the program ODS_BOOTSTRAP we provide a methodology for quickly ordering clones in a genomic library into a physical map and for applying a statistical tool known as the bootstrap to assess the statistical reliability of a clonal ordering. Each clone is assigned a binary fingerprint by one of a variety of experimental approaches to physical mapping. For example, the binary fingerprints might be generated by hybridizing a panel of m probes to a library of n clones. The resulting n x m binary data matrix, X, is input to ODS_BOOTSTRAP, which utilizes the similarity in binary fingerprints of clones to construct a physical map. Under this particular implementation of bootstrap resampling, the m probes (or columns of the data matrix) are sampled randomly with replacement in the computer to generate a new n x m data matrix, X*, from which a second physical map is constructed. The resampling process is repeated 100 or more times to generate 100 or more X* matrices. The resulting 100 or more physical maps are compared with the original physical map based on the original data matrix X by counting how often links in the original physical map reappear. Three confidence statistics are introduced for each link in a physical map. The statistic C1 is defined as the percentage of time two neighboring clones on the original map reappear as neighbors under resampling. The statistic C2 is defined as the percentage of time that two neighboring clones i and j on the original map reappear as neighbors or that a clone with an identical binary fingerprint to clone i reappears as a neighbor to clone j. The statistic C3 is defined as the percentage of time that two neighboring clones on the original map reappear in the same contig under resampling.

Algorithms↗

Extraction of parameters and their error distributions from cyclic voltammograms using bootstrap resampling enhanced by solution maps: Computational study.

The conventional determination of model parameter errors in least-squares regression of experimental cyclic voltammetric data assumes validity of local approximations (e.g., linearization) in the parameter space and normal distributions of the data and parameter errors. Such assumptions may not always be satisfied in practice. Bootstrap resampling techniques present a more universally applicable approach to error estimation, which until now has not been used in cyclic voltammetric studies, owing to the high costs of the required voltammogram simulations. We demonstrate that the burden of computing voltammograms can be significantly reduced by the use of high-dimensional model representation (HDMR) solution mapping techniques, thereby making it feasible to apply the bootstrap data analysis in cyclic voltammetry. We perform computational experiments with bootstrap resampling, enhanced by HDMR maps, for a typical cyclic voltammetric model (i.e., the Eqrev Cirr Eqrev reaction mechanism at a planar macroelectrode under semi-infinite, pure diffusion transport conditions). The experiments reveal that the bootstrap distributions of the estimated parameters provide a satisfactory quantification of the parameter errors and can also be used for detecting statistical correlations of the parameters.

Journal Article↗

Histogram analysis of pharmacokinetic parameters by bootstrap resampling from one-point sampling data in animal experiments.

A bootstrap method is proposed for assessing statistical histograms of pharmacokinetic parameters (AUC, MRT, CL and V(ss)) from one-point sampling data in animal experiments. A computer program, MOMENT(BS), written in Visual Basic on Microsoft Excel, was developed for the bootstrap calculation and the construction of histograms. MOMENT(BS) was applied to one-point sampling data of the blood concentration of three physiologically active proteins ((111)In labeled Hsp70, Suc(20)-BSA and Suc(40)-BSA) administered in different doses to mice. The histograms of AUC, MRT, CL and V(ss) were close to a normal (Gaussian) distribution with the bootstrap resampling number (200), or more, considering the skewness and kurtosis of the histograms. A good agreement of means and SD was obtained between the bootstrap and Bailer's approaches. The hypothesis test based on the normal distribution clearly demonstrated that the disposition of (111)In-Hsp70 and Suc(20)-BSA was almost independent of dose, whereas that of (111)In-Suc(40)-BSA was definitely dose-dependent. In conclusion, the bootstrap method was found to be an efficient method for assessing the histogram of pharmacokinetic parameters of blood or tissue disposition data by one-point sampling.

Algorithms↗

Bootstrap resampling method to estimate confidence intervals of activation-induced CBF changes using laser Doppler imaging.

Laser Doppler imaging (LDI) signal and noise characteristics can vary significantly depending upon the underlying vascular caliber. Further, noise characteristics are not constant over time (non-stationary) and can vary during resting and activated conditions in a typical experiment. Since only a limited number of images can be acquired in a single run, concatenation of data from similar experimental trials becomes necessary which can induce further variation in temporal noise due to instrumental response. In conventional statistical analysis methods such as cross-correlation, a fixed significance threshold is generally used (for the entire image) to detect activation assuming constant noise over time and a normal distribution. As a consequence, statistical significance can become strong or weak due to temporal differences in baseline LD noise, which can possibly deviate from a normal distribution. The main emphasis of this study was the application of bootstrap resampling in conjunction with cross-correlation to estimate the confidence intervals on a pixel-by-pixel basis to avoid distributional specifications on the additive measurement error leading to reliable whisker activation-induced CBF changes. At a 95% confidence level, bootstrap resampling followed by confidence intervals for the correlation coefficient distribution increased the number of active pixels by almost 45% when compared to conventional cross-correlation. These pixels were mostly confined to areas with intermediate and large baseline LD flux with considerable deviation from normality. It is suggested that confidence intervals of the bootstrap estimates can lead to unbiased detection of CBF change in the cerebral cortex, particularly in regions with large temporal variation in noise and low CNR.

Afferent Pathways↗

Bootstrap resampling: a powerful method of assessing confidence intervals for doses from experimental data.

Bootstrap resampling provides a versatile and reliable statistical method for estimating the accuracy of quantities which are calculated from experimental data. It is an empirically based method, in which large numbers of simulated datasets are generated by computer from existing measurements, so that approximate confidence intervals of the derived quantities may be obtained by direct numerical evaluation. A simple introduction to the method is given via a detailed example of estimating 95% confidence intervals for cumulated activity in the thyroid following injection of 99mTc-sodium pertechnetate using activity-time data from 23 subjects. The application of the approach to estimating confidence limits for the self-dose to the kidney following injection of 99mTc-DTPA organ imaging agent based on uptake data from 19 subjects is also illustrated. Results are then given for estimates of doses to the foetus following administration of 99mTc-sodium pertechnetate for clinical reasons during pregnancy, averaged over 25 subjects. The bootstrap method is well suited for applications in radiation dosimetry including uncertainty, reliability and sensitivity analysis of dose coefficients in biokinetic models, but it can also be applied in a wide range of other biomedical situations.

Confidence Intervals↗

Bootstrap resampling for voxel-wise variance analysis of three-dimensional density maps derived by image analysis of two-dimensional crystals.

Difference density maps are commonly used in structural biology for identifying conformational changes in macromolecular complexes. For interpretation of the results, it is essential to estimate the variance or standard deviation of the difference density and the distribution of errors in space. In order to compare three-dimensional density maps of gap junction channels with and without the C-terminal regulatory domain, we developed a bootstrap resampling method for estimation of the voxel-wise standard deviation. The bootstrap approach has been successfully used for estimating the sampling distribution from a limited data set and for estimating the statistical properties of the derived quantities [Efron, B., 1979. Bootstrap methods: another look at the jackknife. Ann. Stat. 7, 1-26]. In our application, the standard deviation map can be estimated by bootstrapping the images. Our results show that, apart from the symmetry axes and small regions bordering the lumen of the extracellular vestibule, difference maps normalized by the mean of the standard deviation map can be used as a good approximation of the t-test map of the gap junction crystals.

Animals↗

The use of bootstrap resampling to assess the uncertainty of cooper statistics.

The predictive abilities of two-group classification models (CMs) are often expressed in terms of their Cooper statistics. These statistics are often reported without any indication of their uncertainty, making it impossible to judge whether the predicted classifications are significantly better than the predictions made by a different CM, or whether the predictive performance of the CM exceeds predefined performance criteria in a statistically significant way. Bootstrap resampling routines are reported that provide a means of expressing the uncertainty associated with Cooper statistics. The usefulness of the bootstrapping routines is illustrated by constructing 95% confidence intervals for the Cooper statistics of four alternative skin-corrosivity tests (the rat skin transcutaneous electrical resistance assay, EPISKIN, Skin(2) and CORROSITEX), and four two-step sequences in which each in vitro test is used in combination with a physicochemical test for skin corrosion based on pH measurements.

Animal Testing Alternatives↗

A bootstrap resampling procedure for model building: application to the Cox regression model.

A common problem in the statistical analysis of clinical studies is the selection of those variables in the framework of a regression model which might influence the outcome variable. Stepwise methods have been available for a long time, but as with many other possible strategies, there is a lot of criticism of their use. Investigations of the stability of a selected model are often called for, but usually are not carried out in a systematic way. Since analytical approaches are extremely difficult, data-dependent methods might be an useful alternative. Based on a bootstrap resampling procedure, Chen and George investigated the stability of a stepwise selection procedure in the framework of the Cox proportional hazard regression model. We extend their proposal and develop a bootstrap-model selection procedure, combining the bootstrap method with existing selection techniques such as stepwise methods. We illustrate the proposed strategy in the process of model building by using data from two cancer clinical trials featuring two different situations commonly arising in clinical research. In a brain tumour study the adjustment for covariates in an overall treatment comparison is of primary interest calling for the selection of even 'mild' effects. In a prostate cancer study we concentrate on the analysis of treatment-covariate interactions demanding that only 'strong' effects should be selected. Both variants of the strategy will be demonstrated analysing the clinical trials with a Cox model, but they can be applied in other types of regression with obvious and straightforward modifications.

Brain Neoplasms↗

The use of bootstrap resampling to assess the variability of Draize tissue scores.

The acute dermal and ocular effects of chemicals are generally assessed by performing the Draize skin and eye tests, respectively. Because the animal data obtained in these tests are also used for the development and validation of alternative methods for skin and eye irritation, it is important to assess the inherent variability of the animal data, since this variability places an upper limit on the predictive performance that can be expected of any alternative model. The statistical method of bootstrap resampling was used to estimate the variability arising from the use of different animals and time-points, and the estimates of variability were used to determine the maximal extent to which Draize test tissue scores can be predicted.

Animal Testing Alternatives↗

An application of bootstrap resampling method to obtain confidence interval for percentile fatness cutoff points in childhood and adolescence overweight diagnoses.

OBJECTIVE: To present a resampling approach to obtain confidence intervals (CIs) and the empirical distributions for the studentized regression residuals percentiles when used as cutoff points for overweight and obesity diagnosis in children and adolescents. METHOD: A tutorial for the nonparametric bootstrap with bias accelerating correction is presented. A classical method, the Binomial interpretation, is used as comparing criterion. SUBJECTS: A case study comprising 418 randomly selected subjects from a private secondary school (age: 10-17 y, boys: 52%). MEASUREMENTS: Body fat percentage (by), age (y) and Tanner criteria. RESULTS: The empirical distributions presented skewness suggesting that the CIs should not be symmetric. CIs obtained by the proposed approach were more realistic than the classical ones. CONCLUSIONS: We propose a simple and efficient way to obtain the interval estimates and the distribution properties of cutoff points for overweight and obese classification using a sample-based method that allows the comparison of cutoffs among many subpopulations.

Adipose Tissue↗

Multireader, multicase receiver operating characteristic methodology: a bootstrap analysis.

RATIONALE AND OBJECTIVES: We evaluated by bootstrapping the conclusions obtained by the Dorfman-Berbaum-Metz (DBM) receiver operating characteristic (ROC) method and by the Toledano-Gatsonis (TG) method on a well-known data set. METHODS: We bootstrapped in two ways, resampled cases while holding readers fixed and resampled both cases and readers. RESULTS: When an analysis of variance of pseudovalues implies that reader variance and all random interactions with treatment are essentially zero, then case-resampling bootstrap and the DBM and TG methods should give the same results. Case-resampling bootstrap and the DBM and TG methods did give highly similar results for both individual readers and the averages over all readers. Both the case-resampling bootstrap and the reader-case resampling bootstrap gave smaller standard errors for group than for individual reader means, thereby providing evidence for a trade-off of readers and cases with regard to precision and power in this data set. CONCLUSION: Case-resampling bootstrap provides some justification for the DBM and TG methods.

Analysis of Variance↗

Resampling approach to statistical inference: bootstrapping from event-related potentials data.

We propose the use of the bootstrap resampling technique as a tool to assess the within-subject reliability of experimental modulation effects on event-related potentials (ERPs). The assessment of the within-subject reliability is relevant in all those cases when the subject score is obtained by some estimation procedure, such as averaging. In these cases, possible deviations from the assumptions on which the estimation procedure relies may lead to severely biased results and, consequently, to incorrect functional inferences. In this study, we applied bootstrap analysis to data from an experiment aimed at investigating the relationship between ERPs and memory processes. ERPs were recorded from two groups of subjects engaged in a recognition memory task. During the study phase, subjects in Group A were required to make an orthographic judgment on 160 visually presented words, whereas subjects in Group B were only required to pay attention to the words. During the test phase all subjects were presented with the 160 previously studied words along with 160 new words and were required to decide whether the current word was "old" or "new." To assess the effect of word imagery value, half of the words had a high imagery value and half a low imagery value. Analyses of variance performed on ERPs showed that an imagery-induced modulation of the old/new effect was evident only for subjects who were not engaged in the orthographic task during the study phase. This result supports the hypothesis that this modulation is due to some aspect of the recognition memory process and not to the stimulus encoding operations that occur during the recognition memory task. However, bootstrap analysis on the same data showed that the old/new effect on ERPs was not reliable for all the subjects. This result suggests that only a cautious inference can be made from these data.

Adult↗

Pvclust: an R package for assessing the uncertainty in hierarchical clustering.

SUMMARY: Pvclust is an add-on package for a statistical software R to assess the uncertainty in hierarchical cluster analysis. Pvclust can be used easily for general statistical problems, such as DNA microarray analysis, to perform the bootstrap analysis of clustering, which has been popular in phylogenetic analysis. Pvclust calculates probability values (p-values) for each cluster using bootstrap resampling techniques. Two types of p-values are available: approximately unbiased (AU) p-value and bootstrap probability (BP) value. Multiscale bootstrap resampling is used for the calculation of AU p-value, which has superiority in bias over BP value calculated by the ordinary bootstrap resampling. In addition the computation time can be enormously decreased with parallel computing option.

Algorithms↗

Investigations of dipole localization accuracy in MEG using the bootstrap.

We describe the use of the nonparametric bootstrap to investigate the accuracy of current dipole localization from magnetoencephalography (MEG) studies of event-related neural activity. The bootstrap is well suited to the analysis of event-related MEG data since the experiments are repeated tens or even hundreds of times and averaged to achieve acceptable signal-to-noise ratios (SNRs). The set of repetitions or epochs can be viewed as a set of independent realizations of the brain's response to the experiment. Bootstrap resamples can be generated by sampling with replacement from these epochs and averaging. In this study, we applied the bootstrap resampling technique to MEG data from somatotopic experimental and simulated data. Four fingers of the right and left hand of a healthy subject were electrically stimulated, and about 400 trials per stimulation were recorded and averaged in order to measure the somatotopic mapping of the fingers in the S1 area of the brain. Based on single-trial recordings for each finger we performed 5000 bootstrap resamples. We reconstructed dipoles from these resampled averages using the Recursively Applied and Projected (RAP)-MUSIC source localization algorithm. We also performed a simulation for two dipolar sources with overlapping time courses embedded in realistic background brain activity generated using the prestimulus segments of the somatotopic data. To find correspondences between multiple sources in each bootstrap, sample dipoles with similar time series and forward fields were assumed to represent the same source. These dipoles were then clustered by a Gaussian Mixture Model (GMM) clustering algorithm using their combined normalized time series and topographies as feature vectors. The mean and standard deviation of the dipole position and the dipole time series in each cluster were computed to provide estimates of the accuracy of the reconstructed source locations and time series.

Brain Mapping↗