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PubMed2005

Random weighted bootstrap method for recurrent events with informative censoring.

Using the data from the AIDS Link to Intravenous Experiences cohort study as an example, an informative censoring model was used to characterize the repeated hospitalization process of a group of patients. Under the informative censoring assumption, the estimators of the baseline rate function and the regression parameters were shown to be related to a latent variable. Hence, it becomes impractical to directly estimate the unknown quantities in the moments of the estimators for the bandwidth selection of a smoothing estimator and the construction of confidence intervals, which are respectively based on the asymptotic mean squared errors and the asymptotic distributions of the estimators. To overcome these difficulties, we develop a random weighted bootstrap procedure to select appropriate bandwidths and to construct approximated confidence intervals. One can see that our method is simple and faster to implement from a practical point of view, and is at least as accurate as other bootstrap methods. In this article, it is shown that the proposed method is useful through the performance of a Monte Carlo simulation. An application of our procedure is also illustrated by a recurrent event sample of intravenous drug users for inpatient cares over time.

Acquired Immunodeficiency Syndrome↗

PubMed1987

The bootstrapped model--Lessons for the acceptance of intellectual technology.

This paper is intended as a non-technical introduction to a growing aspect of what has been termed 'intellectual technology'. The particular area chosen is the use of simple linear additive models for judgement and decision making purposes. Such models are said to either outperform, or perform at least as well as, the human judges on which they are based, hence they are said to 'bootstrap' such human inputs. Although the paper will provide a fairly comprehensive list of recent applications of such models, from postgraduate selection to judgements of marital happiness, the work will concentrate on the topic of Credit Scoring as an exemplar - that is, the assignment of credit by means of a simple additive rule. The paper will also present a simple system, due to Dawes, of classifying such models according to the form and source of their weights. The paper further discusses the reasons for bootstrapping and that other major phenomenon of such models - that is, the one can rarely distinguish between the prescriptions of such models, however the weights have been arrived at. It is argued that this 'principle of the flat maximum' allows us to develop a technology of judgement. The paper continues with a brief historical survey of the reactions of human experts to such models and their superiority, and suggestions for a better mix of expert and model on human engineering lines. Finally, after a brief comparison between expert systems and linear additive models, the paper concludes with a brief survey of possible future developments. A short Appendix describes two applications of such models.

Journal Article↗

PubMed1989

A bootstrap analysis of four in vitro short-term test performances.

The present analysis is aimed at estimating the confidence intervals of a number of association measures that describe the relationships of 4 in vitro short-term tests with rodent carcinogenicity, as well as with each other. The measures considered were: sensitivity, specificity and accuracy of the short-term tests with respect to chemical carcinogens, and performance dissimilarity indices (Hamming distances). The analysis refers to Salmonella, mouse lymphoma L5178Y cell mutation, chromosomal aberrations and sister-chromatid exchanges in Chinese hamster ovary cells, and is based on the data generated in the frame of the U.S. National Toxicology Program (NTP). It exploits the properties of a statistical technique, called bootstrap, to derive from only one sample of chemicals the variability intervals of the associations that the biological systems (mutagenicity assays and rodent carcinogenicity) would show in the 'universe' of the chemical compounds. The combination of the bootstrap technique with multivariate statistical methods pointed to a remarkable robustness and reliability of the information derived from the NTP data base, and provided descriptive insights into the data.

Animals↗

PubMed2006

Using SAS to conduct nonparametric residual bootstrap multilevel modeling with a small number of groups.

In multilevel modeling, researchers often encounter data with a relatively small number of units at the higher levels. As a result, of this and/or non-normality of the residuals, model parameter estimates, particularly the variance components and standard errors of parameter estimates at the group level, may be biased, thus the corresponding statistical inferences may not be trustworthy. This problem can be addressed by using bootstrap methods to estimate the standard errors of the parameter estimates for significance testing. This study illustrates how to use statistical analysis system (SAS) to conduct nonparametric residual bootstrap multilevel modeling. Specific SAS programs for such modeling are provided.

Models, Statistical↗

PubMed2004

Bootstrapped DEPICT for error estimation in PET functional imaging.

Basis pursuit denoising is a new approach for data-driven estimation of parametric images from dynamic positron emission tomography (PET) data. At present, this kinetic modeling technique does not allow for the estimation of the errors on the parameters. These estimates are useful when performing subsequent statistical analysis, such as, inference across a group of subjects or when applying partial volume correction algorithms. The difficulty with calculating the error estimates is a consequence of using an overcomplete dictionary of kinetic basis functions. In this paper, a bootstrap approach for the estimation of parameter errors from dynamic PET data is presented. This paper shows that the bootstrap can be used successfully to compute parameter errors on a region of interest or parametric image basis. Validation studies evaluate the methods performance on simulated and measured PET data ([(11)C]Diprenorphine-opiate receptor and [(11)C]Raclopride-dopamine D(2) receptor). The method is presented in the context of PET neuroreceptor binding studies, however, it has general applicability to a wide range of PET/SPET radiotracers in neurology, oncology and cardiology.

Adult↗

PubMed2005

Bootstrap hypothesis testing and power analysis at low dose levels.

This study demonstrates the variability in dose estimates using the nonparametric bootstrap to estimate the variability in the mean dose when mean values from environmental data are used in the dose calculation. Bootstrap hypothesis testing and power analysis are demonstrated. For the data set shown here, the normal assumption works well if the environmental data can be considered fixed, known constants. However, when there exists a good deal of variability in the environmental data, as is most often the case, or where scarce data are available, making a normal assumption leads to gross underestimation of the variability in the mean dose.

Animals↗

PubMed2006

Accurate prediction of need for invasive treatment in alpha1-blocker treated patients with benign prostatic hyperplasia not possible: bootstrap validation analysis.

OBJECTIVES: Frequently, statistically significant prognostic factors are reported in published studies with suggestions that disease management should be modified. However, the clinical relevance of such factors is rarely quantified. We evaluated the accuracy of predicting the need for invasive treatment among patients with benign prostatic hyperplasia treated conservatively with alpha1-blockers. METHODS: Information on eight prognostic factors was collected from 280 patients treated with alpha1-blockers. Using the proportional hazards regression coefficients, a risk score for retreatment was calculated for each patient. The analyses were repeated on 1000 groups of 280 patients sampled from the original case series. The results from these "bootstrap analyses" were compared with the original results. RESULTS: Three statistically significant predictors of retreatment were identified. The 20% of patients with the greatest risk score had an 18-month risk of retreatment of only 20% (this should ideally approach 100%). Analyses of less than one half of all the bootstrap samples resulted in the same three significant prognostic factors. The 20% of patients with the greatest risk score in each of the 1000 samples experienced a highly variable risk of retreatment of 0% to 42%. CONCLUSIONS: Strongly significant predictors for retreatment suggest the need for a change in disease management, but 4 of the 5 high-risk patients would be overtreated with a modified policy. The subclassification of patients with a relatively low risk and high risk of retreatment appeared far from accurate. Internal validation procedures may warn against the invalid translation of statistical significance into clinical relevance.

Adrenergic alpha-Antagonists↗

PubMed1999

Simple bootstrap statistical inference using the SAS system.

Nonparametric bootstrap statistical inference is a robust computer intensive method for generating estimates of statistical variability for which formulae are not known or asymptotic assumptions are not met. A SAS macro that implements simple nonparametric bootstrap statistical inference is presented with an example. The program code is easily generalized to any SAS procedure which includes a BY statement, and to cases of clustered data.

Data Interpretation, Statistical↗

PubMed2002

Use of the bootstrap technique with small training sets for computer-aided diagnosis in breast ultrasound.

The purpose of this study was to test the efficacy of using small training sets in computer-aided diagnostic systems (CAD) and to increase the capabilities of ultrasound (US) technology in the differential diagnosis of solid breast tumors. A total of 263 sonographic images of solid breast nodules, including 129 malignancies and 134 benign nodules, were evaluated by using a bootstrap technique with 10 original training samples. Texture parameters of a region-of-interest (ROI) were resampled with a bootstrap technique and a decision-tree model was used to classify the tumor as benign or malignant. The accuracy was 87.07% (229 of 263 tumors), the sensitivity was 95.35% (123 of 129), the specificity was 79.10% (106 of 134), the positive predictive value was 81.46% (123 of 151), and the negative predictive value was 94.64% (106 of 112). This analysis method provides a second opinion for physicians with high accuracy. The new method shows a potential to be useful in future application of CAD, especially when a large database cannot be obtained for training or a newly developed ultrasonic system has smaller sets of samples.

Adolescent↗

PubMed2002

Statistical validation of the identification of tuna species: bootstrap analysis of mitochondrial DNA sequences.

Sequencing of the mitochondrial cytochrome b gene has been used to differentiate three tuna species: Thunnus albacares (yellowfin tuna), Thunnus obesus (bigeye tuna), and Katsuwonus pelamis (skipjack). A PCR amplified 528 bp fragment from 30 frozen samples and a 171 bp fragment from 26 canned samples of the three species were analyzed to determine the intraspecific variation and the positions with diagnostic value. Polymorphic sites between the species that did not present intraspecific variation were given a diagnostic value. The genetic distance between the sequences was calculated, and a phylogenetic tree was constructed, showing that the sequences belonging to the same species clustered together. The bootstrap test of confidence was used to determine the statistical validation of the species assignation, allowing for the first time a quantification of the certainty of the species assignation. The bootstrap values obtained from these results indicate that the sequencing of the cytochrome b fragments allows a correct species assignation with a probability > or =95%.

Animals↗

PubMed1997

Bootstrapping regression parameters in multivariate survival analysis.

Bootstrap methods are proposed for estimating sampling distributions and associated statistics for regression parameters in multivariate survival data. We use an Independence Working Model (IWM) approach, fitting margins independently, to obtain consistent estimates of the parameters in the marginal models. Resampling procedures, however, are applied to an appropriate joint distribution to estimate covariance matrices, make bias corrections, and construct confidence intervals. The proposed methods allow for fixed or random explanatory variables, the latter case using extensions of existing resampling schemes (Loughin, 1995), and they permit the possibility of random censoring. An application is shown for the viral positivity time data previously analyzed by Wei, Lin, and Weissfeld (1989). A simulation study of small-sample properties shows that the proposed bootstrap procedures provide substantial improvements in variance estimation over the robust variance estimator commonly used with the IWM.

Acquired Immunodeficiency Syndrome↗

PubMed2006

Phylogeny of Eunicida (Annelida) and exploring data congruence using a partition addition bootstrap alteration (PABA) approach.

Even though relationships within Annelida are poorly understood, Eunicida is one of only a few major annelid lineages well supported by morphology. The seven recognized eunicid families possess sclerotized jaws that include mandibles and a maxillary apparatus. The maxillary apparatuses vary in shape and number of elements, and three main types are recognized in extant taxa: ctenognath, labidognath, and prionognath. Ctenognath jaws are usually considered to represent the plesiomorphic state of Eunicida, whereas taxa with labidognath and prionognath are thought to form a derived monophyletic assemblage. However, this hypothesis has never been tested in a statistical framework even though it holds considerable importance for understanding annelid phylogeny and possibly lophotrochozoan evolution because Eunicida has the best annelid fossil record. Therefore, we used maximum likelihood and Bayesian inference approaches to reconstruct Eunicida phylogeny using sequence data from nuclear 18S and 28S rDNA genes and mitochondrial 16S rDNA and cytochrome c oxidase subunit I genes. Additionally, we conducted three different tests to investigate suitability of combining data sets. Incongruence length difference (ILD) and Shimodaira-Hasegawa (SH) test comparisons of resultant trees under different data partitions have been widely used previously but do not give a good indication as to which nodes may be causing the conflict. Thus, we developed a partition addition bootstrap alteration (PABA) approach that evaluates congruence or conflict for any given node by determining how bootstrap scores are altered when different data partitions are added. PABA shows the contribution of each partition to the phylogeny obtained in the combined analysis. Generally, the ILD test performed worse than the other approaches in detecting incongruence. Both PABA and the SH approach indicated the 28S and COI data sets add conflicting signal, but PABA is more informative for elucidating which data partition may be misleading at a given node. All our analyses indicate that the monophyly of the labidognath/prionognath taxa and even a labidognath clade (i.e., a "Eunicidae"/Onuphidae/Lumbrineridae clade) is significantly rejected. We show that the definition of both the labidognath and ctenognath jaw type does not address adequately the variation within Eunicida and thus misleads our current evolutionary understanding. Based on the presented results a symmetric maxillary apparatus with a carrier and four to six maxillae is most likely the plesiomorphic condition for Eunicida. [COI; conflicting data; fossil record; ILD; Jaw Evolution; molecular phylogeny; rDNA; SH test.].

Animals↗

PubMed2005

Double bootstrapping a tolerance limit.

We consider the problem of constructing tolerance limits in the context of a one-way random effects model The usual parametric method for calculating tolerance intervals is based on the normality assumption. However, in practice, we frequently observe nonnormally distributed data. We propose the use of the double bootstrap (or nested bootstrap) method to estimate tolerance limits, which allows us to relax the normality assumption.

Confidence Intervals↗

PubMed2005

Cost-effectiveness inferences from bootstrap quadrant confidence levels: three degrees of dominance.

When with at least 95% confidence a new treatment is shown to be not only less costly (LC), but also more effective (ME), than a current treatment, that new treatment can be said to "strictly dominate" the current treatment statistically. But what can be said when head-to-head treatment comparisons turn out to be less clear-cut than this? Here, we propose two additional sets of specific LC and/or ME confidence thresholds to define the concepts of "some dominance" and "much dominance." Confidence levels associated with entire quadrants of the incremental cost-effectiveness (ICE) plane are easily computed using the same bootstrapping techniques used to estimate an "acceptability curve." Our two proposed additional "degrees" of dominance, although less stringent than strict dominance, are nevertheless more stringent than commonly accepted approaches using ICE ratio or net benefit calculations. To illustrate analysis concepts, we use data from a randomized, double-blind, placebo- and active comparator-controlled clinical registration trial for treatment of major depressive disorder (MDD). As is typical, our case study is rather small and short term, providing outcome information for a total of only 264 patients during their initial 8 weeks of acute-phase MDD treatment. Thus, we focus attention on sensitivity analyses, showing that the bootstrap distribution of cost-effectiveness uncertainty is robust across two alternative ways of measuring overall effectiveness and three alternative ways of imputing missing values. Evaluation of the balance between cost and benefit is particularly difficult when a new pharmacological treatment is first introduced, yet information of this sort is highly desired by decision makers. We show that, even with only a relatively modest amount of clinical trial information, sensitivity analyses can still confirm that cost-effectiveness comparisons are being made in a consistent fashion. In contrast, extensive follow-up comparisons using data from actual clinical practice will almost always ultimately be needed to better inform health policy makers.

Adult↗

PubMed1999

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↗

PubMed1996

Confidence intervals in QTL mapping by bootstrapping.

The determination of empirical confidence intervals for the location of quantitative trait loci (QTLs) was investigated using simulation. Empirical confidence intervals were calculated using a bootstrap resampling method for a backcross population derived from inbred lines. Sample sizes were either 200 or 500 individuals, and the QTL explained 1, 5, or 10% of the phenotypic variance. The method worked well in that the proportion of empirical confidence intervals that contained the simulated QTL was close to expectation. In general, the confidence intervals were slightly conservatively biased. Correlations between the test statistic and the width of the confidence interval were strongly negative, so that the stronger the evidence for a QTL segregating, the smaller the empirical confidence interval for its location. The size of the average confidence interval depended heavily on the population size and the effect of the QTL. Marker spacing had only a small effect on the average empirical confidence interval. The LOD drop-off method to calculate empirical support intervals gave confidence intervals that generally were too small, in particular if confidence intervals were calculated only for samples above a certain significance threshold. The bootstrap method is easy to implement and is useful in the analysis of experimental data.

Animals↗

PubMed1998

A nonparametric bootstrap method for testing close linkage vs. pleiotropy of coincident quantitative trait loci.

A novel method using the nonparametric bootstrap is proposed for testing whether a quantitative trait locus (QTL) at one chromosomal position could explain effects on two separate traits. If the single-QTL hypothesis is accepted, pleiotropy could explain the effect on two traits. If it is rejected, then the effects on two traits are due to linked QTLs. The method can be used in conjunction with several QTL mapping methods as long as they provide a straightforward estimate of the number of QTLs detectable from the data set. A selection step was introduced in the bootstrap procedure to reduce the conservativeness of the test of close linkage vs. pleiotropy, so that the erroneous rejection of the null hypothesis of pleiotropy only happens at a frequency equal to the nominal type I error risk specified by the user. The approach was assessed using computer simulations and proved to be relatively unbiased and robust over the range of genetic situations tested. An example of its application on a real data set from a saline stress experiment performed on a recombinant population of wheat (Triticum aestivum L. ) doubled haploid lines is also provided.

Computer Simulation↗

PubMed1996

Controlling growth and chemical composition of saplings by iteratively matching nutrient supply to demand: a bootstrap fertilization technique.

We developed a fertilization technique that results in the control, and maintenance at defined rates and levels, of growth and tissue composition of plants of different sizes and developmental stages growing at exponential and nonexponential rates in solid media under naturally fluctuating light and temperature regimes. Clonal cottonwood (Populus deltoides Bartr.) saplings were grown in sand. Low concentrations of nutrient solution were added daily at different constant exponentially increasing rates for 20-30 days to produce plants with different growth rates and tissue nutrient composition. Matching nutrient supply to measured growth demand by bootstrapping, where bootstrapping is the use of an iterative equation that calculates demand from either actual or desired growth rates, maintained these differences for 20-40 days. Nutrient additions controlled growth of saplings with growth rates between 2.0 and 4.0% day(-1), heights between 13.9 and 37.5 cm, dry weights between 0.70 and 3.90 g, leaf nitrogen contents between 1.2 and 3.9%, and leaf carbon/nitrogen ratios between 42.1 and 12.5. The technique was reproducible in a greenhouse without temperature, humidity, or light control, and is easily modified to suit different plant species, plants of various sizes, and various growing conditions.

Journal Article↗