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PubMedDate not supplied

Bootstrapping of gene-expression data improves and controls the false discovery rate of differentially expressed genes.

The ordinary-, penalized-, and bootstrap t-test, least squares and best linear unbiased prediction were compared for their false discovery rates (FDR), i.e. the fraction of falsely discovered genes, which was empirically estimated in a duplicate of the data set. The bootstrap-t-test yielded up to 80% lower FDRs than the alternative statistics, and its FDR was always as good as or better than any of the alternatives. Generally, the predicted FDR from the bootstrapped P-values agreed well with their empirical estimates, except when the number of mRNA samples is smaller than 16. In a cancer data set, the bootstrap-t-test discovered 200 differentially regulated genes at a FDR of 2.6%, and in a knock-out gene expression experiment 10 genes were discovered at a FDR of 3.2%. It is argued that, in the case of microarray data, control of the FDR takes sufficient account of the multiple testing, whilst being less stringent than Bonferoni-type multiple testing corrections. Extensions of the bootstrap simulations to more complicated test-statistics are discussed.

Analysis of Variance↗

PubMed2003

Bootstrap approach to inference and power analysis based on three test statistics for covariance structure models.

We study several aspects of bootstrap inference for covariance structure models based on three test statistics, including Type I error, power and sample-size determination. Specifically, we discuss conditions for a test statistic to achieve a more accurate level of Type I error, both in theory and in practice. Details on power analysis and sample-size determination are given. For data sets with heavy tails, we propose applying a bootstrap methodology to a transformed sample by a downweighting procedure. One of the key conditions for safe bootstrap inference is generally satisfied by the transformed sample but may not be satisfied by the original sample with heavy tails. Several data sets illustrate that, by combining downweighting and bootstrapping, a researcher may find a nearly optimal procedure for evaluating various aspects of covariance structure models. A rule for handling non-convergence problems in bootstrap replications is proposed.

Humans↗

PubMed2006

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↗

PubMed2004

Assessing DTI data quality using bootstrap analysis.

Diffusion tensor imaging (DTI) is an established method for characterizing and quantifying ultrastructural brain tissue properties. However, DTI-derived variables are affected by various sources of signal uncertainty. The goal of this study was to establish an objective quality measure for DTI based on the nonparametric bootstrap methodology. The confidence intervals (CIs) of white matter (WM) fractional anisotropy (FA) and Clinear were determined by bootstrap analysis and submitted to histogram analysis. The effects of artificial noising and edge-preserving smoothing, as well as enhanced and reduced motion were studied in healthy volunteers. Gender and age effects on data quality as potential confounds in group comparison studies were analyzed. Additional noising showed a detrimental effect on the mean, peak position, and height of the respective CIs at 10% of the original background noise. Inverse changes reflected data improvement induced by edge-preserving smoothing. Motion-dependent impairment was also well depicted by bootstrap-derived parameters. Moreover, there was a significant gender effect, with females displaying less dispersion (attributable to elevated SNR). In conclusion, the bootstrap procedure is a useful tool for assessing DTI data quality. It is sensitive to both noise and motion effects, and may help to exclude confounding effects in group comparisons.

Adult↗

PubMed2003

Stability of multivariable fractional polynomial models with selection of variables and transformations: a bootstrap investigation.

Sauerbrei and Royston have recently described an algorithm, based on fractional polynomials, for the simultaneous selection of variables and of suitable transformations for continuous predictors in a multivariable regression setting. They illustrated the approach by analyses of two breast cancer data sets. Here we extend their work by considering how to assess possible instability in such multivariable fractional polynomial models. We first apply the algorithm repeatedly in many bootstrap replicates. We then use log-linear models to investigate dependencies among the inclusion fractions for each predictor and among the simplified classes of fractional polynomial function chosen in the bootstrap samples. To further evaluate the results, we define measures of instability based on a decomposition of the variability of the bootstrap-selected functions in relation to a reference function from the original model. For each data set we are able to identify large, reasonably stable subsets of the bootstrap replications in which the functional forms of the predictors appear fairly stable. Despite the considerable flexibility of the family of fractional polynomials and the consequent risk of overfitting when several variables are considered, we conclude that the multivariable selection algorithm can find stable models.

Algorithms↗

PubMed2004

Bootstrap confidence intervals for medical costs with censored observations.

Medical costs data with administratively censored observations often arise in cost-effectiveness studies of treatments for life-threatening diseases. Mean of medical costs incurred from the start of a treatment until death or a certain time point after the implementation of treatment is frequently of interest. In many situations, due to the skewed nature of the cost distribution and non-uniform rate of cost accumulation over time, the currently available normal approximation confidence interval has poor coverage accuracy. In this paper, we propose a bootstrap confidence interval for the mean of medical costs with censored observations. In simulation studies, we show that the proposed bootstrap confidence interval had much better coverage accuracy than the normal approximation one when medical costs had a skewed distribution. When there is light censoring on medical costs (< or =25 per cent), we found that the bootstrap confidence interval based on the simple weighted estimator is preferred due to its simplicity and good coverage accuracy. For heavily censored cost data (censoring rate > or =30 per cent) with larger sample sizes (n > or =200), the bootstrap confidence intervals based on the partitioned estimator has superior performance in terms of both efficiency and coverage accuracy. We also illustrate the use of our methods in a real example.

Computer Simulation↗

PubMed2005

Bootstrap analysis of multivariate failure time data.

Multivariate failure time data often arise in research. Cox proportional hazards modelling is a widely used method of analysing failure time data for independent observations. However, when failure times are correlated the Cox proportional hazards model does not yield valid estimates of standard errors or significance tests. Many methods for the analysis of multivariate failure time data have been proposed. These methods commonly test hypotheses about the regression parameters, a practice which averages the treatment effect across time. The purpose of this paper is to examine the bootstrap method for obtaining standard errors in the multivariate failure time case, particularly when the focus is the survival probability or the treatment effect at a single time point such as in a surgical trial. Our motivating example comes from the Asymptomatic Carotid and Atherosclerosis Study (ACAS) in which the outcome of stroke or perioperative complications could be observed for either or both carotid arteries within each patient. Extensive simulation studies were conducted to examine the bootstrap procedure for analysing correlated failure time data under a variety of conditions including a range of treatment effects, cluster sizes, intercluster correlation values and for both proportional and non-proportional data. We found that the bootstrap method was able to estimate the standard error adequately for survival probabilities at a specific time and the standard error for the survival difference and the relative risk at a specific time. We illustrated the bootstrap method for calculating the standard error for the survival probability and statistical testing at a specific time value by analysing the two arteries per patient from the ACAS study.

Biometry↗

PubMed2006

Intraclass correlation coefficients and bootstrap methods of hierarchical binary outcomes.

Intraclass correlation coefficients are designed to assess consistency or conformity between two or more quantitative measurements. When multistage cluster sampling is implemented, no methods are readily available to estimate intraclass correlations of binomial-distributed outcomes within a cluster. Because statistical distribution of the intraclass correlation coefficients could be complicated or unspecified, we propose using a bootstrap method to estimate the standard error and confidence interval within the framework of a multilevel generalized linear model. We compared the results derived from a parametric bootstrap method with those from a non-parametric bootstrap method and found that the non-parametric method is more robust. For non-parametric bootstrap sampling, we showed that the effectiveness of sampling on the highest level is greater than that on lower levels; to illustrate the effectiveness, we analyse survey data in China and do simulation studies.

Biometry↗

PubMed1979

Bootstrapping on the adaptive landscape.

Different versions of a gene or of a multigenic system may be essentially equivalent so far as the specific function of the structures which they code for or control is concerned, but very different with respect to their amenability to evolution. The structural features which increase evolutionary amenability are a disadvantage to the organism in terms of energy. Nevertheless, they accumulate in the course of evolution as a consequence of hitchhiking along with the desirable traits whose evolution they make possible. This is the bootstrap principle of evolutionary adaptability. In terms of the adaptive landscape bootstrapping corresponds to populations evolving in such a way that they occupy regions of the landscape which are more amenable to evolutionary hill climbing. The bootstrapping idea has implications for structure-function relations in a number of complex biological information processing systems, including biochemical systems, the immune system, and the brain. Bootstrapping is also discussed in connection with the origin of information processing (the origin of life) and in connection with possible designs for macromolecular computing systems.

Adaptation, Biological↗

PubMed2006

Creating non-parametric bootstrap samples using Poisson frequencies.

This article describes how, in the high-level software packages used by non-statisticians, approximate non-parametric bootstrap samples can be created and analyzed without physically creating new data sets, or resorting to complex programming. The comparable performance of this shortcut method, which uses Poisson rather than multinomial frequencies for the numbers of copies of each observation, is demonstrated theoretically by evaluating the bootstrap variance in an example where the classic estimator of the sampling variance of the statistic of interest has a known closed form. For sample sizes of 50 or more, bootstrap standard errors obtained by this shortcut method exceeded those obtained by the standard version by less than 1%. The proposed method is also evaluated in two worked examples, involving statistics whose sampling distribution is more complex. The second of these is also used to illustrate when one can and cannot use non-parametric bootstrap samples.

Computational Biology↗

PubMed2006

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↗

PubMed1997

Nonparametric bootstrap analysis with applications to demographic effects in demand functions.

"A new bootstrap proposal, labeled smooth conditional moment (SCM) bootstrap, is introduced for independent but not necessarily identically distributed data, where the classical bootstrap procedure fails.... A good example of the benefits of using nonparametric and bootstrap methods is the area of empirical demand analysis. In particular, we will be concerned with their application to the study of two important topics: what are the most relevant effects of household demographic variables on demand behavior, and to what extent present parametric specifications capture these effects."

Behavior↗

PubMed2002

Statistical characteristics of area under the receiver operating characteristic curve for a simple prognostic model using traditional and bootstrapped approaches.

Prognostic models are increasingly common in the biomedical literature. These models are frequently evaluated with respect to their ability to discriminate between those with and without an outcome. The area under the receiver-operating curve (AROC) is often used to assess discrimination. In this study, we introduce a bootstrap method, and, using Monte Carlo simulation, we compare three different bootstrap approaches with four commonly used methods in their ability to accurately estimate 95% confidence intervals (CIs) around the AROC for a simple prognostic model. We also evaluated the power of a bootstrap method and the commonly used trapezoid rule to compare different prognostic models. We show that several good methods exist for calculating 95% CIs of AROC, but the maximum likelihood estimation method should not be used with small sample sizes. We further show that for our simple prognostic model a bootstrap z-statistic approach is preferred over the trapezoidal method when comparing the AROCs of two related models.

Aged↗

PubMed2006

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↗

PubMed1998

On the bootstrap and monotone likelihood in the cox proportional hazards regression model.

Recent literature has provided encouragement for using the bootstrap for inference on regression parameters in the Cox proportional hazards (PH) model. However, generating and performing the necessary partial likelihood computations on multitudinous bootstrap samples greatly increases the chances of incurring problems with monotone likelihood at some point in the analysis. The only symptom of monotone likelihood may be a failure to converge in the numerical maximization procedure, and so the problem might naïvely be dismissed by deleting the offending data set and replacing it with a new one. This strategy is shown to lead to potentially high selection biases in the subsequent summary statistics. This note discusses the importance of keeping track of these monotone likelihood cases and provides recommendations for their use in interpreting bootstrap findings, and for avoiding unwanted biases that may result from high rates of occurrence. In many cases, high monotone likelihood rates indicate that a more highly-specified model may be preferred. Special consideration is given to the problem of high monotone likelihood incidence in Monte Carlo studies of the bootstrap.

Biometry↗

PubMed1998

Bootstrapping for pharmacokinetic models: visualization of predictive and parameter uncertainty.

PURPOSE: We explore use of "bootstrapping" methods to obtain a measure of reliability of predictions made in part from fits of individual drug level data with a pharmacokinetic (PK) model, and to help clarify parameter identifiability for such models. METHODS: Simulation studies use four sets (A-D) of drug concentration data obtained following a single oral dose. Each set is fit with a two compartment PK model, and the "bootstrap" is employed to examine the potential predictive variation in estimates of parameter sets. This yields an empirical distribution of plausible steady state (SS) drug concentration predictions that can be used to form a confidence interval for a prediction. RESULTS: A distinct, narrow confidence region in parameter space is identified for subjects A and B. The bootstrapped sets have a relatively large coefficient of variation (CV) (35-90% for A), yet the corresponding SS drug levels are tightly clustered (CVs only 2-9%). The results for C and D are dramatically different. The CVs for both the parameters and predicted drug levels are larger by a factor of 5 and more. The results reveal that the original data for C and D, but not A and B, can be represented by at least two different PK model manifestations, yet only one provides reliable predictions. CONCLUSIONS: The insights gained can facilitate making decisions about parameter identifiability. In particular, the results for C and D have important implications for the degree of implicit overparameterization that may exist in the PK model. In cases where the data support only a single model manifestation, the "bootstrap" method provides information needed to form a confidence interval for a prediction.

Computer Simulation↗

PubMedDate not supplied

Bootstrap confidence intervals for costs-of-illness of type 2 diabetes mellitus in Germany.

OBJECTIVE: The Costs of Diabetes in Europe-Type 2 study (CODE-2, SmithKline Beecham plc) measures costs of managing patients with type 2 diabetes mellitus in Germany. The aim of this analysis was to assess the uncertainty of these estimates. DESIGN AND SETTING: The German study arm was based on a sample of 809 patients with type 2 diabetes registered in general practices. Information on socioeconomic data, medical resource use, and clinical data was collected retrospectively for 1998. PATIENTS AND PARTICIPANTS: Patients were grouped in five strata based on their complication status, because of the high impact of complications on costs. To obtain higher credibility of resulting estimates, rare complication groups were overrepresented. To be representative, results were weighted using real prevalence data on complications from a prestudy. MAIN OUTCOME MEASURES AND RESULTS: Within each stratum, results were calculated as arithmetic mean except for demographic data, where the median was applied as input for weighted averages. Because the degree of precision of calculated estimates was not accessible analytically, 95% confidence intervals (CIs) were computed via bootstrapping of 10,000 independent bootstrap samples for each of the calculated estimates. All costs are given for the payers' perspective in German Deutsche Mark (DM). Costs per patient and year for ambulatory care were DM 775 with 95% CI (721-835), for hospitalizations DM 2771 (2242-3342), for drug treatment DM 1496 (1399-1598), and for rehabilitation DM 120 (70-177). The indirect cost was DM 372 (144-645). From the perspective of the sickness funds, cost per patient and year was DM 5539 (5184-5894). Mean HbA1c status was 7.51% (7.37-7.66) with the majority of patients not achieving glycemic control below 6.5%. CONCLUSION: Bootstrap CIs are remarkably narrow. Combining a weighted stratification with bootstrap estimation is an appropriate method for analyzing the weighted average of highly variable and skewed parameters such as costs of diabetes.

Adult↗

PubMed2001

Bootstrapping cluster analysis: assessing the reliability of conclusions from microarray experiments.

We introduce a general technique for making statistical inference from clustering tools applied to gene expression microarray data. The approach utilizes an analysis of variance model to achieve normalization and estimate differential expression of genes across multiple conditions. Statistical inference is based on the application of a randomization technique, bootstrapping. Bootstrapping has previously been used to obtain confidence intervals for estimates of differential expression for individual genes. Here we apply bootstrapping to assess the stability of results from a cluster analysis. We illustrate the technique with a publicly available data set and draw conclusions about the reliability of clustering results in light of variation in the data. The bootstrapping procedure relies on experimental replication. We discuss the implications of replication and good design in microarray experiments.

Analysis of Variance↗