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Results for “Bootstrap resampling”

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PubMed1998

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

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

Chromosome Mapping↗

PubMed1999

Using the bootstrap for estimation in group sequential designs: an application to a clinical trial for nasopharyngeal cancer.

We investigate a resampling method for bias correction in group sequential designs with censored survival data using logrank testing. The method draws nested bootstrap samples of different sizes from the observed data in order to mimic the large sample independent increment property of statistics resulting from sequential designs. The motivation for this problem came from the very positive results and early termination of a randomized clinical trial for nasopharyngeal cancer co-ordinated by the Southwest Oncology Group.

Antimetabolites, Antineoplastic↗

PubMed1997

A Markov model for HIV disease progression including the effect of HIV diagnosis and treatment: application to AIDS prediction in England and Wales.

Back-calculation is a widely used method to estimate HIV incidence rates, and is commonly based on times of AIDS diagnosis. Following up earlier work, we extend this method to also incorporate knowledge of times of HIV diagnosis (first positive test). This is achieved through the use of a Markov model which describes the progress of an HIV infected person through various stages, and which allows causal connections between events to be explicitly modelled. Estimation is based on maximum likelihood, the likelihood being calculated within a discretized version of the Markov model. The effect of sampling uncertainty and model uncertainty (sensitivity) is evaluated simultaneously by means of a combined bootstrap and simulation procedure. At each replication we resample both the data and the model (from a set of possible models described by randomizing one or more parameters). For instance, uncertain knowledge about the incubation distribution affects the estimates of some parameters, but not others. The Markov approach is applied to the prediction of AIDS incidence for homosexuals in England and Wales up to the year 2000.

AIDS Serodiagnosis↗

PubMed2004

DNA marker mining of ILSTS035 microsatellite locus on chromosome 6 of Hanwoo cattle.

We describe tests for detecting and locating quantitative trait loci (QTL) for traits in Hanwoo cattle. From results of a permutation test to detect QTL for marbling, we selected the microsatellite locus ILSTS035 on chromosome 6 for further analysis. K-means clustering analysis applied to five traits and nine DNA markers in ILSTS035 resulted in three cluster groups. Finally we employed the bootstrap test method to calculate confidence intervals using the resampling method to find major DNA markers. We conclude that the major markers of ILSTS035 locus on chromosome 6 of Hanwoo cattle are markers 235 bp and 266 bp.

Animals↗

PubMed2004

Determining the number of clusters by sampling with replacement.

A split-sample replication criterion originally proposed by J. E. Overall and K. N. Magee (1992) as a stopping rule for hierarchical cluster analysis is applied to multiple data sets generated by sampling with replacement from an original simulated primary data set. An investigation of the validity of this bootstrap procedure was undertaken using different combinations of the true number of latent populations, degrees of overlap, and sample sizes. The bootstrap procedure enhanced the accuracy of identifying the true number of latent populations under virtually all conditions. Increasing the size of the resampled data sets relative to the size of the primary data set further increased accuracy. A computer program to implement the bootstrap stopping rule is made available via a referenced Web site.

Cluster Analysis↗

PubMed2004

Spatiotemporal wavelet resampling for functional neuroimaging data.

The study of dynamic interdependences between brain regions is currently a very active research field. For any connectivity study, it is important to determine whether correlations between two selected brain regions are statistically significant or only chance effects due to non-specific correlations present throughout the data. In this report, we present a wavelet-based non-parametric technique for testing the null hypothesis that the correlations are typical of the data set and not unique to the regions of interest. This is achieved through spatiotemporal resampling of the data in the wavelet domain. Two functional MRI data sets were analysed: (1) Data from 8 healthy human subjects viewing a checkerboard image, and (2) "Null" data obtained from 3 healthy human subjects, resting with eyes closed. It was demonstrated that constrained resampling of the data in the wavelet domain allows construction of bootstrapped data with four essential properties: (1) Spatial and temporal correlations within and between slices are preserved, (2) The irregular geometry of the intracranial images is maintained, (3) There is adequate type I error control, and (4) Expected experiment-induced correlations are identified. The limitations and possible extensions of the proposed technique are discussed.

Adult↗

PubMed2004

Methods for testing familial aggregation of diseases in population-based samples: application to Hodgkin lymphoma in Swedish registry data.

We use data on lymphoma in families of Hodgkin lymphoma (HL) cases from the Swedish Family Cancer Database (Hemminki et al. 2001) to illustrate survival methods for detecting familial aggregation in first degree relatives of case probands compared to first degree relatives of control probands, from registries that permit sampling of all cases. Because more than one case may occur in a given family, the first degree relatives of case probands are not necessarily independent, and we present procedures that allow for such dependence. A bootstrap procedure also accommodates matching of case and control probands by resampling the matching clusters, defined as the combined set of all first degree relatives of the matched case and control probands. Regarding families as independent sampling units leads to inferences based on "sandwich variance estimators" and accounts for dependencies from having more than one proband in a family, but not for matching. We compare these methods in analysis of familial aggregation of HL and also present simulations to compare survival analyses with analyses of binary outcome data.

Adult↗

PubMed2002

Estimating the variance of disease-prevalence estimates from population-based registries.

We propose a new Poisson method to estimate the variance for prevalence estimates obtained by the counting method described by Gail et al. (1999, Biometrics 55, 1137-1144) and to construct a confidence interval for the prevalence. We evaluate both the Poisson procedure and the procedure based on the bootstrap proposed by Gail et al. in simulated samples generated by resampling real data. These studies show that both variance estimators usually perform well and yield coverages of confidence intervals at nominal levels. When the number of disease survivors is very small, however, confidence intervals based on the Poisson method have supranominal coverage, whereas those based on the procedure of Gail et al. tend to have below-nominal coverage. For these reasons, we recommend the Poisson method, which also reduces the computational burden considerably.

Analysis of Variance↗

PubMed1999

Bootstrap methods for adaptive designs.

Adaptive designs generate dependent sequences of random variables that are not exchangeable. Therefore, it is not obvious how to employ a resampling scheme for confidence interval estimation. We propose a simple procedure where observed response rates from an adaptive experiment are input to a simulation program. The program then generates sequences from the adaptive sampling scheme. We compare, via simulation, three bootstrap confidence intervals with the asymptotic confidence interval for two adaptive designs useful for clinical trials. A simple ranking of simulated response rates yields a confidence interval approximation with coverage close to 1-alpha in most cases. The method allows us to incorporate such complexities as staggered entry and delayed response. We give an example of its utility on a clinical trial of fluoxetine in depression.

Antidepressive Agents, Second-Generation↗

PubMed2002

Penalized partial likelihood regression for right-censored data with bootstrap selection of the penalty parameter.

The Cox proportional hazards model is often used for estimating the association between covariates and a potentially censored failure time, and the corresponding partial likelihood estimators are used for the estimation and prediction of relative risk of failure. However, partial likelihood estimators are unstable and have large variance when collinearity exists among the explanatory variables or when the number of failures is not much greater than the number of covariates of interest. A penalized (log) partial likelihood is proposed to give more accurate relative risk estimators. We show that asymptotically there always exists a penalty parameter for the penalized partial likelihood that reduces mean squared estimation error for log relative risk, and we propose a resampling method to choose the penalty parameter. Simulations and an example show that the bootstrap-selected penalized partial likelihood estimators can, in some instances, have smaller bias than the partial likelihood estimators and have smaller mean squared estimation and prediction errors of log relative risk. These methods are illustrated with a data set in multiple myeloma from the Eastern Cooperative Oncology Group.

Antineoplastic Agents↗

PubMed2006

Age and sex are sufficient for predicting fractures occurring within 1 year of hemodialysis treatment.

BACKGROUND: The incidence of fractures averages 20 per 1000 hemodialysis patient years at risk. This study sought to design and evaluate the utility of a simple prediction rule for fractures in dialysis patients using only standard demographical and biochemical information. METHODS: 1777 prevalent hemodialysis patients of the Austrian dialysis and transplant database who had an evaluation of fractures in 2004 and 2005 were included into analysis. Validation of the prediction rule model by a test set was performed using three different resampling techniques, the split sample approach, a 100-fold cross validation and a 100x bootstrap. Calibration of the model was performed visually by comparing the observed to the expected number of outcomes in each category and by calculating the Hosmer and Lemeshow goodness-of-fit statistic. RESULTS: A multivariable logistic regression model built on clinical expertise yielded a discrimination of c=0.73 (AUC of ROC). Further reduction of the covariables to age and sex as the only predictive variables did not result in loss of discrimination (c=0.71) and at the same time provided adequate calibration (p=0.69). The probability of fractures (PF) occurring within the next year of hemodialysis can be calculated from our prediction model as, PF=e(-6.25+0.4*age(in decades)-0.93(if male))/1+e(-6.25+0.4*age(in decades)-0.93(if male)), e.g., a 70-year-old male would have a fracture probability of 0.01 or 1%, a female 3%. The optimism derived by all resampling techniques was between 1% and 2% suggesting adequate generalizability of the prediction rule. CONCLUSION: A sufficient and parsimonious prediction rule for fractures in hemodialysis patients consists of the independent variables age and sex.

Aged↗

PubMed2006

Comparison of variance estimation approaches in a two-state Markov model for longitudinal data with misclassification.

We examine the behaviour of the variance-covariance parameter estimates in an alternating binary Markov model with misclassification. Transition probabilities specify the state transitions for a process that is not directly observable. The state of an observable process, which may not correctly classify the state of the unobservable process, is obtained at discrete time points. Misclassification probabilities capture the two types of classification errors. Variance components of the estimated transition parameters are calculated with three estimation procedures: observed information, jackknife, and bootstrap techniques. Simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation. The three approaches generally provide similar variance estimates for large samples and moderate misclassification. In these situations, the resampling methods are reasonable alternatives when programming partial derivatives is not appealing. With smaller chains or higher misclassification probabilities, the bootstrap method appears to be the best choice.

Analysis of Variance↗

PubMed1987

Bootstrap variance estimators for the parameters of small-sample sensory-performance functions.

The bootstrap method, due to Bradley Efron, is a powerful, general method for estimating a variance or standard deviation by repeatedly resampling the given set of experimental data. The method is applied here to the problem of estimating the standard deviation of the estimated midpoint and spread of a sensory-performance function based on data sets comprising 15-25 trials. The performance of the bootstrap estimator was assessed in Monte Carlo studies against another general estimator obtained by the classical "combination-of-observations" or incremental method. The bootstrap method proved clearly superior to the incremental method, yielding much smaller percentage biases and much greater efficiencies. Its use in the analysis of sensory-performance data may be particularly appropriate when traditional asymptotic procedures, including the probit-transformation approach, become unreliable.

Animals↗

PubMed2006

Multivariable modeling of radiotherapy outcomes, including dose-volume and clinical factors.

PURPOSE: The probability of a specific radiotherapy outcome is typically a complex, unknown function of dosimetric and clinical factors. Current models are usually oversimplified. We describe alternative methods for building multivariable dose-response models. METHODS: Representative data sets of esophagitis and xerostomia are used. We use a logistic regression framework to approximate the treatment-response function. Bootstrap replications are performed to explore variable selection stability. To guard against under/overfitting, we compare several analytical and data-driven methods for model-order estimation. Spearman's coefficient is used to evaluate performance robustness. Novel graphical displays of variable cross correlations and bootstrap selection are demonstrated. RESULTS: Bootstrap variable selection techniques improve model building by reducing sample size effects and unveiling variable cross correlations. Inference by resampling and Bayesian approaches produced generally consistent guidance for model order estimation. The optimal esophagitis model consisted of 5 dosimetric/clinical variables. Although the xerostomia model could be improved by combining clinical and dose-volume factors, the improvement would be small. CONCLUSIONS: Prediction of treatment response can be improved by mixing clinical and dose-volume factors. Graphical tools can mitigate the inherent complexity of multivariable modeling. Bootstrap-based variable selection analysis increases the reliability of reported models. Statistical inference methods combined with Spearman's coefficient provide an efficient approach to estimating optimal model order.

Carcinoma, Non-Small-Cell Lung↗

PubMed2001

Comparing outcomes of coronary artery bypass surgery: Is the New York Cardiac Surgery Reporting System model sensitive to changes in case mix?

OBJECTIVE: To assess the validity of using the standardized mortality ratio (SMR), based on the New York State Cardiac Surgery Reporting System (CSRS) prediction model to compare coronary artery bypass grafting (CABG) outcomes between hospitals. DESIGN: The study was designed as a retrospective study based on a database containing all patients undergoing isolated CABG surgery in New York State hospitals in 1996 (n = 20,078). In the first part of this study, a computer simulation was used to assess the impact of case mix variation on the SMR. A computer-intensive algorithm was used to create 5,000 random case mixes from the patients in the CSRS database. The SMR associated with each of the 5,000 case mixes was calculated using a resampling algorithm. The second part of this study was designed to determine whether the identity of quality outliers among all of the 32 hospitals in the CSRS database would change after adjusting for the effects of case mix on the SMR. The SMR associated with the case mix of each hospital in the CSRS database (the hospital case mix SMR) was obtained using a resampling algorithm. The hospital SMR (as well as 95% confidence interval) was then calculated using bootstrapping for each of the 32 hospitals within the CSRS database. An adjusted SMR was then derived for each hospital by dividing the hospital SMR by the case mix SMR for that hospital. SETTING: Thirty-two hospitals in New York State performing CABG surgery. INTERVENTIONS: None. RESULTS: Changes in patient case mix are associated with statistically significant changes in the SMR. However, there was no difference in the identity of quality outliers in the New York State CSRS database when using either the SMR or the SMR adjusted for the effects of case mix. CONCLUSION: Risk-adjusted measures of outcomes in CABG patients may be potentially biased by differences in case mix between institutions because of the influence of case mix on the process of risk adjustment. There was, however, no evidence of bias in the specific application of the CSRS model to the hospitals in the CSRS database.

Benchmarking↗

PubMed2005

Prediction error estimation: a comparison of resampling methods.

MOTIVATION: In genomic studies, thousands of features are collected on relatively few samples. One of the goals of these studies is to build classifiers to predict the outcome of future observations. There are three inherent steps to this process: feature selection, model selection and prediction assessment. With a focus on prediction assessment, we compare several methods for estimating the 'true' prediction error of a prediction model in the presence of feature selection. RESULTS: For small studies where features are selected from thousands of candidates, the resubstitution and simple split-sample estimates are seriously biased. In these small samples, leave-one-out cross-validation (LOOCV), 10-fold cross-validation (CV) and the .632+ bootstrap have the smallest bias for diagonal discriminant analysis, nearest neighbor and classification trees. LOOCV and 10-fold CV have the smallest bias for linear discriminant analysis. Additionally, LOOCV, 5- and 10-fold CV, and the .632+ bootstrap have the lowest mean square error. The .632+ bootstrap is quite biased in small sample sizes with strong signal-to-noise ratios. Differences in performance among resampling methods are reduced as the number of specimens available increase. SUPPLEMENTARY INFORMATION: A complete compilation of results and R code for simulations and analyses are available in Molinaro et al. (2005) (http://linus.nci.nih.gov/brb/TechReport.htm).

Algorithms↗

PubMed1993

An evaluation of some methods for fitting dose-response models to quantal-response developmental toxicology data.

The analysis of quantal-response developmental toxicology data by dose-response modeling is discussed, with emphasis on methods that avoid exact distributional assumptions. These methods (quasi-likelihood, bootstrapping, and jackknifing) are contrasted with analyses based on the beta-binomial distribution. For the resampling procedures, dose-response models are fit under a binomial likelihood. A justification for this choice of estimator in resampling plans is given, based on an extension of the standard results for asymptotic normality and consistency of maximum likelihood estimators. This justification depends only on the true distribution of the data having the usual binomial expectation. A quasi-likelihood approach is also considered, in which simple assumptions about the intralitter correlation structure are made. Quasi-likelihood methods are in theory asymptotically robust to misspecification of the intralitter correlation structure. The practical implications of these asymptotic results are evaluated in a simulation study.

Abnormalities, Drug-Induced↗

PubMed2004

A post-processing/region of interest (ROI) method for discriminating patterns of activity in statistical maps of fMRI data.

To combine functional neuroimaging studies across subjects, anatomical and functional data are typically either transformed to a common space or averaged across regions of interest (ROIs). However, if there are (1) anatomical variations within the subject pool (as in clinical or aging populations), (2) non-Gaussian distributions of task-related activity within a typical ROI or, (3) more ROIs than subjects, neither spatial transformation of the data to a common space nor averaging across all subjects' ROIs is suitable for standard discriminant analysis. To solve these problems, we describe a post-processing method that uses voxel-based statistics representing task-related activity (pooled within ROIs) to establish combinations of ROIs that maximally differentiate tasks across all subjects. The method involves randomized resampling from multiple ROIs within each subject, multivariate linear discriminant analysis across all subjects and validation with bootstrapping techniques. When applied to experimental data from healthy subjects performing two motor tasks, the method detected some brain regions, including the supplementary motor area (SMA), that participated in a distributed network differentially active between tasks. However there was not a significant difference in SMA activity when this region was examined in isolation. We suggest this method is a practical means to combine voxel-based statistics within anatomically defined ROIs across subjects.

Brain↗