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

Background: The concept of resampling data - more commonly referred to as bootstrapping - has been in use for more than three decades. Bootstrapping has considerable theoretical advantages when it is applied to non-Gaussian data. Most of the published literature is concerned with the mathematical aspects of the bootstrap but increasingly this technique is being utilized in medical and other fields. Methods: I reviewed the published literature following a 1994 publication assessing the transfer of technology, including the bootstrap, to the biomedical literature. Results: In the ten-year period following that 1994 paper there were 1679 published references to the technique in Medline. In that same time period the following citations were found in the four major medical journals-British Medical Journal (48), JAMA (51), Lancet (52) and the New England Journal of Medicine (45). Content: I introduce the basic theory of the bootstrap, the jackknife, and permutation tests. The bootstrap is used to estimate the accuracy of an estimator such as the standard error, a confidence interval, or the bias of an estimator. The technique may be useful for analysing smallish expensive-to-collect data sets where prior information is sparse, distributional assumptions are unclear, and where further data may be difficult to acquire. Some of the elementary uses of bootstrapping are illustrated by considering the calculation of confidence intervals such as for reference ranges or for experimental data findings, hypothesis testing such as comparing experimental findings, linear regression, and correlation when studying association and prediction of variables, non-linear regression such as used in immunoassay techniques, and ROC curve processing. Conclusions: These techniques can supplement current nonparametric statistical methods and should be included, where appropriate, in the armamentarium of data processing methodologies. (c) 2005 Elsevier B.V All rights reserved.