Hi, In the boot package, the original statistic is simply the statistic function evaluated on the original data (called t0). However, in Harrell et al 1996 "Multivariable prognostic models..." Stats Med vol 15, pp. 361--387, it is different (p. 372): The statistic function evaluated on the original data is called "D_app" (apparent statistic), whereas "D_orig" (original statistic) is derived by first fitting the model to a bootstrap sample, then freezing the model and applying it to the original data. The bootstrap statistic D_boot is derived by applying the function to the bootstrap sample. Then optimism O = average(D_boot - D_orig), and the bias-corrected estimate is D_app - O. Can someone explain this difference, and especially why boot doesn't evaluate the frozen model again on the original data? Thanks, Gad -- Gad Abraham Department of Mathematics and Statistics The University of Melbourne Parkville 3010, Victoria, Australia email: g.abraham at ms.unimelb.edu.au web: http://www.ms.unimelb.edu.au/~gabraham
Gad Abraham wrote:> Hi, > > In the boot package, the original statistic is simply the statistic > function evaluated on the original data (called t0). > > However, in Harrell et al 1996 "Multivariable prognostic models..." > Stats Med vol 15, pp. 361--387, it is different (p. 372): > The statistic function evaluated on the original data is called > "D_app" (apparent statistic), whereas "D_orig" (original statistic) > is derived by first fitting the model to a bootstrap sample, then > freezing the model and applying it to the original data. The > bootstrap statistic D_boot is derived by applying the function to > the bootstrap sample. Then optimism O = average(D_boot - D_orig), > and the bias-corrected estimate is D_app - O. > > Can someone explain this difference, and especially why boot > doesn't evaluate the frozen model again on the original data? > > Thanks, > Gad > >The optimism bootstrap is a different kind of bootstrap to estimate bias from overfitting. boot is for the regular bootstrap. -- Frank E Harrell Jr Professor and Chair School of Medicine Department of Biostatistics Vanderbilt University