A comparison of bootstrap methods and an adjusted bootstrap approach for estimating prediction error in microarray classification Short title: Bootstrap Prediction Error Estimation

SUMMARY This paper first provides a critical review on some existing methods for estimating prediction error in classifying microarray data where the number of genes greatly exceeds the number of specimen. Special attention is given to the bootstrap-related methods. When the sample size n is small, we find that all the reviewed methods suffer from either substantial bias or variability. We introduce a repeated leave-one-out bootstrap method which predicts for each specimen in the sample using bootstrap learning sets of size ln. We then propose an adjusted bootstrap method that fits a learning curve to the repeated leave-one-out bootstrap estimates calculated with different bootstrap learning set sizes. The adjusted bootstrap method is robust across the situations we investigate and provides slightly conservative estimate for the prediction error. Even with small samples, it does not suffer from large upward bias as the leave-one-out bootstrap and the .632+ bootstrap, and it does not suffer from large variability as the leave-one-out cross-validation in microarray applications.