A Bayesian approach to efficient differential allocation for resampling-based significance testing

Large-scale statistical analyses have become hallmarks of post-genomic era biological research due to advances in high-throughput assays and the integration of large biological databases. One accompanying issue is the simultaneous estimation of p-values for a large number of hypothesis tests. In many applications, a parametric assumption in the null distribution such as normality may be unreasonable, and resampling-based p-values are the preferred procedure for establishing statistical significance. Using resampling-based procedures for multiple testing is computationally intensive and typically requires large numbers of resamples.

We present a new approach to more efficiently assign resamples (such as bootstrap samples or permutations) within a nonparametric multiple testing framework. We formulated a Bayesian-inspired approach to this problem, and devised an algorithm that adapts the assignment of resamples iteratively with negligible space and running time overhead. In two experimental studies, a breast cancer microarray dataset and a genome wide association study dataset for Parkinson's disease, we demonstrated that our differential allocation procedure is substantially more accurate compared to the traditional uniform resample allocation.

Our experiments demonstrate that using a more sophisticated allocation strategy can improve our inference for hypothesis testing without a drastic increase in the amount of computation on randomized data. Moreover, we gain more improvement in efficiency when the number of tests is large. R code for our algorithm and the shortcut method are available at http://people.pcbi.upenn.edu/~lswang/pub/bmc2009/.