Title: Bagged Empirical Null p-values: A Method to Account for Model Uncertainty in Large Scale Inference,
Abstract: When conducting large scale inference, such as genome-wide association
studies or image analysis, nominal $p$-values are often adjusted to improve
control over the family-wise error rate (FWER). When the majority of tests are
null, procedures controlling the False discovery rate (Fdr) can be improved by
replacing the theoretical global null with its empirical estimate. However,
these other adjustment procedures remain sensitive to the working model
assumption. Here we propose two key ideas to improve inference in this space.
First, we propose $p$-values that are standardized to the empirical null
distribution (instead of the theoretical null). Second, we propose model
averaging $p$-values by bootstrap aggregation (Bagging) to account for model
uncertainty and selection procedures. The combination of these two key ideas
yields bagged empirical null $p$-values (BEN $p$-values) that often
dramatically alter the rank ordering of significant findings. Moreover, we find
that a multidimensional selection criteria based on BEN $p$-values and bagged
model fit statistics is more likely to yield reproducible findings. A
re-analysis of the famous Golub Leukemia data is presented to illustrate these
ideas. We uncovered new findings in these data, not detected previously, that
are backed by published bench work pre-dating the Gloub experiment. A
pseudo-simulation using the leukemia data is also presented to explore the
stability of this approach under broader conditions, and illustrates the
superiority of the BEN $p$-values compared to the other approaches.