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Biostatistics
2017[Apr]; 18
(2
): 275-294
PMID27756721
show ga
We introduce a new Empirical Bayes approach for large-scale hypothesis testing,
including estimating false discovery rates (FDRs), and effect sizes. This
approach has two key differences from existing approaches to FDR analysis. First,
it assumes that the distribution of the actual (unobserved) effects is unimodal,
with a mode at 0. This "unimodal assumption" (UA), although natural in many
contexts, is not usually incorporated into standard FDR analysis, and we
demonstrate how incorporating it brings many benefits. Specifically, the UA
facilitates efficient and robust computation-estimating the unimodal distribution
involves solving a simple convex optimization problem-and enables more accurate
inferences provided that it holds. Second, the method takes as its input two
numbers for each test (an effect size estimate and corresponding standard error),
rather than the one number usually used ($p$ value or $z$ score). When available,
using two numbers instead of one helps account for variation in measurement
precision across tests. It also facilitates estimation of effects, and unlike
standard FDR methods, our approach provides interval estimates (credible regions)
for each effect in addition to measures of significance. To provide a bridge
between interval estimates and significance measures, we introduce the term
"local false sign rate" to refer to the probability of getting the sign of an
effect wrong and argue that it is a superior measure of significance than the
local FDR because it is both more generally applicable and can be more robustly
estimated. Our methods are implemented in an R package ashr available from
http://github.com/stephens999/ashr.
free
free
free
