The statistical tests that are commonly used for detecting mean or median
treatment effects suffer from low power when the two distribution functions
differ only in the upper (or lower) tail, as in the assessment of the Total
Sharp Score (TSS) under different treatments for rheumatoid arthritis. In this
article, we propose a more powerful test that detects treatment effects through
the expected shortfalls.
Probe-level microarray data are usually stored in matrices, where the row and
column correspond to array and probe, respectively. Scientists routinely
summarize each array by a single index as the expression level of each probe
set (gene). We examine the adequacy of a unidimensional summary for
characterizing the data matrix of each probe set. To do so, we propose a
low-rank matrix model for the probe-level intensities, and develop a useful
framework for testing the adequacy of unidimensionality against targeted
alternatives.
Response-adaptive randomization has recently attracted a lot of attention in
the literature. In this paper, we propose a new and simple family of
response-adaptive randomization procedures that attain the Cramer--Rao lower
bounds on the allocation variances for any allocation proportions, including
optimal allocation proportions. The allocation probability functions of
proposed procedures are discontinuous. The existing large sample theory for
adaptive designs relies on Taylor expansions of the allocation probability
functions, which do not apply to nondifferentiable cases.