  Modern high-throughput biomedical devices routinely produce data on a large
scale, and the analysis of high-dimensional datasets has become commonplace in
biomedical studies. However, given thousands or tens of thousands of measured
variables in these datasets, extracting meaningful features poses a challenge.
In this article, we propose a procedure to evaluate the strength of the
associations between a nominal (categorical) response variable and multiple
features simultaneously. Specifically, we propose a framework of large-scale
multiple testing under arbitrary correlation dependency among test statistics.
First, marginal multinomial regressions are performed for each feature
individually. Second, we use an approach of multiple marginal models for each
baseline-category pair to establish asymptotic joint normality of the stacked
vector of the marginal multinomial regression coefficients. Third, we estimate
the (limiting) covariance matrix between the estimated coefficients from all
marginal models. Finally, our approach approximates the realized false
discovery proportion of a thresholding procedure for the marginal p-values, for
each baseline-category pair. The proposed approach offers a sensible trade-off
between the expected numbers of true and false rejections. Furthermore, we
demonstrate a practical application of the method on hyperspectral imaging
data. This dataset is obtained by a matrix-assisted laser desorption/ionization
(MALDI) instrument. MALDI demonstrates tremendous potential for clinical
diagnosis, particularly for cancer research. In our application, the nominal
response categories represent cancer subtypes.
