  Large-scale hypothesis testing has become a ubiquitous problem in
high-dimensional statistical inference, with broad applications in various
scienfitic disciplines. One relevant application is constituted by imaging mass
spectrometry (IMS) association studies, where a large number of tests are
performed simultaneously in order to identify molecular masses that are
associated with a particular phenotype, e. g., a cancer subtype. Mass spectra
obtained from Matrix-assisted laser desorption/ionization (MALDI) experiments
are dependent, when considered as statistical quantities. False discovery
proportion (FDP) control under arbitrary dependency structure among test
statistics is an active topic in modern multiple testing research. In this
context, we are concerned with the evaluation of associations between the
binary outcome variable (describing the phenotype) and multiple predictors
derived from MALDI measurements. We propose an inference procedure in which the
correlation matrix of the test statistics is utilized. The approach is based on
multiple marginal models (MMM). Specifically, we fit a marginal logistic
regression model for each predictor individually. Asymptotic joint normality of
the stacked vector of the marginal regression coefficients is established under
standard regularity assumptions, and their (limiting) correlation matrix is
estimated. The proposed method extracts common factors from the resulting
empirical correlation matrix. Finally, we estimate the realized FDP of a
thresholding procedure for the marginal $p$-values. We demonstrate a practical
application of the proposed workflow to MALDI IMS data in an oncological
context.
