  The rapidly expanding field of metabolomics presents an invaluable resource
for understanding the associations between metabolites and various diseases.
However, the high dimensionality, presence of missing values, and measurement
errors associated with metabolomics data can present challenges in developing
reliable and reproducible methodologies for disease association studies.
Therefore, there is a compelling need to develop robust statistical methods
that can navigate these complexities to achieve reliable and reproducible
disease association studies. In this paper, we focus on developing such a
methodology with an emphasis on controlling the False Discovery Rate during the
screening of mutual metabolomic signals for multiple disease outcomes. We
illustrate the versatility and performance of this procedure in a variety of
scenarios, dealing with missing data and measurement errors. As a specific
application of this novel methodology, we target two of the most prevalent
cancers among US women: breast cancer and colorectal cancer. By applying our
method to the Wome's Health Initiative data, we successfully identify
metabolites that are associated with either or both of these cancers,
demonstrating the practical utility and potential of our method in identifying
consistent risk factors and understanding shared mechanisms between diseases.
