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

Variable selection with FDR control for noisy data -- an application to screening metabolites that are associated with breast and colorectal cancer