  The intricate interplay between host organisms and their gut microbiota has
catalyzed research into the microbiome's role in disease, shedding light on
novel aspects of disease pathogenesis. However, the mechanisms through which
the microbiome exerts its influence on disease remain largely unclear. In this
study, we first introduce a structural equation model to delineate the pathways
connecting the microbiome, metabolome, and disease processes, utilizing a
target multiview microbiome data. To mitigate the challenges posed by hidden
confounders, we further propose an integrative approach that incorporates data
from an external microbiome cohort. This method also supports the
identification of disease-specific and microbiome-associated metabolites that
are missing in the target cohort. We provide theoretical underpinnings for the
estimations derived from our integrative approach, demonstrating estimation
consistency and asymptotic normality. The effectiveness of our methodologies is
validated through comprehensive simulation studies and an empirical application
to inflammatory bowel disease, highlighting their potential to unravel the
complex relationships between the microbiome, metabolome, and disease.
