  The human microbiome can contribute to pathogeneses of many complex diseases
by mediating disease-leading causal pathways. However, standard mediation
analysis methods are not adequate to analyze the microbiome as a mediator due
to the excessive number of zero-valued sequencing reads in the data that is
compounded by its compositional structure. The two main challenges raised by
the zero-inflated data structure are: (a) disentangling the mediation effect
induced by the point mass at zero; and (b) identifying the observed zero-valued
data points that are actually not zero (i.e., false zeros). We develop a novel
marginal mediation analysis method under the potential-outcomes framework to
fill this gap and show the marginal model can also account for the
compositional structure. The mediation effect can be decomposed into two
components that are inherent to the two-part nature of zero-inflated
distributions. With probabilistic models to account for observing zeros, we
also address the challenge with false zeros. A comprehensive simulation study
and the application in a real microbiome study showcase our approach in
comparison with existing approaches.
