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Environmental health studies are increasingly measuring endogenous omics data($\boldsymbol{M}$) to study intermediary biological pathways by which anexogenous exposure ($\boldsymbol{A}$) affects a health outcome($\boldsymbol{Y}$), given confounders ($\boldsymbol{C}$). Mediation analysis isfrequently carried out to understand such mechanisms. If intermediary pathwaysare of interest, then there is likely literature establishing statistical andbiological significance of the total effect, defined as the effect of$\boldsymbol{A}$ on $\boldsymbol{Y}$ given $\boldsymbol{C}$. For mediationmodels with continuous outcomes and mediators, we show that leveraging externalsummary-level information on the total effect improves estimation efficiency ofthe natural direct and indirect effects. Moreover, the efficiency gain dependson the asymptotic partial $R^2$ between the outcome($\boldsymbol{Y}\mid\boldsymbol{M},\boldsymbol{A},\boldsymbol{C}$) and totaleffect ($\boldsymbol{Y}\mid\boldsymbol{A},\boldsymbol{C}$) models, with smaller(larger) values benefiting direct (indirect) effect estimation. We robustifyour estimation procedure to incongenial external information by assuming thetotal effect follows a random distribution. This framework allows shrinkagetowards the external information if the total effects in the internal andexternal populations agree. We illustrate our methodology using data from thePuerto Rico Testsite for Exploring Contamination Threats, where Cytochrome p450metabolites are hypothesized to mediate the effect of phthalate exposure ongestational age at delivery. External information on the total effect comesfrom a recently published pooled analysis of 16 studies. The proposed frameworkblends mediation analysis with emerging data integration techniques.

Mediation with External Summary Statistic Information (MESSI)