  Transported mediation effects provide an avenue to understand how upstream
interventions (such as improved neighborhood conditions like green spaces)
would work differently when applied to different populations as a result of
factors that mediate the effects. However, when mediators are missing in the
population where the effect is to be transported, these estimates could be
biased. We study this issue of missing mediators, motivated by challenges in
public health, wherein mediators can be missing, not at random. We propose a
sensitivity analysis framework that quantifies the impact of missing mediator
data on transported mediation effects. This framework enables us to identify
the settings under which the conditional transported mediation effect is
rendered insignificant for the subgroup with missing mediator data.
Specifically, we provide the bounds on the transported mediation effect as a
function of missingness. We then apply the framework to longitudinal data from
the Moving to Opportunity Study, a large-scale housing voucher experiment, to
quantify the effect of missing mediators on transport effect estimates of
voucher receipt, an upstream intervention on living location, in childhood on
subsequent risk of mental health or substance use disorder mediated through
parental health across sites. Our findings provide a tangible understanding of
how much missing data can be withstood for unbiased effect estimates.
