A novel quantile-based decomposition of the indirect effect in mediation analysis with an application to infant mortality in the US population

In mediation analysis, the effect of an exposure (or treatment) on an outcome variable is decomposed into two components: a direct effect, which pertains to an immediate influence of the exposure on the outcome, and an indirect effect, which the exposure exerts on the outcome through a third variable called mediator. Our motivating example concerns the relationship between maternal smoking (the exposure, $X$), birthweight (the mediator, $M$), and infant mortality (the outcome, $Y$), which has attracted the interest of epidemiologists and statisticians for many years. We introduce new causal estimands, named $u$-specific direct and indirect effects, which describe the direct and indirect effects of the exposure on the outcome at a specific quantile $u$ of the mediator, $0 < u < 1$. Under sequential ignorability we derive an interesting and novel decomposition of $u$-specific indirect effects. The components of this decomposition have a straightforward interpretation and can provide new insights into the complexity of the mechanisms underlying the indirect effect. We illustrate the proposed methods using data on infant mortality in the US population. We provide analytical evidence that supports the hypothesis that the risk of sudden infant death syndrome is not predicted by changes in the birthweight distribution.