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Abstract:
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While causal mediation analysis has seen considerable recent development for a single measured mediator (M) and final outcome (Y), less attention has been given to repeatedly measured M and Y. Previously offered structural equation model (SEM) approaches limit inference to the particular measurement times used, and do not recognize the continuous nature of the mediation process over time. To overcome such limitations, we present a new continuous time causal mediation approach that uses differential equations, in a potential outcomes framework, to describe the dynamic causal relationships among model variables over time. A connection between the differential equations models and standard repeated measures models allows for model fitting to the data. Assuming an extension of sequential ignorability, we provide an approach to inference for extended 'natural' direct and indirect effects, as well as predicted effects of new interventions. The new methodology is applied to a cohort study of dental caries in children.
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