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Abstract:
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Many variables of epidemiological, medical, and social interest are trajectories that may be regarded as continuous-time “functional data”, e.g. body mass index (BMI), treatment doses, and socioeconomic status. To study the causal effect of an exposure on an outcome with observational data, where the exposure, outcome, and confounders are all trajectories, established causal inference methods (the G-formula and marginal structural models) rely on the user to specify a temporal discretization of the subject timeline. In this work, we define causal estimands based on functional trajectory data using Potential Outcomes, and provide a novel causal identification framework that allows feedback between exposures and outcomes/covariates, and enables researchers to circumvent the choice of discretization scales.
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