Causal Mediation Analysis for Sparse and Irregular Longitudinal Data
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Causal mediation analysis aims to investigate how the treatment effect of an exposure on outcomes is mediated through intermediate variables. Although many applications involve longitudinal data, the existing methods are not directly applicable to the settings where the mediator and outcome are measured on sparse and irregular time grids. We extend the existing causal mediation framework from a functional data analysis perspective, viewing the sparse and irregular longitudinal data as realizations of underlying smooth stochastic processes. We define causal estimands of direct and indirect effects accordingly and provide corresponding identification assumptions. For estimation and inference, we employ a functional principal component analysis approach for dimension reduction and use the first few functional principal components instead of the whole trajectories in the structural equation models. We adopt the Bayesian paradigm to accurately quantify the uncertainties. The operating characteristics of the proposed methods are examined via simulations. We apply the proposed methods to a longitudinal data set from a wild baboon population in Kenya to estimate the causal effects between early adversity, the strength of social bonds, and adult glucocorticoid hormone concentrations. We find that early adversity has a significant direct effect (a 9-14 females' glucocorticoid concentrations across adulthood, but find little evidence that these effects were mediated by weak social bonds.
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