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Estimation of direct effects for survival data by using the Aalen additive hazards model

Summary.  We extend the definition of the controlled direct effect of a point exposure on a survival outcome, other than through some given, time‐fixed intermediate variable, to the additive hazard scale. We propose two‐stage estimators for this effect when the exposure is dichotomous and randomly assigned and when the association between the intermediate variable and the survival outcome is confounded only by measured factors, which may themselves be affected by the exposure. The first stage of the estimation procedure involves assessing the effect of the intermediate variable on the survival outcome via Aalen's additive regression for the event time, given exposure, intermediate variable and confounders. The second stage involves applying Aalen's additive model, given the exposure alone, to a modified stochastic process (i.e. a modification of the observed counting process based on the first‐stage estimates). We give the large sample properties of the estimator proposed and investigate its small sample properties by Monte Carlo simulation. A real data example is provided for illustration.