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 proposed estimator and investigate its small sample properties by Monte Carlo simulation. A real data example is provided for illustration.
Keywords: Aalen additive model; Counterfactuals; Survival analysis
Biography: Stijn is Associate Professor in Statistics in the Department of Applied Mathematics and Computer Science at Ghent University. His main research areas are Causal Inference from observational data, and statistical methods for handling of missing data. A characteristic feature of his research is the use of semi-parametric models.