In epidemiologic and social science studies, researchers are often interested in understanding the causal effect from an exposure variable to an outcome variable. In this thesis, we develop two different models and methods to conduct causal inference: (1). causal mediation analysis under the additive hazards model with exposure-mediator interaction; (2). marginal structural additive hazards model. The existing literature requires accurate measurements of the mediator and the confounders, which could be infeasible in biomedical studies. Furthermore, the current identification results of causal effects under the additive hazards model do not allow for exposure-mediator interaction. In this thesis, we derive identification results of causal effects under the additive hazards model with exposure-mediator interaction. Furthermore, we propose consistent measurement error correction methods in the absence/presence of exposure-mediator interaction. In the second part of the thesis, we propose a marginal structural additive hazards model. We develop an estimation method for the marginal structural additive hazards model and apply the simulation-extrapolation (SIMEX) method to correct for the bias resulting from measurement error.