Statistical issues in survival analysis (Causal mediation additive hazards)
February 12, 2025 The authors focused on causal mediation analysis in survival analysis, more specifically with additive hazards modeling with an exposure by mediator interaction term. The causal mediation framework had come about over time from the mediation area and then was also proposed for survival analysis where one of the first was by Lange and Hansen (2011). They suggested measuring the natural direct and indirect effects based on the hazard difference scale. Their estimation method worked under the Aalen additive hazards model, which they said had advantages over the Cox model in both causal interpretation and mathematical consistency. Since then, many other authors proposed methods in this area, but so far, none of the studies considered an exposure-mediator interaction effect when the additive hazards model was used. The authors extended work from Vansteelandt et al (2019) and Aalen et al (2020) to accommodate this interaction under additive hazards modeling. Mediation analysis has also been shown in other survival models. VandereWeele (2011) presented identification results for causal survival effect under the Cox model and the accelerate failure time model, where his work even allowed for an exposure-mediator interaction on the survival outcome. Ongoing work has been conducted and there has even been work on survival analysis with multiple mediators by multiple authors. One issue is that the prior research in this area typically assumed that the mediator and confounders were precisely measured. It has been well known that measurement error can distort statistical inference. Though methods have been proposed to handle measurement error in survival analysis, some progress has been made in causal mediation by several other authors including VanderWeele (2015). An adjustment method by Cessie et al (2012) and VanderWeele, Valeri, and Ogburn (2012) was developed solely for the linear and logistic models but could not eliminate bias in the setup by Aalen. The authors have compared this method to their proposed method for measurement error correction. In their setup they make an assumption that there is not unmeasured confounding of the various relationship between mediator and exposure or outcome. They showed their formulas for direct and indirect effects estimation with the incorporation of the exposure by meditator interaction. For their measurement error correction, they allowed covariate effects to be piecewise constant. They then re-estimated the direct and indirect effects with their corrections. They also showed adjusted for measurement error in the mediator and the confounder as well. They also proposed a measurement error correction method for the parameter estimation under the additive hazards