The additive hazard estimator is consistent for continuous time marginal structural models
share
Marginal structural models (MSMs) allow for causal interpretations of longitudinal data. The standard MSM is based on discrete time models, but the continuous time MSM is a conceptually appealing alternative for survival analysis. In particular, the additive hazard model allows for flexible estimation of treatment weights in continuous time MSMs. In applied analyses, it is often assumed that the theoretical treatment weights are known, but usually these weights are fundamentally unknown and must be estimated from the data. Here we provide a sufficient condition for continuous time MSM to be consistent even when the weights are estimated, and we show how additive hazard models can be used to estimate such weights. Our results suggest that continuous time weights perform better than discrete weights when the underlying process is continuous. Furthermore, we may wish to transform effect estimates of hazards to other scales that are easier to interpret causally, and here we show that a general transformation strategy also can be used on weighted cumulative hazard estimates. Finally we explain how this strategy can be applied on data using our R-package ahw.
READ FULL TEXT