  Marginal structural models (MSMs) allow for causal analysis of longitudinal
data. The MSMs were originally developed as discrete time models. Recently,
continuous-time MSMs were presented as a conceptually appealing alternative for
survival analysis. In applied analyses, it is often assumed that the
theoretical treatment weights are known, but these weights are usually unknown
and must be estimated from the data. Here we provide a sufficient condition for
a class of continuous-time MSMs 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 the continuous-time weights perform better
than IPTW when the underlying treatment process is continuous. Furthermore, we
may wish to transform effect estimates of hazards to other scales that are
easier to interpret causally. We show that a general transformation strategy
can be used on weighted cumulative hazard estimates to obtain a range of other
parameters in survival analysis, and demonstrate how this strategy can be
applied on data using our R packages ahw and transform.hazards.
