  Observational longitudinal data on treatments and covariates are increasingly
used to investigate treatment effects, but are often subject to time-dependent
confounding. Marginal structural models (MSMs), estimated using inverse
probability of treatment weighting or the g-formula, are popular for handling
this problem. With increasing development of advanced causal inference methods,
it is important to be able to assess their performance in different scenarios
to guide their application. Simulation studies are a key tool for this, but
their use to evaluate causal inference methods has been limited. This paper
focuses on the use of simulations for evaluations involving MSMs in studies
with a time-to-event outcome. In a simulation, it is important to be able to
generate the data in such a way that the correct form of any models to be
fitted to those data is known. However, this is not straightforward in the
longitudinal setting because it is natural for data to be generated in a
sequential conditional manner, whereas MSMs involve fitting marginal rather
than conditional hazard models. We provide general results that enable the form
of the correctly-specified MSM to be derived based on a conditional data
generating procedure, and show how the results can be applied when the
conditional hazard model is an Aalen additive hazard or Cox model. Using
conditional additive hazard models is advantageous because they imply additive
MSMs that can be fitted using standard software. We describe and illustrate a
simulation algorithm. Our results will help researchers to effectively evaluate
causal inference methods via simulation.
