  Hazard ratios are frequently reported in time-to-event and epidemiological
studies to assess treatment effects. In observational studies, the combination
of propensity score weights with the Cox proportional hazards model facilitates
the estimation of the marginal hazard ratio (MHR). The methods for estimating
MHR are analogous to those employed for estimating common causal parameters,
such as the average treatment effect. However, MHR estimation in the context of
high-dimensional data remain unexplored. This paper seeks to address this gap
through a simulation study that consider variable selection methods from causal
inference combined with a recently proposed multiply robust approach for MHR
estimation. Additionally, a case study utilizing stroke register data is
conducted to demonstrate the application of these methods. The results from the
simulation study indicate that the double selection covariate selection method
is preferable to several other strategies when estimating MHR. Nevertheless,
the estimation can be further improved by employing the multiply robust
approach to the set of propensity score models obtained during the double
selection process.
