  In medical and epidemiological studies, one of the most common settings is
studying the effect of a treatment on a time-to-event outcome, where the
time-to-event might be censored before end of study. A common parameter of
interest in such a setting is the marginal hazard ratio (MHR). When a study is
based on observational data, propensity score (PS) based methods are often
used, in an attempt to make the treatment groups comparable despite having a
non-randomized treatment. Previous studies have shown censoring to be a factor
that induces bias when using PS based estimators. In this paper we study the
magnitude of the bias under different rates of non-informative censoring when
estimating MHR using PS weighting or PS matching. A bias correction involving
the probability of event is suggested and compared to conventional PS based
methods.
