  The use of observational time series data to assess the impact of multi-time
point interventions is becoming increasingly common as more health and activity
data are collected and digitized via wearables, social media, and electronic
health records. Such time series may involve hundreds or thousands of
irregularly sampled observations. One common analysis approach is to simplify
such time series by first discretizing them into sequences before applying a
discrete-time estimation method that adjusts for time-dependent confounding. In
certain settings, this discretization results in sequences with many time
points; however, the empirical properties of longitudinal causal estimators
have not been systematically compared on long sequences. We compare three
representative longitudinal causal estimation methods on simulated and real
clinical data. Our simulations and analyses assume a Markov structure and that
longitudinal treatments/exposures are binary-valued and have at most a single
jump point. We identify sources of bias that arise from temporally discretizing
the data and provide practical guidance for discretizing data and choosing
between methods when working with long sequences. Additionally, we compare
these estimators on real electronic health record data, evaluating the impact
of early treatment for patients with a life-threatening complication of
infection called sepsis.
