  We focus on causal inference for longitudinal treatments, where units are
assigned to treatments at multiple time points, aiming to assess the effect of
different treatment sequences on an outcome observed at a final point. A common
assumption in similar studies is Sequential Ignorability (SI): treatment
assignment at each time point is assumed independent of future potential
outcomes given past observed outcomes and covariates. SI is questionable when
treatment participation depends on individual choices, and treatment assignment
may depend on unobservable quantities associated with future outcomes. We rely
on Principal Stratification to formulate a relaxed version of SI: Latent
Sequential Ignorability (LSI) assumes that treatment assignment is
conditionally independent on future potential outcomes given past treatments,
covariates and principal stratum membership, a latent variable defined by the
joint value of observed and missing intermediate outcomes. We evaluate SI and
LSI, using theoretical arguments and simulation studies to investigate the
performance of the two assumptions when one holds and inference is conducted
under both. Simulations show that when SI does not hold, inference performed
under SI leads to misleading conclusions. Conversely, LSI generally leads to
correct posterior distributions, irrespective of which assumption holds.
