Bayesian Inference for Sequential Treatments under Latent Sequential Ignorability

Abstract: 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.