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.

Keywords:

• Longitudinal treatments
• Principal stratification
• Rubin causal model
• Sequential ignorablity

Supplementary Materials

Supplementary materials available online contain further details on MCMC and Data Augmentation algorithms, as well as the true parameters’ values used in the simulation analyses. Furthermore we give results obtained using Marginal Structural models and we investigate sensitivity of the results with respect to prior distribution specification.

Notes

1 Note

We also conducted our Bayesian analyses conditioning on covariates. Results change only slightly; the presence of covariates mainly affects the posterior variability of the causal estimands, introducing noise. Therefore, we preferred to focus on results derived without conditioning on covariates, also in line with our simulation study.

Additional information

Funding

Financial support for this research was provided through the grant “Programma Futuro in Ricerca 2012—RBFR12SHVV_003,” financed by the Italian Ministero dell’Istruzione, dell’Università e della Ricerca.