Exploiting multiple outcomes in Bayesian principal stratification analysis with application to the evaluation of a job training program. (English) Zbl 1283.62054

Mattei, Alessandra; Li, Fan; Mealli, Fabrizia

Ann. Appl. Stat. 7, No. 4, 2336-2360 (2013).

Summary: The causal effects of a randomized job training program, the JOBS II study, on trainees’ depression is evaluated. Principal stratification is used to deal with noncompliance to the assigned treatment. Due to the latent nature of the principal strata, strong structural assumptions are often invoked to identify principal causal effects. Alternatively, distributional assumptions may be invoked using a model-based approach. These often lead to weakly identified models with substantial regions of flatness in the posterior distribution of the causal effects. Information on multiple outcomes is routinely collected in practice, but is rarely used to improve inference.
This article develops a Bayesian approach to exploit multivariate outcomes to sharpen inferences in weakly identified principal stratification models. We show that inference for the causal effects on depression is significantly improved by using the re-employment status as a secondary outcome in the JOBS II study. Simulation studies are also performed to illustrate the potential gains in the estimation of principal causal effects from jointly modeling more than one outcome. This approach can also be used to assess plausibility of structural assumptions and sensitivity to deviations from these structural assumptions. Two model checking procedures via posterior predictive checks are also discussed.

MSC:

62F15	Bayesian inference
62P25	Applications of statistics to social sciences
62H25	Factor analysis and principal components; correspondence analysis
62H12	Estimation in multivariate analysis
65C60	Computational problems in statistics (MSC2010)

Keywords:

causal inference; intermediate variables; mixtures; multivariate outcomes; non-compliance

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