## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 7, Number 4 (2013), 2336-2360.

### Exploiting multiple outcomes in Bayesian principal stratification analysis with application to the evaluation of a job training program

Alessandra Mattei, Fan Li, and Fabrizia Mealli

#### Abstract

The causal effect 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 effect 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.

#### Article information

**Source**

Ann. Appl. Stat., Volume 7, Number 4 (2013), 2336-2360.

**Dates**

First available in Project Euclid: 23 December 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1387823322

**Digital Object Identifier**

doi:10.1214/13-AOAS674

**Mathematical Reviews number (MathSciNet)**

MR3161725

**Zentralblatt MATH identifier**

1283.62054

**Keywords**

Bayesian causal inference intermediate variables job training program mixture multivariate outcomes noncompliance principal stratification

#### Citation

Mattei, Alessandra; Li, Fan; Mealli, Fabrizia. Exploiting multiple outcomes in Bayesian principal stratification analysis with application to the evaluation of a job training program. Ann. Appl. Stat. 7 (2013), no. 4, 2336--2360. doi:10.1214/13-AOAS674. https://projecteuclid.org/euclid.aoas/1387823322

#### Supplemental materials

- Supplementary material: Supplement to “Exploiting multiple outcomes in Bayesian principal stratification analysis with application to the evaluation of a job training program.”. Supplement A: Details of calculation. We describe in detail the Markov Chain Monte Carlo (MCMC) methods used to simulate the posterior distributions of the parameters of the models introduced in Section 5 in the main text. Supplement B: Posterior inference conditional on pretreatment variables. We describe details of calculation and results under the alternative models conditioning on the pretreatment variables. Supplement C: Additional simulation results. We present additional simulations aimed at investigating the role of the partial exclusion restriction assumption and assessing the repeated sampling properties of the proposed approach.Digital Object Identifier: doi:10.1214/13-AOAS674SUPP