Bayesian Causal Mediation Analysis with Latent Mediators and Survival Outcome

ABSTRACT

This study develops a joint modeling approach that incorporates latent traits into causal mediation analysis with multiple mediators and a survival outcome. A linear structural equation model is used to characterize the latent mediators with several highly correlated observable surrogates and depicts the relationships among multiple parallel or causally ordered mediators and the exposure. A proportional hazards model is used to derive the path-specific causal effects on the scale of hazard ratio under the counterfactual framework with a set of sequential ignorability assumptions. A Bayesian approach with Markov chain Monte Carlo algorithm is developed to perform efficient estimation of the causal effects. Posterior propriety theory is established for the proportional hazards model with latent variables. Empirical performance of the proposed method is verified through simulation studies. The proposed model is then applied to a study on the Alzheimer’s Disease Neuroimaging Initiative dataset to investigate the causal effects of APOE-$\epsilon 4$ allele on the disease progression, either directly or through potential mediators, such as hippocampus atrophy, ventricle expansion, and cognitive impairment.

KEYWORDS:

• Bayesian method
• causal mediation
• latent variable
• posterior propriety
• survival outcome

Supplementary material

Supplemental data for this article can be accessed on the publisher’s website.

Additional information

Funding

This work was supported by the Research Grants Council, University Grants Committee [14301918, 14302519].