Causal Mediation Analysis With Latent Subgroups for Survival Model

Causal mediation analysis is an effective method for understanding the mechanism between the exposure and the outcome, often assuming that the mediation model is consistent for each individual in the target population. In practice, however, the natural indirect effect (NIE) may vary across individuals due to their distinct characteristics. As a result, the population can be partitioned into subgroups according to the varying sizes of the NIEs. Distinguishing subgroups within the study population enables the development of more precise and targeted treatment strategies. In this paper, we propose an identifiable mixture mediation model with latent subgroups for the survival data, where the outcome follows an accelerated failure time model and the mediator is Gaussian distributed. We further employ three information criteria including the AIC, BIC, and singular BIC (sBIC) to select the number of subgroups, followed by the expectation–maximization (EM) algorithm to estimate the model parameters and NIEs. Simulation study shows that the sBIC is the most robust and efficient criterion for selecting the number of subgroups; therefore, we recommend the sBIC-EM algorithm for practical use. Lastly, we apply our algorithm to the lung cancer data and discover two latent groups with opposing NIEs.