Natural Indirect Effects in Survival Mediation Analysis

1^ST PAPER WITHIN ORGANIZED POSTER FORUM

ABSTRACT BODY: Survival (time-to-event) data are inherent in direct observational data and longitudinal studies in prevention science. The event of interest can be a state change (e.g., end of coercive interactions between parent and child), a return to a specific state (e.g., recidivism, substance use relapse), or a first experience (e.g., first tobacco use in life). Prevention scientists might want to prolong or shorten the time-to-event as a final outcome of their intervention or as a mediator, which in turn changes the final outcome of interest. This study focuses on the latter case and examines a mediation model where the mediator is a survival variable. For example, after a smoking cessation program, the time to relapse tobacco use can be studied followed by the effect of the relapse time on later health issues.

A survival mediation model is introduced where a Cox regression model is used for the X (binary predictor) → M (survival mediator) relationship (a-path) and a normal OLS regression with complete data assuming MCAR is used for the M (survival mediator) → Y (continuous outcome) relationship (b-path). In this model, the product of two coefficients, a*b does not properly quantify the indirect effect. This is because the survival mediator is used differently between the X → M regression and the M → Y regression. In the former regression, a one unit increase in X predicts a-increase in the log hazard function and in the latter regression, a one unit increase in continuous time predicts b-increase in the continuous outcome. The disagreement between using the survival variable as an outcome and a predictor causes difficulty in interpreting the a*b indirect effect. A better way to understand the indirect effect of a survival mediation model is through causal mediation. Using the potential outcomes approach, a general case where an exposure-mediation interaction and covariates are included in the model is discussed and the natural indirect effect is derived for this model.

As an illustrative example, a simulated dataset in context of prevention research is studied. In conclusion, the estimated natural indirect effect is in the unit of the outcome and can be interpreted with substantial meanings. The corresponding a-coefficient in the natural indirect effect is the average time difference between two values of X (e.g., X=0=control and X=1=treatment). The actual estimate of this value can be realized by the difference between the integrals of the conditional survival functions which can be obtained by numerical integration methods.