Mediation Analysis with a Survival Mediator: Dealing with the Missing Predictor Problem in the Y-Regression

Introduction: This study investigates a single mediator model where the mediator is a time-to-event variable with censored data. In prevention science, the mediator of interest can be a variable that measures duration of an event. For example, X can be a treatment indicator such as random assignment to a smoking cessation program or a control, M can be a timing variable such as the duration of tobacco non-use until relapse, and Y can be a continuous variable such as lung health measure by a spirometer. The single survival-mediator model consists of an M-regression which regresses the M variable on X (a parameter) and a Y-regression which regresses the Y variable on both X (c’ parameter) and M (b parameter) simultaneously. A Cox regression (Cox, 1972) can be used for the M-regression to adjust for the censoring data. Censoring occurs when information about survival time is missing. A normal OLS regression can be used for the Y-regression but b or c’ can have bias if M is censored. A solution is to treat the censored values as missing and use modern missing data techniques to model the Y-regression. If the missing mechanism is missing completely at random (MCAR), complete case analysis (i.e., listwise deletion) can be used to get unbiased estimates of b and c’. A more realistic missing data mechanism can be the missing at random (MAR) assumption. Full information maximum likelihood (FIML) estimation can be used to get unbiased estimates in the Y-regression assuming MAR.

Methods: A simulation investigated the single survival-mediator model. Type I error rate, statistical power, parameter coverage, raw and relative bias, and mean squared error were examined by using different methods of handling censoring data under different missing data mechanisms.

Results: Preliminary results show that the complete case analysis works well when the MCAR assumption is true. When the MAR assumption is true, the complete case analysis will produce biased estimates and in contrary, the FIML estimation would work well in terms of recovering the parameter values.

Conclusions: A remedy to the bias issue in the Y-regression of a single survival-mediator model is to treat censoring as missing in the M variable and apply modern missing data techniques. Researchers should think about the underlying missing data mechanism and apply appropriate missing data methods for the single survival-mediator model.