Mediation analysis with a survival mediator: a simulation study of different indirect effect testing methods

Time-to-event analysis or equivalently, survival analysis deals with two variables simultaneously: when (time information) an event occurs and whether an event occurrence is observed or not during the observation period (censoring information). In behavioral and social sciences, the event of interest usually does not lead to a terminal state such as death. Other outcomes after the event can be collected and thus, the survival variable can be considered as a predictor as well as an outcome in a study. One example of a case where the survival variable serves as a predictor as well as an outcome is a survival-mediator model. In a single survival-mediator model an independent variable, X predicts a survival variable, M which in turn, predicts a continuous outcome, Y. The survival-mediator model consists of two regression equations: X predicting M (M-regression), and M and X simultaneously predicting Y (Y-regression). To estimate the regression coefficients of the survival-mediator model, Cox regression is used for the M-regression. Ordinary least squares regression is used for the Y-regression using complete case analysis assuming censored data in M are missing completely at random so that the Y-regression is unbiased. In this dissertation research, different measures for the indirect effect were proposed and a simulation study was conducted to compare performance of different indirect effect test methods. Bias-corrected bootstrapping produced high Type I error rates as well as low parameter coverage rates in some conditions. In contrast, the Sobel test produced low Type I error rates as well as high parameter coverage rates in some conditions. The bootstrap of the natural indirect effect produced low Type I error and low statistical power when the censoring proportion was non-zero. Percentile bootstrapping, distribution of the product and the joint-significance test showed best performance. Statistical analysis of the survival-mediator model is discussed. Two indirect effect measures, the ab-product and the natural indirect effect are compared and discussed. Limitations and future directions of the simulation study are discussed. Last, interpretation of the survival-mediator model for a made-up empirical data set is provided to clarify the meaning of the quantities in the survival-mediator model.