An Empirical Illustration of Discrete-Time Survival Mediation Analysis: A New Tool to Assess the How and When of Event Occurrence

New research has demonstrated an approach to test mediation effects with discrete time survival outcomes, permitting evaluation of mediating mechanisms of event occurrence.  To help substantive researchers successfully apply the new method, this presentation illustrates the discrete time survival mediation (DTSM) model in a fully worked empirical example. We demonstrate how to carry out the analysis in Mplus under the finite mixture model approach and work through interpretation of model parameters.  Our data example includes 750 children (52% male, 95% African American) with annual assessments from kindergarten through grade eight for the child, primary caregiver, and teacher.  We chose to focus on smoking onset prior to high school because early-onset substance involvement is associated with heightened risk for adverse social, psychological, and behavioral outcomes including later accelerated substance use itself.  In particular, tobacco use is the primary cause of preventable deaths in the United States each year and is a critical public health problem.  Here we examine how the predictor of parental stress in kindergarten affects smoking onset measured at grades five through eight via the mediator of child externalizing behavior in grade four.  In addition to illustrating the specification of a general DTSM model, our data example provides the opportunity to demonstrate how to estimate the model with missing data on the predictors.  Results indicate that there was a significant mediated effect (ab=.083, p<.05) of parenting stress on smoking onset through child externalizing behavior.  Interpretation of the estimate indicated that the mediated effect corresponded to a 0.083 unit decrease in the log-odds of latent propensity for smoking onset.  In other words, for every one-unit increase in the mediated effect the odds of the latent propensity to experience substance use increased 8.7%.  Plotting the hazard function of observed hazard probability estimates for smoking onset in the sample shows us that the risk of experiencing smoking onset does not have a clear pattern over time.  Unlike conventional logistic regression which only allows us to model the occurrence (or not) of an event, the DTSM allows us to model the timing of event occurrence in discrete intervals which is often how longitudinal data are collected. This empirical example can serve as a guide for substantive researchers to apply a DTSM model in their own data and answer questions of how an event occurs and when.