Indirect Effects Via the Timing of an Event: An Application of Dual-Process Discrete-Time Survival Analysis

Dual-process models have been advanced in methodological research on continuous variables, including the well-established (if flawed) autoregressive cross-lagged model and dual latent growth models. The current work extends the literature on dual-process models for discrete data – specifically, discrete-time survival models – by exploring the use of a survival process as a mediator. The Dual-Process Discrete-Time Survival Analysis (DPDTSA) model is a highly constrained implementation of associative latent transition analysis that models associations between two time-to-event outcomes. This paper examines and demonstrates the applicability of both product-of-coefficients and counterfactual approaches to testing indirect effects to the DPDTSA model.

In the current study, we look specifically at initiation of alcohol and cigarette use (collectively, ATU) as a predictor of secondary-school dropout and vice versa, using data from the National Longitudinal Study of Youth 1997. The former realtion has been clearly demonstrated, while initiation of ATU after dropout is relatively unstudied. Our hypothesized exogenous predictor, parental monitoring, has been shown to be a significant predictor of both dropout and of ATU.

The DPDTSA approach allows for two possible indirect paths: poor parental monitoring may predict earlier and more probable dropout by way of its prediction of earlier initiation of substance use or poor monitoring may predict earlier initiation of substance use preceded by earlier dropout. Our results using a product-of-coefficients method showed no indirect effect on ATU via dropout by either paternal monitoring or maternal monitoring. Effects of monitoring on dropout via earlier substance use initiation, however, indicated indirect effects of maternal monitoring and of paternal and maternal monitoring taken together. The extension of methods for estimating natural indirect effects from a counterfactual framework to the discrete-time survival analysis approach is less intuitive, and is discussed.