Estimating and Testing Causal Mediation Effects in Single-Case Experimental Designs Using State-Space Modeling

In this article, we present single-case causal mediation analysis as the application of causal mediation analysis to data collected within a single-case experiment. This method combines the focus on the individual with the focus on mechanisms of change, rendering it a promising approach for both mediation and single-case researchers. For this purpose, we propose a new method based on time-discrete state-space modeling to estimate the direct and indirect treatment effects. We demonstrate how to estimate the model for a single-case experiment on stress and craving in a routine alcohol consumer before and after an imposed period of abstinence. Furthermore, we present a simulation study that examines the estimation and testing of the standardized indirect effect. All parameters used to generate the data were recovered with acceptable precision. We use maximum likelihood and permutation procedures to calculate p-values and standard errors of the parameters estimates. The new method is promising for testing mediated effects in single-case experimental designs. We further discuss limitations of the new method with respect to causal inference, as well as more technical concerns, such as the choice of the time lags between the measurements.