Dealing With Autocorrelation in the Single Case AB-Design: A Study Assessing the Mediating Effect of Infant Crying on the Relation Between Responsive Soothing and Infant Sleep

Abstract

Mediation analysis is widely adopted by researchers to disentangle the causal pathways by which an intervention affects an outcome. This paper describes a model to estimate the direct and indirect effect from a single subject AB-design with repeated assessments of both the mediator and the outcome. We discuss the plausibility of the modeling assumptions and contrast different approaches to deal with the autocorrelation in the time series data. While there are only small differences between those approaches when the number of timepoints is small (T = 15), the Generalized Least Squares approach performs best in medium (T = 30) to large (T = 90) time series. We apply the proposed methodology to data from a single case AB-design that was conducted with a mother of an excessively crying baby. Daily crying and baby sleep during the night were assessed with online diaries during a baseline phase and intervention phase. Between both phases, the pediatrician instructed the mother how to apply a responsive soothing intervention, the happiest baby (THB) method. We find that the direct effect of THB on sleeping is positive. THB also reduces crying but decreased crying during the day is associated with decreased sleeping during the night and hence a negative indirect effect of THB on sleeping via crying is found.