2.5.5. Hierarchical modelling analysis of FA values and EMA variables

To assess a potential indirect relation between white matter integrity and substance use in the SUD group, we conducted generalized linear mixed‐effects models (for binomial outcomes) using the lmer4 packages available on R. ⁴¹

EMA enables the assessment of target variables repeatedly and intensively in real time, resulting in numerous successive observations of a variable at different time points t. We modelled a time lag in our raw EMA measures to predict substance use at time t + 1 from momentary Stroop performance and substance use at time t. In other words, each observation of the Stroop performance at the given time predicted substance use at the following assessment time, and this prediction was repeated for every successive time point (Time 1 predicts Time 2 that predicts Time 3, …). To avoid contamination of night‐time effects, this time lag excluded all predictions of the first assessment of a new day by the last assessment of the previous days.

We entered Stroop performance at time t into our model centred around the subject's own mean for the week as a first‐level predictor of substance use at t + 1 while controlling for previous use at time t. We then entered the interaction between FA values in the significant clusters from the whole brain analysis and each time point assessment of Stroop (FA values * Stroop time t) as a predictor of subsequent use at time t + 1 while controlling for previous use at time t, age, sex, primary substance type and addiction severity as control variables. This iterative interaction model (FA values * Stroop) is equivalent to moderation testing where white matter FA values could modify the relation between Stroop and subsequent use. To ensure that the moderation effect was specific to the Stroop, we tested for a potential interaction between FA values and craving at time t (FA values * craving time t). In each model, control and independent variables were entered as fixed effects, and random effects on the first‐level slope equations were added. First‐level continuous predictors were centred around the participant's own level, and second‐level continuous predictors were centred around the group mean. Dichotomous predictors at each level were entered uncentred. Missing data at the first level were discarded from the analyses. All analyses were considered significant at p < 0.05 uncorrected. Illustrations of the procedure, from the raw data to the mixed model, are presented in Figure 1.

Mixed model procedure from the raw data. Legend: During a typical day of EMA assessment, participants had to report if they used anysubstance and their primary substance (for the SUD sample) 5 times and had to complete theStroop mobile testing twice. The week of assessment hence results in 35‐time point assessmentsof substance use and 14 assessments of inhibition functioning that can be lagged in time topredict the next time point's assessments (Time t+1) from the immediately preceding time pointassessments (Time t). By treating each time point as a repetition, we modeled the prediction offuture use (at time t+1) by the current Stroop performance (at time t) while controlling fromprevious use (at time t). FA values within each cluster were then entered as a moderator of theStroop / use link. To do so the Stroop scores at each time point is multiplied by FA values ofeach cluster, resulting in an interaction term FA value * Stroop for each time t. This interactionterm is entered as predictor of subsequent use (at time t +1) while correcting for previous use(at time t). This is similar to a moderation analysis where FA values (indicated by the red arrow)modified the strength of the prediction between inhibition and use (indicated by the blackarrow).