Association chain graphs: modelling etiological pathways.

Multiple time-dynamic and interrelated risk factors are usually involved in the complex etiology of disorders. This paper presents a strategy to explore and display visually the relative importance of different association pathways for the onset of disorder over time. The approach is based on graphical chain models, a tool that is powerful but still under-utilized in most fields. Usually, the results of these models are displayed using directed acyclic graphs (DAGs). These draw an edge between a pair of variables whenever the assumption of conditional independence given variables on an earlier or equal temporal footing is violated to a statistically significant extent. In the present paper, the graphs are modified in that confidence intervals for the strengths of associations (statistical main effects) are visualized. These new graphs are called association chain graphs (ACGs). Statistical interactions cause 'edges' between the respective variables within the DAG framework (because the assumption of conditional independence is violated). In contrast they are represented as separate graphs within the subsample where the different association chains may work within the ACG framework. With this new type of graph, more specific information can be displayed whenever the data are essentially described only with statistical main- and two-way interaction effects.