SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

Visualizing etiological pathways with association chain graphs

Michael Höfler
Max-Planck-Institut für Psychiatrie

The etiology of most physical diseases and mental disorder is quite complex and usually there are a vast number of time-dynamic and inter-related risk factors involved. Previously, the results for such etiological pathways were typically visualized with directed acyclic graphs (DAGs). DAGs 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, otherwise not. In a recent paper (Höfler et al., 2003), a new type of graphs has been proposed that provides a richer visualization, so-called association chain graphs (ACGs).

The basic idea of ACGs is to display the degree of association as the contrast to the background colour of the graph. ACGs display confidence intervals for statistical main effects, i.e., the degrees of association that are compatible with the data. Whereas statistical interactions cause edges between the resp. pairs of variables within the DAG framework (because conditional independence between the respective pairs of variables is violated then), interactions can be visualized by separate graphs in subsamples among the ACG framework.

In this paper, ACGs are discussed and extended in the case where all the variables are binary by illustrating also the confidence intervals for the relative frequencies of risk factors and outcome. This also allows to visually assess the magnitude of associations on the public health level. The approach is applied on an example about risk factors for incident depression using data from the EDSP (Early Developmental Stages of Psychopathology) study. Clearly, ACGs are not restricted to be used for medical research and might prove beneficial in other fields like social sciences or economy as well.


Höfler M., Wittchen H.U, Lieb R., Hoyer J., Friis R.H. (2003) Association chain graphs: modelling etiological pathways. International Journal of Methods in Psychiatric Research 12, 77-84