Indirect Comparison of Interaction Graphs

Astrategy for testing differential conditional independence structures (CIS) between two graphs is introduced. The graphs have the same set of nodes and are estimated from data sampled under two different conditions. The test uses the entire pathplot in a Lasso regression as the information on how a node connects with the remaining nodes in the graph. The interpretation of the paths as random processes allows defining stopping times which make the statistical properties of the test statistic accessible to analytic reasoning. A resampling approach is proposed to calculated p-values simultaneously for a hierarchical testing procedure. The hierarchical testing steps through a given hierarchy of clusters. First, collective effects are measured at the coarsest level possible (the global null hypothesis that no node in the graph shows a differential CIS). If the global null hypothesis can be rejected, finer resolution levels are tested for an effect until the level of individual nodes is reached. The strategy is applied to association patterns of categories from the ICF in patients under post-acute rehabilitation. The patients are characterized by two different conditions. Acomprehensive understanding of differences in the conditional independence structures between the patient groups is pivotal for evidence-based intervention design on the policy, the service and the clinical level related to their treatment. Due to extensive computation, parallel computing offers an effective approach to implement our explorative tool and to locate nodes in a graph which show differential CIS between two conditions.