Criteria for Stable Unconfoundedness with Descendants

For a causal interpretation of an observed association between an ordered pair of variables (X,Y) one has to assure that the association is not generated by a set of other variables T that influence both, X and Y. The term confounding is used to describe the phenomenon when an association is possibly due to other factors. In the framework of graphical modeling, Pearl (1998a) introduced the term of stable unconfoundedness. Kischka and Eherler (1999) generalized this definition. This concept of unconfoundedness can be charaterized in graphical terms. The graphical charaterization is the starting point to introduce operational criteria that rule out or confirm stable unconfoundedness based on weak structutral, i.e. graphical assumptions. One key assumption is to find nondescendants of the treatment variable X with specific properties. In this paper we suggest, how operational criteria can be derived using descendants of the treatment variable.