Effects of an unobserved confounder on a system with an intermediate outcome

Abstract

In der Theorie graphischer Markov Modelle, in denen Beziehungen zwischen vielen Variablen über konditionale Interdependenzen vereinfacht werden, spielen azyklische Graphen eine spezielle Rolle. Sie können dazu benutzt werden, um statistische Modelle zu representieren, in denen Daten schrittweise generiert werden. Responses und intermediäre Variablen können event histories sein . Wir diskutieren ein derartiges System mit sequentieller Behandlung und einem Confounder, das ist eine Variable mit Auswirkungen auf den endgültigen Output und eine der erklärenden Vaiablen. Es werden Verfahren aufgezeigt, wie mit diesem Problem umgegangen werden kann. (Lo)

'In the theory of graphical Markov models in which relations between many variables are simplified via conditional independencies a special rote is played by directed acyclic graphs. They can be used to represent statistical models in which data are generated in a stepwise fashion. Responses and intermediate variables may be event histories. We discuss such a system with sequentially administered treatments and a confounder, that is a variable which affects both the final outcome and one of its explanatory variables. The effect of not observing the confounder is to obtain the final and an intermediate outcome as Joint responses and leads to the important observation by Robins and Wasserman (1997) that any univariate conditional distribution for the final outcome will be inappropriate for analysis no matter whether the intermediate outcome is conditioned on or not. It means in particular that the independence structure of the observed variables can no longer be fully described by a directed acyclic graph, that criteria for reading independencies off graphs have to be modified and that joint instead of univariate regression models are needed. These modifications resolve directly the puzzling situation which has been discussed by the above authors for randomized clinical trials as a case in which a true hypothesis of no treatment effect is always falsely rejected. Joint response models provide an alternative route for avoiding this unpleasant situation.' (author's abstract)|