Rosenbaum (1984) "The Consequences of Adjustment for a Concomitant Variable That Has Been Affected by the Treatment"

Rosenbaum, Paul R. 1984. "The Consequences of Adjustment for a Concomitant Variable That Has Been Affected by the Treatment." Journal of the Royal Statistical Society Series A 147:656-66.

 重要な論文だとは思いつつも、難しいのでしっかり読み通せていなかったものです。処置変数に先行する変数(pretreatment variables)に観察されないものがある際に、処置変数に後続する変数(posttreatment variables)を統制することは、平均因果効果の推定に役に立つのかどうか、というのが問われていることです。



   In observational studies, the situation is more complicated: no single course of action is appropriate for all such studies. Estimators that adjust for the pretreatment covariate ( \bf{X}) alone and estimators that adjust for both pretreatment and posttreatment variables ( \bf{X, S_{Z}}) can each lead to biased estimates, but for quite different reasons. Adjustment for a posttreatment variables may be advisable in either of two circumstances: (a) when, as in Section 1.2, a posttreatment variables (e.g., sophomore test scores) is a plausible surrogate for a clearly relevant but unobserved pretreatment variable (e.g., test scores before high school), or (b) when, as in Section 1.3, even after adjustment for  \bf{X}, the treated and control groups differ substantially with respect to a posttreatment variable (e.g., hormone use) for which a large treatment effect was not expected. In both cases, it will typically be necessary to examine the sensitivity of conclusions to a range of plausible assumptions about the effect of the treatment on the posttreatment variable (e.g. Sections 4.3, and 4.4).