Bounds on Direct Effects in the Presence of Confounded Intermediate Variables (2007)
| Citations: | 4 - 0 self |
BibTeX
@MISC{Cai07boundson,
author = {Zhihong Cai and Manabu Kuroki and Judea Pearl and Jin Tian},
title = {Bounds on Direct Effects in the Presence of Confounded Intermediate Variables},
year = {2007}
}
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Abstract
Summary. This paper considers the problem of estimating the average con-trolled direct effect (ACDE) of a treatment on an outcome, in the presence of unmeasured confounders between an intermediate variable and the outcome. Such confounders render the direct effect unidentifiable even in cases where the total effect is unconfounded (hence identifiable). Kaufman et al. (2005) applied a linear programming software to find the minimum and maximum possible values of the ACDE for specific numerical data. In this paper, we apply the symbolic Balke-Pearl (1997) linear programming method to derive closed-form formulas for the upper and lower bounds on the ACDE under various assumptions of monotonicity. These universal bounds enable clini-cal experimenters to assess the direct effect of treatment from observed data with minimum computational effort, and they further shed light on the sign of the direct effect and the accuracy of the assessments.
