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Bounds on potential risks and causal risk differences under assumptions about confounding parameters
Author(s) -
Chiba Yasutaka,
Sato Tosiya,
Greenland Sander
Publication year - 2007
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2927
Subject(s) - confounding , observational study , econometrics , nonparametric statistics , outcome (game theory) , causal inference , statistics , randomized controlled trial , mathematics , medicine , mathematical economics
Nonparametric bounds on causal effects in observational studies are available under deterministic potential‐outcome models. We derive narrower bounds by adding assumptions regarding bias due to confounding. This bias is defined as the difference between the expectation of potential outcomes for the exposed group and that for the unexposed group. We show that crude effect measures bound causal effects under the given assumptions. We then derive bounds for randomized studies with noncompliance, which are given by the per protocol effect. With perfect compliance in one treatment group, the direction of effect becomes identifiable under our assumptions. Although the assumptions are not themselves identifiable, they are nonetheless reasonable in some situations. Copyright © 2007 John Wiley & Sons, Ltd.