title: Bounds on controlled direct effects under monotonic assumptions about mediators and confounders.
abstract: Adjusting for intermediate variables is a common analytic strategy for estimating a direct effect. Even if the total effect is unconfounded, the direct effect is not identified when unmeasured variables affect the intermediate and outcome variables. Therefore, some researchers presented bounds on the controlled direct effects via linear programming. They applied a monotonic assumption about treatment and intermediate variables and a no-interaction assumption to derive narrower bounds. Here, we improve their bounds without using linear programming and hence derive a bound under the monotonic assumption about an intermediate variable only. To improve the bounds, we further introduce the monotonic assumption about confounders. While previous studies assumed that an outcome is a binary variable, we do not make that assumption. The proposed bounds are illustrated using two examples from randomized trials.
authors.affiliation: Department of Environmental Medicine and Behavioral Science, Kinki University School of Medicine, Osakasayama, Osaka, Japan. chibay@med.kindai.ac.jp
authors.forename: Yasutaka
authors.initials: Y
authors.lastname: Chiba
mesh_terms: D000465:Algorithms; D001699:Biometry / Q000379:methods*; D002792:Cholestyramine Resin / Q000627:therapeutic use; D015986:Confounding Factors, Epidemiologic; D003327:Coronary Disease / Q000517:prevention & control; D006801:Humans; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D009203:Myocardial Infarction / Q000517:prevention & control; D010919:Placebos; D011379:Prognosis; D016032:Randomized Controlled Trials as Topic; D012107:Research Design; D016896:Treatment Outcome
chemical_list: D010919:Placebos; D002792:Cholestyramine Resin