Alternative monotonicity assumptions for improving bounds on natural direct effects

Abstract

Estimating the direct effect of a treatment on an outcome is often the focus of epidemiological and clinical research, when the treatment has more than one specified pathway to the defined outcome. Even if the total effect is unconfounded, the direct effect is not identified when unmeasured variables affect the intermediate and outcome variables. Therefore, bounds on direct effects have been presented via linear programming under two common definitions of direct effects: controlled and natural. Here, we propose bounds on natural direct effects without using linear programming, because such bounds on controlled direct effects have already been proposed. To derive narrow bounds, we introduce two monotonicity assumptions that are weaker than those in previous studies and another monotonicity assumption. Furthermore, we do not assume that an outcome variable is binary, whereas previous studies have made that assumption. An additional advantage of our bounds is that the bounding formulas are extremely simple. The proposed bounds are illustrated using a randomized trial for coronary heart disease.