Interval identification of natural effects in the presence of outcome-related unmeasured confounding

TL;DR

This paper develops a semi-parametric method to derive bounds for natural effects with outcome-related unmeasured confounding, using a logistic model and fewer assumptions.

Contribution

It introduces a novel approach for interval identification of natural effects under minimal assumptions, including a new condition called PC-CWD.

Findings

Derived bounds for natural effects with fewer assumptions.

Provided delta-method standard errors for uncertainty intervals.

Applied method to assess smoking's mediation effect on lung cancer.

Abstract

With reference to a binary outcome and a binary mediator, we derive identification bounds for natural effects under a reduced set of assumptions. Specifically, no assumptions about confounding are made that involve the outcome; we only assume no unobserved exposure-mediator confounding as well as a condition termed partially constant cross-world dependence (PC-CWD), which poses fewer constraints on the counterfactual probabilities than the usual cross-world independence assumption. The proposed strategy can be used also to achieve interval identification of the total effect, which is no longer point identified under the considered set of assumptions. Our derivations are based on postulating a logistic regression model for the mediator as well as for the outcome. However, in both cases the functional form governing the dependence on the explanatory variables is allowed to be arbitrary, thereby resulting in a semi-parametric approach. To account for sampling variability, we provide delta-method approximations of standard errors in order to build uncertainty intervals from identification bounds. The proposed method is applied to a dataset gathered from a Spanish prospective cohort study. The aim is to evaluate whether the effect of smoking on lung cancer risk is mediated by the onset of pulmonary emphysema.