Sensitivity Analysis of the Consistency Assumption

TL;DR

This paper introduces a new sensitivity analysis method to evaluate the impact of hidden versions of treatment on causal inference, addressing a gap in existing methods focused on unmeasured confounding.

Contribution

It develops a novel mathematical framework for assessing violations of the consistency assumption due to hidden treatment versions.

Findings

New mathematical notation for sensitivity analysis

Application examples demonstrating the method

Addresses confounding by hidden treatment versions

Abstract

Sensitivity analysis informs causal inference by assessing the sensitivity of conclusions to departures from assumptions. The consistency assumption states that there are no hidden versions of treatment and that the outcome arising naturally equals the outcome arising from intervention. When reasoning about the possibility of consistency violations, it can be helpful to distinguish between covariates and versions of treatment. In the context of surgery, for example, genomic variables are covariates and the skill of a particular surgeon is a version of treatment. There may be hidden versions of treatment, and this paper addresses that concern with a new kind of sensitivity analysis. Whereas many methods for sensitivity analysis are focused on confounding by unmeasured covariates, the methodology of this paper is focused on confounding by hidden versions of treatment. In this paper, new mathematical notation is introduced to support the novel method, and example applications are described.