Sensitivity Analysis of the Consistency Assumption
Brian Knaeble, Qinyun Lin, Erich Kummerfeld, Kenneth A. Frank
TL;DR
This work addresses violations of the consistency assumption in causal inference by developing a two-stage sensitivity analysis that separates background confounding from hidden versions of treatment using stochastic potential outcomes defined on filtered probability spaces. It introduces a novel bias parameter $K$ for version confounding and entropy-based bounds $f$ and $g$ for background confounding, yielding partial identification of the estimand $\tau$ via bounds $(L,U)$ on $\psi$ adjusted by $K$ (i.e., $L-K<\tau<U-K$). The methodology is demonstrated through three applications (golf, marijuana and hard drug use, and vaccine effectiveness) to illustrate how hidden versions and co-interventions can bias conclusions and how to calibrate bias and uncertainty in practice. Compared with instrumental-variable or intention-to-treat approaches, this framework provides a transparent, data-driven way to assess robustness to consistency violations and to quantify the potential impact of unobserved treatment versions on causal estimates.
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.