[Paper Review] Simple Sensitivity Analysis for Differential Measurement Error

Tyler J. VanderWeele, Yige Li|arXiv (Cornell University)|Nov 1, 2018

Probabilistic and Robust Engineering DesignDecision Sciences11 references3 citations

TL;DR

This paper presents simple sensitivity analysis methods for differential measurement error in either exposure or outcome, using risk ratios to bound the true causal effect. It shows that the true risk ratio must be at least as large as the observed association divided by the maximum strength of differential measurement error, assessed via controlled direct effects or conditional effects on mis-measured variables.

ABSTRACT

Simple sensitivity analysis results are given for differential measurement error of either the exposure or the outcome. In the case of differential measurement error of the outcome it is shown that the true effect of the exposure on the outcome on the risk ratio scale must be at least as large as the observed association between the exposure and the mis-measured outcome divided by the maximum strength of differential measurement error, assessed as the risk ratio of the controlled direct effect of the exposure on mis-measured outcome not through the true outcome. In the case of differential measurement error of the exposure it is shown that the true effect on the risk ratio scale of the exposure on the outcome must be at least as large as the observed association between the mis-measured exposure measurement and the outcome divided by the maximum strength of differential measurement error, assessed as the risk ratio of the effect of the outcome on mis-measured exposure measurement conditional on the true exposure. The results can also be immediately used to indicate the minimum strength of differential measurement error that would be needed to explain away an observed association between an exposure measurement and an outcome measurement.

Motivation & Objective

• To develop accessible sensitivity analysis tools for differential measurement error in epidemiological and statistical studies.
• To address the challenge of unmeasured confounding due to differential misclassification of exposure or outcome.
• To provide interpretable bounds on the true causal effect using observable data and plausible assumptions about measurement error.
• To enable researchers to assess how strong differential measurement error would need to be to explain away an observed association.

Proposed method

• Uses risk ratios to quantify the strength of differential measurement error in both exposure and outcome misclassification.
• For outcome misclassification, derives a bound based on the controlled direct effect of exposure on mis-measured outcome, not through the true outcome.
• For exposure misclassification, derives a bound based on the risk ratio of the effect of the outcome on mis-measured exposure, conditional on the true exposure.
• Applies these bounds to compute the minimum strength of differential error needed to explain away an observed association.
• Employs structural causal models to formalize the relationships between true exposure, true outcome, and their mis-measured counterparts.
• Provides closed-form expressions for sensitivity bounds that are easy to implement without simulation.

Experimental results

Research questions

• RQ1 How can researchers assess the robustness of an observed association to differential measurement error in the outcome?
• RQ2 What is the minimum strength of differential measurement error required to fully explain away an observed association between exposure and outcome?
• RQ3 How does differential misclassification of exposure affect the interpretation of observed associations on the risk ratio scale?
• RQ4 Can simple, interpretable bounds be derived for the true causal effect under differential measurement error?
• RQ5 What role do controlled direct effects and conditional effects play in sensitivity analysis for differential error?

Key findings

• The true risk ratio of exposure on outcome must be at least as large as the observed association between exposure and mis-measured outcome divided by the maximum strength of differential measurement error.
• For outcome misclassification, the maximum strength of differential error is measured as the risk ratio of the controlled direct effect of exposure on mis-measured outcome not through the true outcome.
• For exposure misclassification, the maximum strength of differential error is measured as the risk ratio of the effect of the outcome on mis-measured exposure, conditional on the true exposure.
• The method provides a direct way to compute the minimum differential error strength needed to explain away an observed association.
• The bounds are valid on the risk ratio scale and are interpretable without requiring complex modeling or simulation.
• The approach is applicable to both exposure and outcome misclassification, offering a unified framework for sensitivity analysis under differential error.