Methodological Details of medrobust

Introduction

This vignette provides a brief overview of the statistical theory and methods implemented in the medrobust package. For a complete treatment, please refer to Tofighi (2025).

Causal Framework

We define the natural direct effect (NDE) and natural indirect effect (NIE) under the counterfactual framework…

Partial Identification under Differential Misclassification

Let A^* be the misclassified version of the true exposure A. The relationship is governed by sensitivity and specificity parameters that depend on the outcome Y:

• Sn_y = P(A^* = 1|A = 1, Y = y)
• Sp_y = P(A^* = 0|A = 0, Y = y)

The core of the method involves expressing the observed data distribution as a function of the true, unobserved distribution and the sensitivity parameters.

Testable Implications

The model is not point-identified, but it does have testable implications. Specifically, the observed probabilities must lie within certain bounds for any valid set of sensitivity parameters. These constraints are used to falsify regions of the parameter space.

References

Tofighi, D. (2025). Partial identification bounds for causal mediation effects under differential misclassification. Manuscript in preparation.