Conditional Differential Measurement Error: Partial Identifiability and Estimation

Abstract

Differential measurement error, which occurs when the error in the measured out-come is correlated with the treatment renders the causal effect unidentifiable from observational data. In this work, we study conditional differential measurement error, where a subgroup of the population is known to be prone to differential measurement error. Under an assumption about the direction (but not magnitude) of the measurement error, we derive sharp bounds on the conditional average treatment effect and present an approach to estimate them. We empirically validate our approach on semi-synthetic da, showing that it gives more credible and informativebound than other approaches. In addition, we implement our approach on real data, showing its utility in guiding decisions about dietary modification intervals to improve nutritional intake.