All your data are always missing: incorporating bias due to measurement error into the potential outcomes framework

Epidemiologists often use the potential outcomes framework to cast causal inference as a missing data problem. Here, we demonstrate how bias due to measurement error can be described in terms of potential outcomes and considered in concert with bias from other sources. In addition, we illustrate how acknowledging the uncertainty that arises due to measurement error increases the amount of missing information in causal inference. We use a simple example to show that estimating the average treatment effect requires the investigator to perform a series of hidden imputations based on strong assumptions.