The Trouble with Triples: Examining the Impact of Measurement Error in Mediation Analysis

Mediation analysis is a class of statistical methods used to determine whether the effect of an exogenous variable (X) on a target variable (ϒ) is mediated through an intermediate variable (M). Mediation analysis relies on propagation of variation through the variables in a causal system to produce characteristic patterns of correlation in the observed data. However, data often include measurement error that does not propagate, and in many applications of mediation analysis the potential effects of measurement error are not accounted for. In this work, we evaluate the reliability of mediation analysis in the presence of measurement error. We define a measurement error model and show that mediation analysis can infer partial mediation, i.e., X affects ϒ both directly and indirectly through M, even when there is no causal relationship between M and ϒ. This becomes more likely as sample size increases. When partial mediation is excluded from the set of possible models, the relative measurement errors of X, M, and ϒ play a large role in determining whether mediation analysis will infer the correct causal relationship. Using examples from genetic studies of molecular traits, we demonstrate how to assess the reliability of mediation analysis in the presence of measurement error and highlight common scenarios that can lead to incorrect inferences.