The impact of measurement error in mediation analysis
Authors: Madeleine Gastonguay; Gregory Keele; Gary Churchill
Affiliation: The Jackson Laboratory, Bar Harbor, ME
Keywords: Theory & Method Development
Mediation analysis is a class of statistical techniques used to investigate the relationship among interacting variables in a causal system. In the context of genetics, it can be used to identify causal intermediaries of genetic effects on phenotypes and thus illuminate genetic regulatory systems. Mediation relies on variation due to causal effects that propagates through the system to produce characteristic patterns of covariation in the observed data. In addition to this causal variation, observed data also include measurement error that does not propagate through the causal relationships. Typically, mediation analyses do not attempt to distinguish between these sources of variation. In this work, we evaluate the reliability of mediation analysis for determining the structure of a causal system in the presence of measurement error and identify ways to diagnose cases where the resulting inference may be misleading. We focus on the biological context where a quantitative trait locus (QTL; X) regulates a target phenotype (Y), potentially completely or partially through a candidate mediator (M). For example, M could represent transcript or protein expression levels of a gene that co-localizes with the QTL. We define a measurement error model to relate the true unobserved variables to their measured quantities and simulated from various causal models. We confirm that measurement error in the mediator when the causal relationship is complete mediation results in mediation analysis incorrectly inferring partial mediation. Notably, this issue occurs more frequently as sample size increases. We observed similar results from simulations of a co-local relationship in which the QTL affects M and Y independently and there is error in X, indicating that partial mediation may be inferred even when there is no causal relationship between M and Y. Furthermore, in cases when partial mediation is not inferred, the relative errors of X, M, and Y will determine which model is preferred. Based on these observations, we derived guidelines for cases where mediation inferences will be consistent or inconsistent with the unobserved causal relationship. Using examples in data from genetically diverse mouse populations, we demonstrate how these guidelines can be used to assess the reliability of mediation inferences and highlight common scenarios in which they will be incorrect.