Errors in causal inference: an organizational schema for systematic error and random error

Purpose
To provide an organizational schema for systematic error and random error in estimating causal measures, aimed at clarifying the concept of errors from the perspective of causal inference.

Methods
We propose to divide systematic error into structural error and analytic error. With regard to random error, our schema shows its four major sources: nondeterministic counterfactuals, sampling variability, a mechanism that generates exposure events and measurement variability.

Results
Structural error is defined from the perspective of counterfactual reasoning and divided into nonexchangeability bias (which comprises confounding bias and selection bias) and measurement bias. Directed acyclic graphs are useful to illustrate this kind of error. Nonexchangeability bias implies a lack of “exchangeability” between the selected exposed and unexposed groups. A lack of exchangeability is not a primary concern of measurement bias, justifying its separation from confounding bias and selection bias. Many forms of analytic errors result from the small-sample properties of the estimator used and vanish asymptotically. Analytic error also results from wrong (misspecified) statistical models and inappropriate statistical methods.

Conclusions
Our organizational schema is helpful for understanding the relationship between systematic error and random error from a previously less investigated aspect, enabling us to better understand the relationship between accuracy, validity, and precision.

© 2016 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0 License. http://creativecommons.org/licenses/by-nc-nd/4.0/.
This is the accepted manuscript version. The formal published version is available at [https://doi.org/10.1016/j.annepidem.2016.09.008] .