title: Errors in causal inference: an organizational schema for systematic error and random error.
abstract: 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.
  
  
  
  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.
  
  
  
  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.
  
  
  
  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.
authors: Department of Epidemiology, Graduate School of Medicine, Dentistry and Pharmaceutical Sciences, Okayama University, Okayama, Japan. Electronic address: etsuji-s@cc.okayama-u.ac.jp.
authors: Etsuji
authors: E
authors: Suzuki
authors: Department of Human Ecology, Graduate School of Environmental and Life Science, Okayama University, Okayama, Japan.
authors: Toshihide
authors: T
authors: Tsuda
authors: Center for Innovative Clinical Medicine, Okayama University Hospital, Okayama University, Okayama, Japan.
authors: Toshiharu
authors: T
authors: Mitsuhashi
authors: Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran.
authors: Mohammad Ali
authors: MA
authors: Mansournia
authors: Department of Information Science, Faculty of Informatics, Okayama University of Science, Okayama, Japan.
authors: Eiji
authors: E
authors: Yamamoto
mesh_terms: D015986:Confounding Factors, Epidemiologic; D004812:Epidemiologic Methods; D006801:Humans; D019300:Medical Errors; D015233:Models, Statistical; D015983:Selection Bias
keywords: Bias; Causality; Epidemiologic methods