Criteria for confounders in epidemiological studies

The paper addresses a formal definition of a confounder based on the qualitative definition that is commonly used in standard epidemiology text-books. To derive the criterion for a factor to be a confounder given by Miettinen and Cook and to clarify inconsistency between various criteria for a confounder, we introduce the concepts of an irrelevant factor, an occasional confounder and a uniformly irrelevant factor. We discuss criteria for checking these and show that Miettinen and Cook's criterion can also be applied to occasional confounders. Moreover, we consider situations with multiple potential confounders, and we obtain two necessary conditions that are satisfied by each confounder set. None of the definitions and results presented in this paper require the ignorability and sufficient control confounding assumptions which are commonly employed in observational and epidemiological studies.