Conditions for uniformly non-confounding of causal distribution effects over multiple covariates

Causation is a distinct concept from association and more important than association in epidemiologic studies. This paper proposes the concept of uniform non-confounding for causal distribution effects over multiple covariates, and gives the sufficient conditions for uniform non-confounding over a covariate set C including confounders or non-confounders, and also shows the conditions for conditionally non-confounding in the subpopulations. All these conditions can be tested by observed data.