Conditions for non-confounding and collapsibility without knowledge of completely constructed causal diagrams

In this paper, we discuss several concepts in causal inference in terms of causal diagrams proposed by Pearl (1993, 1995a, b), and we give conditions for non-confounding, homogeneity and collapsibility for causal effects without knowledge of a completely constructed causal diagram. We first introduce the concepts of non-confounding, conditional non-confounding, uniform non-confounding, homogeneity, collapsibility and strong collapsibility for causal effects, then we present necessary and sufficient conditions for uniform non confounding, homegeneity and collapsibilities, and finally we show sufficient conditions for, non-confounding, conditional non-confounding and uniform non-confounding.