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 e€ects without knowledge of a completely constructed
causal diagram. We ®rst introduce the concepts of non-confounding, conditional non-confounding,
uniform non-confounding, homogeneity, collapsibility and strong collapsibility for causal e€ects,
then we present necessary and sucient conditions for uniform non-confounding, homegeneity and
collapsibilities, and ®nally we show sucient conditions for non-confounding, conditional non-
confounding and uniform non-confounding.