Consecutive Collapsibility of Odds Ratios over an Ordinal Background Variable

G. R. Ducharme and Y. Lepage (1986, J. Roy. Statist. Soc. Ser. B48, 197–205) presented the strong collapsibility of odds ratio in 2×2×K tables. However, the concept is not suitable for an ordinal background variable since it is meaningless to pool nonadjacent levels in this case. In this paper, we introduce the consecutive collapsibility of odds ratios over an ordinal background in an I×J×K table and present necessary and sufficient conditions for consecutive collapsibility of odds ratios. The conditions are important for guiding the possible merging of consecutive levels of the background.