In the discrete data models considered thus far, the outcomes or study units were statistically independent. Now this assumption is relaxed to examine models with some form of relationship or dependency between the outcomes or units. That may be induced by the study design, or may be intrinsic to the phenomena under study. We show that exact distributions from several studies of this type can be formulated in a polynomial form, and give methods for inference and efficient computation for them. The specific aims of this chapter are:

• To present the exact analysis of matched case-control studies with two unmatched variables. • To present exact analysis of logit models for paired binary outcome data with covariates. • To present exact analysis of data from a two state time homogeneous Markov chain. • To introduce efficient computational methods for analyzing these models.