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In this work, we extend causal inference approaches to validate such a surrogate using potential outcomes. The causal association paradigm assesses the relationship of the treatment effect on the surrogate with the treatment effect on the true endpoint. Using the principal surrogacy criteria, we utilize the joint conditional distribution of the potential outcomes <jats:italic>T<\/jats:italic>, given the potential outcomes <jats:italic>S<\/jats:italic>. In particular, our setting of interest allows us to assume the surrogate under the placebo, , is zero\u2010valued, and we incorporate baseline covariates in the setting of normally distributed endpoints. We develop Bayesian methods to incorporate conditional independence and other modeling assumptions and explore their impact on the assessment of surrogacy. 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