  A surrogate endpoint S in a clinical trial is an outcome that may be measured
earlier or more easily than the true outcome of interest T. 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 T, given the potential
outcomes S. In particular, our setting of interest allows us to assume the
surrogate under the placebo, S(0), is zero-valued, 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. We
demonstrate our approach via simulation and data that mimics an ongoing study
of a muscular dystrophy gene therapy.
