A surrogate marker (S) is often an intermediate physical or laboratory indicator in a disease progression process. It can be measured earlier and cost less than the true endpoint (T). A surrogate marker may be able to facilitate early prediction of the treatment ( Z) effect on T and thus can be very useful in reducing the duration and cost of a clinical trial. In practice, it can either serve as a substitute for T or as an auxiliary variable. One part of my dissertation focuses on its role as an auxiliary variable. We aim to directly investigate its usage in predicting the treatment effect and identify the situations when S can be beneficial in improving the precision in both single- and multiple-trial settings when T is not completely observed. When the individual-level correlation is relatively high, there is substantial efficiency gain by using S, particularly in a multiple-trial setting. We also study the extent of efficiency gain with respect to different model assumptions that are used to describe the relationship among S, T and Z. The results motivate a generalized ridge regression method which strikes a balance between bias reduction and efficiency gain without the need to specify correct models. The other part of the dissertation directly models the relationship of T, S and Z in a causal framework. Previous work on surrogate markers often requires one to fit models for the distribution of T given S and Z. It is well known that it usually does not have a causal interpretation because the models condition on a post randomization variable S. To solve this problem, we adapt a causal framework using the principal stratification approach introduced by Frangakis and Rubin (2002). We propose a Bayesian method to estimate the causal associations between the potential outcomes of S and T. To not only overcome some non-identifiability problems but also improve the precision of the statistical inference, we incorporate assumptions that are plausible in the surrogate context into prior distributions. The method is explored in both single trial and multiple trial settings.