A surrogate marker (S) is often an intermediate physical orlaboratory indicator in a disease progression process. It can bemeasured earlier and cost less than the true endpoint (T). Asurrogate marker may be able to facilitate early prediction of thetreatment (Z) effect on T and thus can be very useful inreducing the duration and cost of a clinical trial. In practice, itcan either serve as a substitute for T or as an auxiliaryvariable. One part of my dissertation focuses on its role as anauxiliary variable. We aim to directly investigate its usage inpredicting the treatment effect and identify the situations when Scan be beneficial in improving the precision in both single- andmultiple-trial settings when T is not completely observed. Whenthe individual-level correlation is relatively high, there issubstantial efficiency gain by using S, particularly in amultiple-trial setting. We also study the extent of efficiency gainwith respect to different model assumptions that are used todescribe the relationship among S, T and Z. The resultsmotivate a generalized ridge regression method which strikes abalance between bias reduction and efficiency gain without the needto specify correct models. The other part of the dissertationdirectly models the relationship of T, S and Z in a causalframework. Previous work on surrogate markers often requires one tofit models for the distribution of T given S and $Z$. It is wellknown that it usually does not have a causal interpretation becausethe models condition on a post randomization variable S. To solvethis problem, we adapt a causal framework using the principalstratification approach introduced by Frangakis and Rubin (2002). Wepropose a Bayesian method to estimate the causal associationsbetween the potential outcomes of S and T. To not only overcomesome non-identifiability problems but also improve the precision ofthe statistical inference, we incorporate assumptions that areplausible in the surrogate context into prior distributions. Themethod is explored in both single trial and multiple trial settings.
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Statistical Methods in Surrogate Marker Research for Clinical Trials.