A Shrinkage Approach for Estimating a Treatment Effect Using Intermediate Biomarker Data in Clinical Trials

Summary In clinical trials, a biomarker ( S  ) that is measured after randomization and is strongly associated with the true endpoint ( T ) can often provide information about  T  and hence the effect of a treatment ( Z  ) on  T . A useful biomarker can be measured earlier than  T  and cost less than  T . In this article, we consider the use of  S  as an auxiliary variable and examine the information recovery from using  S  for estimating the treatment effect on  T , when  S  is completely observed and  T  is partially observed. In an ideal but often unrealistic setting, when  S  satisfies Prentice’s definition for perfect surrogacy, there is the potential for substantial gain in precision by using data from  S  to estimate the treatment effect on  T . When  S  is not close to a perfect surrogate, it can provide substantial information only under particular circumstances. We propose to use a targeted shrinkage regression approach that data‐adaptively takes advantage of the potential efficiency gain yet avoids the need to make a strong surrogacy assumption. Simulations show that this approach strikes a balance between bias and efficiency gain. Compared with competing methods, it has better mean squared error properties and can achieve substantial efficiency gain, particularly in a common practical setting when  S  captures much but not all of the treatment effect and the sample size is relatively small. We apply the proposed method to a glaucoma data example.