There is growing body of research devoted to designing imaging-based biomarkers that identify Alzheimer's disease (AD) in its prodromal stage using statistical machine learning methods. Recently several authors investigated how clinical trials for AD can be made more efficient (i.e., smaller sample size) using predictive measures from such classification methods. In this paper, we explain why predictive measures given by such SVM type objectives may be less than ideal for use in the setting described above. We give a solution based on a novel deep learning model, randomized denoising autoencoders (rDA), which regresses on training labels y while also accounting for the variance, a property which is very useful for clinical trial design. Our results give strong improvements in sample size estimates over strategies based on multi-kernel learning. Also, rDA predictions appear to more accurately correlate to stages of disease. Separately, our formulation empirically shows how deep architectures can be applied in the large d, small n regime--the default situation in medical imaging. This result is of independent interest.