Modern genomic and neuroimaging studies collect data at an ever finer scale in the hope of understanding the architecture of complex disease systems. However, the moderate sample size typically encountered in these studies complicates the use of complex prediction models that can easily contain hundreds of parameters to estimate. In this work, we look at how nonlinear dimension reduction methods can be used to extract nonlinear features that can then be used in a simple prediction model. We investigate two classes of methods: nonlinear extensions of traditional linear methods (e.g. kernel PCA) and manifold learning methods (e.g. Locally Linear Embedding). We introduce a nonlinear simulation framework to assess the ability of these methods to accurately estimate latent structures. We also compare the gains in predictive accuracy over traditional linear methods. Finally, we explore the applicability of this framework in predicting Alzheimer’s disease from structural neuroimaging data.