Recently, enhanced and advanced biomedical technology, such as high-throughput microarrays and molecular imaging to monitor SNPs and gene and protein expressions, has been available to provide exhaustive medical information on a single person. In principle, we could obtain much more information about the biological and medical status of an individual from such data sets, which are viewed as biomarkers in a wide sense, for use in identification, association, and prediction studies regarding phenotypes such as disease subtypes, prognosis, treatment responsiveness, and adverse reactions as part of personalized medicine. However, it is frequently difficult to extract only the informative part in such data sets that include a garbage heap of uninformative observations. In particular, we cannot confirm statistical evidence because of the small sample size relative to the dimension of the data when attempting the practical use of such statistical applications. For example, if we implement machine learning methods for the prediction of treatment effects, then we are typically faced with difficulties in trying to confirm reproducibility and robustness as performance measures. At the same time, an effective study design is crucial for developing and validating biomarkers. We focus in this special issue on the difficulties of the statistical analysis of biomarkers, including statistical design, estimation, and prediction. Potential topics include, but are not limited to:

• Kernel machine learning methods for predicting phenotypes
• Matrix and tensor data learning
• Sparse learning and boosting
• Multiple testing/ranking and selection in biomarker screening
• Hierarchical and/or mixture modeling of interindividual heterogeneity
• Design of clinical studies with biomarkers

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