MOTIVATION: Until now, much of the focus in cancer has been on biomarker discovery and generating lists of univariately significant genes, as well as epidemiological and clinical measures. These approaches, although significant on their own, are not effective for elucidating the synergistic qualities of the numerous components in complex diseases. These components do not act one at a time, but rather in concert with numerous others. A compelling need exists to develop analytically sound and computationally advanced methods that elucidate a more biologically meaningful understanding of the mechanisms of cancer initiation and progression by taking these interactions into account. RESULTS: We propose a novel algorithm, partDSA, for prediction when several variables jointly affect the outcome. In such settings, piecewise constant estimation provides an intuitive approach by elucidating interactions and correlation patterns in addition to main effects. As well as generating 'and' statements similar to previously described methods, partDSA explores and chooses the best among all possible 'or' statements. The immediate benefit of partDSA is the ability to build a parsimonious model with 'and' and 'or' conjunctions that account for the observed biological phenomena. Importantly, partDSA is capable of handling categorical and continuous explanatory variables and outcomes. We evaluate the effectiveness of partDSA in comparison to several adaptive algorithms in simulations; additionally, we perform several data analyses with publicly available data and introduce the implementation of partDSA as an R package. AVAILABILITY: http://cran.r-project.org/web/packages/partDSA/index.html CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: In genomic studies, thousands of features are collected on relatively few samples. One of the goals of these studies is to build classifiers to predict the outcome of future observations. There are three inherent steps to this process: feature selection, model selection and prediction assessment. With a focus on prediction assessment, we compare several methods for estimating the 'true' prediction error of a prediction model in the presence of feature selection. RESULTS: For small studies where features are selected from thousands of candidates, the resubstitution and simple split-sample estimates are seriously biased. In these small samples, leave-one-out cross-validation (LOOCV), 10-fold cross-validation (CV) and the .632+ bootstrap have the smallest bias for diagonal discriminant analysis, nearest neighbor and classification trees. LOOCV and 10-fold CV have the smallest bias for linear discriminant analysis. Additionally, LOOCV, 5- and 10-fold CV, and the .632+ bootstrap have the lowest mean square error. The .632+ bootstrap is quite biased in small sample sizes with strong signal-to-noise ratios. Differences in performance among resampling methods are reduced as the number of specimens available increase. SUPPLEMENTARY INFORMATION: A complete compilation of results and R code for simulations and analyses are available in Molinaro et al. (2005) (http://linus.nci.nih.gov/brb/TechReport.htm).