The mean function is a central object of inquiry in the analysis of functional data. Typical questions related to the mean function include quantifying estimation uncertainty, testing parametric models, and making comparisons between populations. To make probabilistic statements about the mean function over its entire domain, rather than at a single location, it is necessary to infer all of its values simultaneously. Pointwise inference is not appropriate for this task and indeed produces anticonservative results, i.e., the coverage level of confidence regions is too low and the significance level of hypothesis tests too high. In contrast, simultaneous confidence bands (SCB) provide a flexible framework for conducting simultaneous inference on the mean function and other functional parameters. They also offer powerful visualization tools for communicating analytic results to interdisciplinary audiences. The construction ofSCBin the context of functional data requires specific theory and methods. In particular, it is not addressed by the nonparametric regression literature. Although software is available to perform individual steps of anSCBprocedure, resources that provide end‐to‐end computations are scarce. Applications ofSCBto one‐ and two‐sample inferences are illustrated here with the R package SCBmeanfd.WIREs Comput Stat2017, 9:e1397. doi: 10.1002/wics.1397This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

Discovery of robust diagnostic or prognostic biomarkers is a key to optimizing therapeutic benefit for select patient cohorts - an idea commonly referred to asprecision medicine. Most discovery studies to derive such markers from high-dimensional transcriptomics datasets are weakly powered with sample sizes in the tens of patients. Therefore, highly regularized statistical approaches are essential to making generalizable predictions. At the same time, prior knowledge-driven approaches have been successfully applied to the manual interpretation of high-dimensional transcriptomics datasets. In this work, we assess the impact of combining two orthogonal approaches for the discovery of biomarker signatures, namely (1) well-known lasso-based regression approaches and its more recent derivative, the group lasso, and (2) the discovery of significant upstream regulators in literature-derived biological networks. Our method integrates both approaches in aweighted group-lassomodel and differentially weights gene sets based on inferred active regulatory mechanism. Using nested cross-validation as well as independent clinical datasets, we demonstrate that our approach leads to increased accuracy and generalizable results. We implement our approach in a computationally efficient, user-friendly R package calledcreNET. The package can be downloaded at https://github.com/kouroshz/creNethttps://github.com/kouroshz/creNet and is accompanied by a parsed version of the STRING DB data base.