MOTIVATION: There is a growing interest in longitudinal omics data paired with some longitudinal clinical outcome. Given a large set of continuous omics variables and some continuous clinical outcome, each measured for a few subjects at only a few time points, we seek to identify those variables that co-vary over time with the outcome. To motivate this problem we study a dataset with hundreds of urinary metabolites along with Tuberculosis mycobacterial load as our clinical outcome, with the objective of identifying potential biomarkers for disease progression. For such data clinicians usually apply simple linear mixed effects models which often lack power given the low number of replicates and time points. We propose a penalized regression approach on the first differences of the data that extends the lasso + Laplacian method [Li and Li (Network-constrained regularization and variable selection for analysis of genomic data. Bioinformatics 2008;24:1175-82.)] to a longitudinal group lasso + Laplacian approach. Our method, PROLONG, leverages the first differences of the data to increase power by pairing the consecutive time points. The Laplacian penalty incorporates the dependence structure of the variables, and the group lasso penalty induces sparsity while grouping together all contemporaneous and lag terms for each omic variable in the model. RESULTS: With an automated selection of model hyper-parameters, PROLONG correctly selects target metabolites with high specificity and sensitivity across a wide range of scenarios. PROLONG selects a set of metabolites from the real data that includes interesting targets identified during EDA. AVAILABILITY AND IMPLEMENTATION: An R package implementing described methods called "prolong" is available at https://github.com/stevebroll/prolong. Code snapshot available at 10.5281/zenodo.14804245.

Tree ensembles such as Random Forests have achieved impressive empirical success across a wide variety of applications. To understand how these models make predictions, people routinely turn to feature importance measures calculated from tree ensembles. It has long been known that Mean Decrease Impurity (MDI), one of the most widely used measures of feature importance, incorrectly assigns high importance to noisy features, leading to systematic bias in feature selection. In this paper, we address the feature selection bias of MDI from both theoretical and methodological perspectives. Based on the original definition of MDI by Breiman et al. \cite{Breiman1984} for a single tree, we derive a tight non-asymptotic bound on the expected bias of MDI importance of noisy features, showing that deep trees have higher (expected) feature selection bias than shallow ones. However, it is not clear how to reduce the bias of MDI using its existing analytical expression. We derive a new analytical expression for MDI, and based on this new expression, we are able to propose a debiased MDI feature importance measure using out-of-bag samples, called MDI-oob. For both the simulated data and a genomic ChIP dataset, MDI-oob achieves state-of-the-art performance in feature selection from Random Forests for both deep and shallow trees.

MOTIVATION: Recent technological advances in mass spectrometry, development of richer mass spectral libraries and data processing tools have enabled large scale metabolic profiling. Biological interpretation of metabolomics studies heavily relies on knowledge-based tools that contain information about metabolic pathways. Incomplete coverage of different areas of metabolism and lack of information about non-canonical connections between metabolites limits the scope of applications of such tools. Furthermore, the presence of a large number of unknown features, which cannot be readily identified, but nonetheless can represent bona fide compounds, also considerably complicates biological interpretation of the data. RESULTS: Leveraging recent developments in the statistical analysis of high-dimensional data, we developed a new Debiased Sparse Partial Correlation algorithm (DSPC) for estimating partial correlation networks and implemented it as a Java-based CorrelationCalculator program. We also introduce a new version of our previously developed tool Metscape that enables building and visualization of correlation networks. We demonstrate the utility of these tools by constructing biologically relevant networks and in aiding identification of unknown compounds. AVAILABILITY AND IMPLEMENTATION: http://metscape.med.umich.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum likelihood estimator for Gaussian multi-layered graphical models, based on a computational approach involving screening of variables, iterative estimation of the directed edges between layers and undirected edges within layers and a final refitting and stability selection step that provides improved performance in finite sample settings. We establish the consistency of the estimator in a high-dimensional setting. To obtain this result, we develop a strategy that leverages the biconvexity of the likelihood function to ensure convergence of the developed iterative algorithm to a stationary point, as well as careful uniform error control of the estimates over iterations. The performance of the maximum likelihood estimator is illustrated on synthetic data.