Lucas Mentch

Integrative modelling of tumour DNA methylation quantifies the contribution of metabolism.

Altered DNA methylation is common in cancer and often considered an early event in tumorigenesis. However, the sources of heterogeneity of DNA methylation among tumours remain poorly defined. Here we capitalize on the availability of multi-platform data on thousands of human tumours to build integrative models of DNA methylation. We quantify the contribution of clinical and molecular factors in explaining intertumoral variability in DNA methylation. We show that the levels of a set of metabolic genes involved in the methionine cycle is predictive of several features of DNA methylation in tumours, including the methylation of cancer genes. Finally, we demonstrate that patients whose DNA methylation can be predicted from the methionine cycle exhibited improved survival over cases where this regulation is disrupted. This study represents a comprehensive analysis of the determinants of methylation and demonstrates the surprisingly large interaction between metabolism and DNA methylation variation. Together, our results quantify links between tumour metabolism and epigenetics and outline clinical implications.

Formal Hypothesis Tests for Additive Structure in Random Forests

ABSTRACT While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the natural structure of ensemble learners like bagged trees and random forests has been shown to admit desirable asymptotic properties when base learners are built with proper subsamples. In this work, we demonstrate that by defining an appropriate grid structure on the covariate space, we may carry out formal hypothesis tests for both variable importance and underlying additive model structure. To our knowledge, these tests represent the first statistical tools for investigating the underlying regression structure in a context such as random forests. We develop notions of total and partial additivity and further demonstrate that testing can be carried out at no additional computational cost by estimating the variance within the process of constructing the ensemble. Furthermore, we propose a novel extension of these testing procedures using random projections to allow for computationally efficient testing procedures that retain high power even when the grid size is much larger than that of the training set.

R-CMap-An open-source software for concept mapping.

Planning and evaluating projects often involves input from many stakeholders. Fusing and organizing many different ideas, opinions, and interpretations into a coherent and acceptable plan or project evaluation is challenging. This is especially true when seeking contributions from a large number of participants, especially when not all can participate in group discussions, or when some prefer to contribute their perspectives anonymously. One of the major breakthroughs in the area of evaluation and program planning has been the use of graphical tools to represent the brainstorming process. This provides a quantitative framework for organizing ideas and general concepts into simple-to-interpret graphs. We developed a new, open-source concept mapping software called R-CMap, which is implemented in R. This software provides a graphical user interface to guide users through the analytical process of concept mapping. The R-CMap software allows users to generate a variety of plots, including cluster maps, point rating and cluster rating maps, as well as pattern matching and go-zone plots. Additionally, R-CMap is capable of generating detailed reports that contain useful statistical summaries of the data. The plots and reports can be embedded in Microsoft Office tools such as Word and PowerPoint, where users may manually adjust various plot and table features to achieve the best visual results in their presentations and official reports. The graphical user interface of R-CMap allows users to define cluster names, change the number of clusters, select rating variables for relevant plots, and importantly, select subsets of respondents by demographic criteria. The latter is particularly useful to project managers in order to identify different patterns of preferences by subpopulations. R-CMap is user-friendly, and does not require any programming experience. However, proficient R users can add to its functionality by directly accessing built-in functions in R and sharing new features with the concept mapping community.

Bootstrap bias corrections for ensemble methods

This paper examines the use of a residual bootstrap for bias correction in machine learning regression methods. Accounting for bias is an important obstacle in recent efforts to develop statistical inference for machine learning. We demonstrate empirically that the proposed bootstrap bias correction can lead to substantial improvements in both bias and predictive accuracy. In the context of ensembles of trees, we show that this correction can be approximated at only double the cost of training the original ensemble. Our method is shown to improve test set accuracy over random forests by up to 70% on example problems from the UCI repository.

Multiphase segmentation for simultaneously homogeneous and textural images

Segmentation remains an important problem in image processing. For homogeneous (piecewise smooth) images, a number of important models have been developed and refined over the past several decades. However, these models often fail when applied to the substantially larger class of natural images that simultaneously contain regions of both texture and homogeneity. This work introduces a bi-level constrained minimization model for simultaneous multiphase segmentation of images containing both homogeneous and textural regions. We develop novel norms defined in different functional Banach spaces for the segmentation which results in a non-convex minimization. Finally, we develop a generalized notion of segmentation delving into approximation theory and demonstrating that a more refined decomposition of these images results in multiple meaningful components. Both theoretical results and demonstrations on natural images are provided.

The Importance of Calibration in Clinical Psychology

Accuracy has several elements, not all of which have received equal attention in the field of clinical psychology. Calibration, the degree to which a probabilistic estimate of an event reflects the true underlying probability of the event, has largely been neglected in the field of clinical psychology in favor of other components of accuracy such as discrimination (e.g., sensitivity, specificity, area under the receiver operating characteristic curve). Although it is frequently overlooked, calibration is a critical component of accuracy with particular relevance for prognostic models and risk-assessment tools. With advances in personalized medicine and the increasing use of probabilistic (0% to 100%) estimates and predictions in mental health research, the need for careful attention to calibration has become increasingly important.

Integrative modeling of tumor DNA methylation identifies a role for metabolism

DNA methylation varies across genomic regions, tissues and individuals in a population. Altered DNA methylation is common in cancer and often considered an early event in tumorigenesis. However, the sources of heterogeneity of DNA methylation among tumors remain poorly defined. Here, we capitalize on the availability of multi-platform data on thousands of molecularly-and clinically-annotated human tumors to build integrative models that identify the determinants of DNA methylation. We quantify the relative contribution of clinical and molecular factors in explaining within-cancer (inter-individual) variability in DNA methylation. We show that the levels of a set of metabolic genes involved in the methionine cycle that are constituents of one-carbon metabolism are predictive of several features of DNA methylation status in tumors including the methylation of genes that are known to drive oncogenesis. Finally, we demonstrate that patients whose DNA methylation status can be predicted from the genes in one-carbon metabolism exhibited improved survival over cases where this regulation is disrupted. To our knowledge, this study is the first comprehensive analysis of the determinants of methylation and demonstrates the surprisingly large contribution of metabolism in explaining epigenetic variation among individual tumors of the same cancer type. Together, our results illustrate links between tumor metabolism and epigenetics and outline future clinical implications.