dCortools: Distance Correlation Methods for Detecting Nonlinear Associations in High-Dimensional Molecular Data
Final Report Abstract
The project dealt with the concept of distance correlation, which is a novel and powerful dependence criterion. Contrary to Pearson or Spearman correlation, distance correlation measures any kind of dependence between random vectors, including nonlinear or even nonmonotone associations. In this project, the concept of distance correlation was extended to survival data allowing to test for independence between any kind of predictor variable (such as e.g. clinical or demographical data) and a time-to-event response. For this purpose, two approaches were derived. The first approach is based on the distance correlation of the predictor variable and the martingale residuals in an empty Cox model, the second approach is based on inverse-probability of censoring-weighted U-statistics. Both approaches have been shown to perform well in practice. Moreover, we created an R package dcortools, which is freely available on the Comprehensive R Archive Network (CRAN). Different to other R packages that provide resampling-based tests, this R package features asymptotic testing procedures that are typically substantially faster. Moreover, a highly efficient computation of the distance correlation coefficient itself is implemented. Finally, the R package also features methods for generalized distance correlation and the distance correlation methods for survival data developed in the course of the project. One of the original goals of the project was further the development of iterative variable screening methods for high-dimensional data. This goal was dropped for the moment, since we could establish a unifying results between the distance correlation and other measures of dependence. Using this result, we obtain a regression interpretation for distance correlation, which provides new insights on how to establish iterative variable screening methods. We plan to pursue this direction in future research.
Publications
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Marginal variable screening for survival endpoints. Biometrical Journal, 62(3), 610-626.
Edelmann, Dominic; Hummel, Manuela; Hielscher, Thomas; Saadati, Maral & Benner, Axel
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A global test for competing risks survival analysis. Statistical Methods in Medical Research, 29(12), 3666-3683.
Edelmann, Dominic; Saadati, Maral; Putter, Hein & Goeman, Jelle
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The distance standard deviation. The Annals of Statistics, 48(6).
Edelmann, Dominic; Richards, Donald & Vogel, Daniel
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A consistent version of distance covariance for right‐censored survival data and its application in hypothesis testing. Biometrics, 78(3), 867-879.
Edelmann, Dominic; Welchowski, Thomas & Benner, Axel
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A Regression Perspective on Generalized Distance Covariance and the Hilbert–Schmidt Independence Criterion. Statistical Science, 37(4).
Edelmann, Dominic & Goeman, Jelle
