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Computational and Mathematical Methods in Medicine
Volume 2017 (2017), Article ID 7847531, 18 pages
Research Article

Correcting Classifiers for Sample Selection Bias in Two-Phase Case-Control Studies

1Institute of Computational Biology, Helmholtz Zentrum München, German Research Center for Environmental Health, Munich, Germany
2Department of Mathematics, Technische Universität München, Munich, Germany

Correspondence should be addressed to Christiane Fuchs; ed.nehcneum-ztlohmleh@shcuf.enaitsirhc

Received 10 February 2017; Accepted 6 June 2017; Published 24 September 2017

Academic Editor: Matthias Schmid

Copyright © 2017 Norbert Krautenbacher et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Epidemiological studies often utilize stratified data in which rare outcomes or exposures are artificially enriched. This design can increase precision in association tests but distorts predictions when applying classifiers on nonstratified data. Several methods correct for this so-called sample selection bias, but their performance remains unclear especially for machine learning classifiers. With an emphasis on two-phase case-control studies, we aim to assess which corrections to perform in which setting and to obtain methods suitable for machine learning techniques, especially the random forest. We propose two new resampling-based methods to resemble the original data and covariance structure: stochastic inverse-probability oversampling and parametric inverse-probability bagging. We compare all techniques for the random forest and other classifiers, both theoretically and on simulated and real data. Empirical results show that the random forest profits from only the parametric inverse-probability bagging proposed by us. For other classifiers, correction is mostly advantageous, and methods perform uniformly. We discuss consequences of inappropriate distribution assumptions and reason for different behaviors between the random forest and other classifiers. In conclusion, we provide guidance for choosing correction methods when training classifiers on biased samples. For random forests, our method outperforms state-of-the-art procedures if distribution assumptions are roughly fulfilled. We provide our implementation in the R package sambia.