Regression and subgroup detection for heterogeneous samples

Abstract

Regression analysis of heterogeneous samples with subgroup structure is essential to the development of precision medicine. In practice, this task is often challenging owing to the lack of prior knowledge of subgroup labels. Therefore, detecting the subgroups with similar characteristics becomes critical, which often controls the accuracy of regression analysis. In this article, we investigate a new framework for detecting the subgroups that have similar characters in feature space and similar treatment effects. The key idea is that we incorporate K-means clustering into the regression framework of concave pairwise fusion, so that the regression and subgroup detection tasks can be performed simultaneously. Our method is specifically tailored for handling the situations where the sample is not homogeneous in the sense that the response variables in different domains of feature space are generated through different mechanisms.

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Acknowledgements

The authors thank AE and two anonymous reviewers for their helpful comments and valuable suggestions on earlier versions of this article. The authors also thank professor Shujie Ma for her constructive comments on our work during the meeting at LICAS 2019. This research was supported by the Fundamental Research Funds for the Central Universities, Beijing Natural Science Foundation (No. 1204031), and the National Natural Science Foundation of China (No. 11901013).

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Correspondence to Yanping Qiu.

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Liang, B., Wu, P., Tong, X. et al. Regression and subgroup detection for heterogeneous samples. Comput Stat 35, 1853–1878 (2020). https://doi.org/10.1007/s00180-020-00965-5

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Keywords

  • Concave fusion
  • Heterogeneous problem
  • K-means clustering
  • Regression
  • Subgroup detection