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Model-free Feature Screening via Revised Chatterjee's Rank Correlation for Ultra-high Dimensional Censored Data

Shuya Chen, Heng Peng, Min Zhou

Abstract

In large-scale biomedical research, it's common to gather ultra-high dimensional data that includes right-censored survival times. Feature screening has emerged as a crucial statistical technique for handling such data. In this paper, we introduce a straightforward and robust feature screening approach, leveraging the modified Chatterjee's rank correlation, suitable for a broad range of survival models. With reasonably mild regularity assumptions, we establish the properties of sure screening and ranking consistency. The computation involved in our proposed method is quite direct and simple. Through simulation studies and real gene expression data analysis, we demonstrate the superior efficacy of our proposed approach.

Model-free Feature Screening via Revised Chatterjee's Rank Correlation for Ultra-high Dimensional Censored Data

Abstract

In large-scale biomedical research, it's common to gather ultra-high dimensional data that includes right-censored survival times. Feature screening has emerged as a crucial statistical technique for handling such data. In this paper, we introduce a straightforward and robust feature screening approach, leveraging the modified Chatterjee's rank correlation, suitable for a broad range of survival models. With reasonably mild regularity assumptions, we establish the properties of sure screening and ranking consistency. The computation involved in our proposed method is quite direct and simple. Through simulation studies and real gene expression data analysis, we demonstrate the superior efficacy of our proposed approach.

Paper Structure

This paper contains 8 sections, 5 theorems, 51 equations, 11 tables.

Table of Contents

  1. Introduction
  2. Methodologies and main results
  3. The correlation $\xi$ and revised Chatterjee’s rank correlation $\xi_{n,M}$
  4. Revised Chatterjee’s rank correlation screening
  5. Simulation Study
  6. Real Data Analysis
  7. Conclusion and Discussion
  8. Proof of Main Theorems

Key Result

Theorem 2.1

Under condition (C1), there exists a positive constant $\Gamma >0$, such that Under Condition (C2), we have where $s=|\mathcal{A}|$ is the cardinality of $\mathcal{A}$.

Theorems & Definitions (14)

  • Theorem 2.1: Sure screening property
  • Theorem 2.2: Controlling false discoveries
  • Theorem 2.3
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Lemma A.1
  • proof : Proof of Lemma \ref{['lemma.1']}:
  • Lemma A.2
  • ...and 4 more