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Machine Learning for Two-Sample Testing under Right-Censored Data: A Simulation Study

Petr Philonenko, Sergey Postovalov

TL;DR

This paper presents the results of training the proposed ML methods, examines their statistical power compared to classical two-sample tests, analyzes the null distribution of the proposed methods when the null hypothesis is true, and evaluates the significance of the features incorporated into the proposed methods.

Abstract

The focus of this study is to evaluate the effectiveness of Machine Learning (ML) methods for two-sample testing with right-censored observations. To achieve this, we develop several ML-based methods with varying architectures and implement them as two-sample tests. Each method is an ensemble (stacking) that combines predictions from classical two-sample tests. This paper presents the results of training the proposed ML methods, examines their statistical power compared to classical two-sample tests, analyzes the null distribution of the proposed methods when the null hypothesis is true, and evaluates the significance of the features incorporated into the proposed methods. In total, this work covers 18 methods for two-sample testing under right-censored observations, including the proposed methods and classical well-studied two-sample tests. All results from numerical experiments were obtained from a synthetic dataset generated using the inverse transform sampling method and replicated multiple times through Monte Carlo simulation. To test the two-sample problem with right-censored observations, one can use the proposed two-sample methods (scripts, dataset, and models are available on GitHub and Hugging Face).

Machine Learning for Two-Sample Testing under Right-Censored Data: A Simulation Study

TL;DR

This paper presents the results of training the proposed ML methods, examines their statistical power compared to classical two-sample tests, analyzes the null distribution of the proposed methods when the null hypothesis is true, and evaluates the significance of the features incorporated into the proposed methods.

Abstract

The focus of this study is to evaluate the effectiveness of Machine Learning (ML) methods for two-sample testing with right-censored observations. To achieve this, we develop several ML-based methods with varying architectures and implement them as two-sample tests. Each method is an ensemble (stacking) that combines predictions from classical two-sample tests. This paper presents the results of training the proposed ML methods, examines their statistical power compared to classical two-sample tests, analyzes the null distribution of the proposed methods when the null hypothesis is true, and evaluates the significance of the features incorporated into the proposed methods. In total, this work covers 18 methods for two-sample testing under right-censored observations, including the proposed methods and classical well-studied two-sample tests. All results from numerical experiments were obtained from a synthetic dataset generated using the inverse transform sampling method and replicated multiple times through Monte Carlo simulation. To test the two-sample problem with right-censored observations, one can use the proposed two-sample methods (scripts, dataset, and models are available on GitHub and Hugging Face).
Paper Structure (19 sections, 26 equations, 4 figures, 5 tables)

This paper contains 19 sections, 26 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Materials & Methods
  4. Problem Statement
  5. Two-Sample Tests
  6. Log-rank test
  7. Generalizations of Wilcoxon test
  8. Weighted tests
  9. Bagdonavičius-Nikulin tests
  10. Two-Stage tests
  11. Proposed ML-based Methods for Two Sample Problem
  12. Alternative Hypotheses
  13. Numerical Experiments
  14. Dataset
  15. Proposed Methods Training
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Implementation flow chart of the proposed methods
  • Figure 2: Groups of alternative hypotheses
  • Figure 3: Average rank (AVG) of tests including the Wald and Savage criteria on the groups $H_{\text{I}}-H_{\text{IX}}$
  • Figure 4: $G(S|H_0)$ distributions for the proposed methods. White line is the middle line. Color stripe is the region between minorant and majorant.