Asymptotic based bootstrap approach for matched pairs with missingness in a single-arm

TL;DR

This paper introduces an asymptotic bootstrap method for matched pairs with missing data in only one arm, providing robust tests under heteroscedasticity and skewed distributions, validated through simulations and a real breast cancer study.

Contribution

It develops a novel resampling test approach specifically for single-arm missingness in matched pairs, addressing a gap in existing methods.

Findings

The proposed tests maintain correct size under various missingness mechanisms.

Simulations show robustness under heteroscedasticity and skewness.

Application to breast cancer data demonstrates practical utility.

Abstract

The issue of missing values is an arising difficulty when dealing with paired data. Several test procedures are developed in the literature to tackle this problem. Some of them are even robust under deviations and control type-I error quite accurately. However, most these methods are not applicable when missing values are present only in a single arm. For this case, we provide asymptotic correct resampling tests that are robust under heteroscedasticity and skewed distributions. The tests are based on a clever restructuring of all observed information in a quadratic form-type test statistic. An extensive simulation study is conducted exemplifying the tests for finite sample sizes under different missingness mechanisms. In addition, an illustrative data example based on a breast cancer gene study is analyzed.