Sage Journals: Discover world-class research

Abstract

Missing data is a common issue in many biomedical studies. Under a paired design, some subjects may have missing values in either one or both of the conditions due to loss of follow-up, insufficient biological samples, etc. Such partially paired data complicate statistical comparison of the distribution of the variable of interest between the two conditions. In this article, we propose a general class of test statistics based on the difference in weighted sample means without imposing any distributional or model assumption. An optimal weight is derived from this class of tests. Simulation studies show that our proposed test with the optimal weight performs well and outperforms existing methods in practical situations. Two cancer biomarker studies are provided for illustration.

Keywords

Paired data missing data biomarker data nonparametric tests mean difference tests

Get full access to this article

View all access options for this article.

References

Plattner

Rangnekar

, et al. Potential protein markers for breast cancer recurrence: a retrospective cohort study. Cancer Causes Control 2019; 30: 41–51.

Little

Rubin

. Statistical analysis with missing data. 793. Hoboken, NJ: John Wiley & Sons, 2019.

Dubnicka

Blair

Hettmansperger

. Rank-based procedures for mixed paired and two-sample designs. J Mod Appl Stat Methods 2002; 1: 6.

Brunner

Domhof

Langer

. Nonparametric analysis of longitudinal data in factorial experiments. New York: Wiley, 2002.

Konietschke

Harrar

Lange

, et al. Ranking procedures for matched pairs with missing data-asymptotic theory and a small sample approximation. Comput Stat Data Anal 2012; 56: 1090–1102.

Fong

Huang

Lemos

, et al. Rank-based two-sample tests for paired data with missing values. Biostatistics 2018; 19: 281–294.

Bhoj

. Testing equality of means of correlated variates with missing observations on both responses. Biometrika 1978; 65: 225–228.

Martínez-Camblor

Corral

María de la Hera

. Hypothesis test for paired samples in the presence of missing data. J Appl Stat 2013; 40: 76–87.

Kuan

Huang

. A simple and robust method for partially matched samples using the p-values pooling approach. Stat Med 2013; 32: 3247–3259.

10.

Yan

Tian

. Testing equality of means in partially paired data with incompleteness in single response. Stat Methods Med Res 2019; 28: 1508–1522.

11.

Yan

Tian

. Analyzing partially paired data: when can the unpaired portion(s) be safely ignored? J Appl Stat 2022; 49: 1402–1420.

12.

Pinheiro

Bates

DebRoy

, et al. nlme: Linear and nonlinear mixed effects models. R Foundation for Statistical Computing, Vienna, Austria, 2021. https://CRAN.R-project.org/package=nlme. R package version 3.1-153.

13.

Fong

. robustrank: robust rank-based tests. R Foundation for Statistical Computing, Vienna, Austria, 2020. https://cran. r-project.org/web/packages/robustrank/index.html. R package version 2019.9-10.

14.

Christensen

RHB

. A tutorial on fitting cumulative link mixed models with clmm2 from the ordinal package, 2019. https://cran.r-project.org/web/packages/ordinal/vignettes/clmm2˙tutorial.pdf.

15.

Little

. A test of missing completely at random for multivariate data with missing values. J Am Stat Assoc 1988; 83: 1198–1202.

16.

Tierney

Cook

McBain

, et al. Data structures, summaries, and visualisations for missing data. R Foundation for Statistical Computing, Vienna, Austria, 2021. https://CRAN.R-project.org/package=naniar. R package version 0.6.1.

17.

Komsta

. outliers: Tests for outliers. R Foundation for Statistical Computing, Vienna, Austria, 2015. https://CRAN. R-project.org/package=outliers. R-package version 0.14.

18.

Van der Vaart

Wellner

. Weak convergence and empirical processes: with applications to statistics. New York: Springer Science & Business Media, 1996.

19.

Van der Vaart

. Asymptotic statistics. 3. New York: Cambridge University Press, 1998.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.07 MB