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Estimation of the Mann–Whitney effect in the two-sample problem under dependent censoring

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  • Emura, Takeshi
  • Hsu, Jiun-Huang

Abstract

The Mann–Whitney effect is a nonparametric measure for comparing the distribution between two groups, which can be estimated by right-censored data. However, the traditional estimator of the Mann–Whitney effect based on the Kaplan–Meier estimators can be inconsistent when the independent censoring assumption fails to hold. Investigation is made on the asymptotic bias of the traditional estimator of the Mann–Whitney effect when the independent censoring assumption is violated due to dependence between survival time and censoring time. A new estimator of the Mann–Whitney effect is proposed by applying the copula-graphic estimator to adjust for the effect of dependent censoring. The proposed estimator and test are consistent when the assumed copulas for the two groups are correct. Some consistency properties under misspecified copulas are also given. Simulations are conducted to verify the proposed method under possible misspecification on copulas. The method is illustrated by a real data set. We provide an R function “MW.test” to implement the proposed estimator and test.

Suggested Citation

  • Emura, Takeshi & Hsu, Jiun-Huang, 2020. "Estimation of the Mann–Whitney effect in the two-sample problem under dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:csdana:v:150:y:2020:i:c:s0167947320300815
    DOI: 10.1016/j.csda.2020.106990
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    References listed on IDEAS

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    1. Deresa, Negera Wakgari & Van Keilegom , Ingrid, 2020. "Flexible parametric model for survival data subject to dependent censoring," LIDAM Reprints ISBA 2020043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    7. Takeshi Emura & Chi-Hung Pan, 2020. "Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach," Statistical Papers, Springer, vol. 61(1), pages 479-501, February.
    8. Dennis Dobler & Markus Pauly, 2018. "Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 639-658, September.
    9. Deresa, Negera Wakgari & Van Keilegom, Ingrid, 2020. "A multivariate normal regression model for survival data subject to different types of dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. T. Emura & K. Murotani, 2015. "An algorithm for estimating survival under a copula-based dependent truncation model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 734-751, December.
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