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Adjustments of multi-sample U-statistics to right censored data and confounding covariates

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  • Chen, Yichen
  • Datta, Somnath

Abstract

U-statistics that can be used for comparing distribution of outcomes in two groups are considered. Adjustments to the classical U-statistics are proposed for overcoming potential biases arising from right-censoring of the outcomes and presence of confounding covariates. These newly proposed U-statistics are appropriate when, in addition to right censored outcomes, some fixed covariates are observed and deemed as confounders in an observational study. The summands of U-statistics are re-weighted and normalized based on a combination of inverse probability of censoring weights and propensity score based weights. Censoring times may depend on the group membership, confounders or some potentially observed time-dependent covariates, which may result in censoring mechanisms of varying degrees of complexity. In total, four censoring mechanisms are considered for the two-group comparison. Simulation results are used to illustrate the impact of right-censoring and confounding covariates on the performance of the newly proposed U-statistics under different censoring mechanisms. It is also demonstrated that large sample inferences for the adjusted U-statistics are valid using jackknife variance estimator. Comparisons of more than two groups are also considered from certain ways of pairwise two-group comparisons. The procedure is applied to analyze two real data sets for comparing two or more groups of event times. R codes of our procedure are available under supplementary material.

Suggested Citation

  • Chen, Yichen & Datta, Somnath, 2019. "Adjustments of multi-sample U-statistics to right censored data and confounding covariates," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 1-14.
    • Handle: RePEc:eee:csdana:v:135:y:2019:i:c:p:1-14
    DOI: 10.1016/j.csda.2019.01.012
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    References listed on IDEAS

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    1. Somnath Datta & Dipankar Bandyopadhyay & Glen A. Satten, 2010. "Inverse Probability of Censoring Weighted U‐statistics for Right‐Censored Data with an Application to Testing Hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 680-700, December.
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    Cited by:

    1. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    2. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.

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