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A non-parametric U-statistic testing approach for multi-arm clinical trials with multivariate longitudinal data

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  • Ghosh, Dhrubajyoti
  • Luo, Sheng

Abstract

Randomized clinical trials (RCTs) often involve multiple longitudinal primary outcomes to comprehensively assess treatment efficacy. The Longitudinal Rank-Sum Test (LRST) Xu et al. (2025), a robust U-statistics-based, non-parametric, rank-based method, effectively controls Type I error and enhances statistical power by leveraging the temporal structure of the data without relying on distributional assumptions. However, the LRST is limited to two-arm comparisons. To address the need for comparing multiple doses against a control group in many RCTs, we extend the LRST to a multi-arm setting. This novel multi-arm LRST provides a flexible and powerful approach for evaluating treatment efficacy across multiple arms and outcomes, with a strong capability for detecting the most effective dose in multi-arm trials. Extensive simulations demonstrate that this method maintains excellent Type I error control while providing greater power compared to the two-arm LRST with multiplicity adjustments. Application to the Bapineuzumab (Bapi) 301 trial further validates the multi-arm LRST’s practical utility and robustness, confirming its efficacy in complex clinical trial analyses.

Suggested Citation

  • Ghosh, Dhrubajyoti & Luo, Sheng, 2025. "A non-parametric U-statistic testing approach for multi-arm clinical trials with multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:jmvana:v:209:y:2025:i:c:s0047259x25000429
    DOI: 10.1016/j.jmva.2025.105447
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    References listed on IDEAS

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    1. Victor H. Lachos & Dipankar Bandyopadhyay & Dipak K. Dey, 2011. "Linear and Nonlinear Mixed-Effects Models for Censored HIV Viral Loads Using Normal/Independent Distributions," Biometrics, The International Biometric Society, vol. 67(4), pages 1594-1604, December.
    2. Edgar Brunner & Frank Konietschke & Markus Pauly & Madan L. Puri, 2017. "Rank-based procedures in factorial designs: hypotheses about non-parametric treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1463-1485, November.
    3. Lu, Zeng-Hua, 2013. "Halfline tests for multivariate one-sided alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 479-490.
    4. Umlauft, Maria & Placzek, Marius & Konietschke, Frank & Pauly, Markus, 2019. "Wild bootstrapping rank-based procedures: Multiple testing in nonparametric factorial repeated measures designs," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 176-192.
    5. Peng Huang & Barbara C. Tilley & Robert F. Woolson & Stuart Lipsitz, 2005. "Adjusting O'Brien's Test to Control Type I Error for the Generalized Nonparametric Behrens–Fisher Problem," Biometrics, The International Biometric Society, vol. 61(2), pages 532-539, June.
    6. Wei Zhang & Aiyi Liu & Larry L. Tang & Qizhai Li, 2019. "A cluster‐adjusted rank‐based test for a clinical trial concerning multiple endpoints with application to dietary intervention assessment," Biometrics, The International Biometric Society, vol. 75(3), pages 821-830, September.
    7. Liu, Aiyi & Li, Qizhai & Liu, Chunling & Yu, Kai & Yu, Kai F., 2010. "A Rank-Based Test for Comparison of Multidimensional Outcomes," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 578-587.
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