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

arXiv: https://arxiv.org/abs/2408.10149 · HTML: https://mlsanity.com/paper/2408.10149/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2024.

## Built on by (most cited first, 1 of 1)

- [Integrating Causal Inference with Graph Neural Networks for Alzheimer's Disease Analysis](https://mlsanity.com/paper/2511.14922/) (2025)

## Abstract (arXiv)

Randomized clinical trials (RCTs) often involve multiple longitudinal primary outcomes to comprehensively assess treatment efficacy. The Longitudinal Rank-Sum Test (LRST), 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.