Abstract

In clinical studies, assessing statistical associations between covariates and survival

outcomes is crucial.

To date, there has been no formally defined model-free correlation

coefficient for right-censored data that can measure the strength of associations. Traditional

methods, such as the Cox proportional hazards model, often struggle with the complexities

of non-monotonic or nonlinear relationships. This paper introduces a censored rank-based

correlation coefficient (CRC). It consistently estimates a new dependence measure—taking

values in [0, 1] and equaling 0 or 1 if and only if the variables are independent or one is a

measurable function of the other. The CRC is entirely model-free without depending on the

distributions of the variables. It facilitates quick computation with a complexity of O(n log n)

and can effectively detect nonlinear and non-monotonic effects, even under heavy censoring.

The p-values for testing independence can be obtained using a power-consistent permutation

method. The CRC shows strong consistency and asymptotic normality, outperforming the

Cox model and other methods in detecting nonlinear associations in both simulations and real

data from the Alzheimer’s Disease Neuroimaging Initiative, successfully identifying proteins

that existing methods fail to detect.

Key words and phrases: Chatterjee’s rank correlation; Nonparametric correlation; Right- censoring; Permutation test

Information

Preprint No.SS-2025-0207
Manuscript IDSS-2025-0207
Complete AuthorsLinlin Dai, Tengfei Li, Kani Chen
Corresponding AuthorsKani Chen
Emailsmakchen@ust.hk

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Acknowledgments

Data used in this paper were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within

the ADNI contributed to the design and implementation of ADNI and/or provided

data but did not participate in analysis or writing of this paper. A complete listing

of ADNI investigators can be found at http://adni.loni.usc.edu/wp-content/

uploads/how_to_apply/ADNI_Acknowledgement_List.pdf. Linlin Dai and Tengfei

Li contributed equally. Linlin Dai’s research was supported by the General Project of

Ministry of Education Foundation on Humanities and Social Sciences (Nos. 24YJC910001)

and the Sichuan Provincial Natural Science Foundation Project (Nos.

2025ZNS-

FSC0816). Kani Chen’s research was supported by the grants T32-615-24-R and

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Log Hazard Ratio

Log Hazard Ratio

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Normalized B7H1

Normalized VEGF

Figure 2: Nonlinear hazard function estimates for associations between survival time

and protein levels of B7H1 and VEGF in the Alzheimer’s Disease Neuroimaging

Initiative (ADNI) cohort. Protein levels were normalized to the interval [0, 1] for

visualizations.

Supplementary Materials

present technical proofs and additional simulation and

real data results.

Supplementary materials are available for download.