Abstract

In recent years, there has been growing interest among researchers in

modeling right-censored survival data with functional covariates. While existing

functional methods primarily focus on the Cox model, its proportional hazards

assumption can be challenging to verify and may be violated in practice. To address this issue, we extend the ordinary differential equation (ODE) framework

for survival data to incorporate functional covariates and develop an inference

procedure for both scalar and functional parameters. Specifically, we establish

asymptotic normality and semiparametric efficiency for the scalar coefficient estimators, enabling a valid inference procedure. Additionally, we derive an asymp-

totic simultaneous confidence band for the functional parameter. Simulations are

conducted to evaluate the finite sample performance of the proposed method.

Information

Preprint No.SS-2024-0180
Manuscript IDSS-2024-0180
Complete AuthorsHongyi Zhou, Wenqing Su, Qixian Zhong, Ying Yang
Corresponding AuthorsHongyi Zhou
Emailszhouhongyi99@126.com

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Acknowledgments

The authors would like to thank the editor, the associate editor and the two

reviewers for their constructive and insightful comments that greatly improved this article. Zhong’s research was supported by National Key R&D

Program of China (1003800, 1015600), the National Natural Science Foundation of China grant (12201527). Yang’s research was supported by the

National Natural Science Foundation of China grant (12271286, 11931001).

Supplementary Materials

contain implementation details of our estimators,

some additional simulation results and the auxiliary lemmas and technical

proofs for propositions and theorems of the paper.

8.

Supplementary materials are available for download.