Abstract

A time-dependent covariate (e.g., time-varying treatment or exposure) is often encountered in

survival studies within biomedical research. The varying nature of the time-dependent covariate, evolving

alongside the survival outcome, poses extra complications in assessing the covariate-survival association.

In this work, we propose a new nonparametric testing framework that is designed to robustly evaluate the

effect of a time-dependent covariate on a survival outcome. By adopting the landmark perspective and

utilizing a generalized interval quantile correlation index, our testing procedure does not require parametric or semiparametric modeling of the relationship between the time-dependent covariate and the survival

outcome, while flexibly accommodating dynamic covariate effects on the survival outcome. We provide

theoretical justifications for our proposals. The new method is applied to probe the effect of time-varying

breastmilk and infant formula feeding patterns on a key pulmonary outcome of young children with cystic

fibrosis in their first 3 years of life.

Key words and phrases: Landmark analysis; Nonparametric hypothesis testing; Survival outcome; Time- dependent covariate

Information

Preprint No.SS-2025-0478
Manuscript IDSS-2025-0478
Complete AuthorsYing Cui, HuiChuan Lai, Limin Peng
Corresponding AuthorsLimin Peng
Emailslpeng@emory.edu

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Acknowledgments

We sincerely thank the FIRST cohort of children and their families for participating in our

longitudinal study, as well as the funding support from the National Institutes of Health grants

(R01HL113548, R01DK136023, R01DK072126, R01DK109692, and R56DK109692) and

the US Cystic Fibrosis Foundation (LAI14A0, LAI15A0 and LAI17A0).

Supplementary Materials

available online includes technical proofs.