# Functional Censored Quantile Regression for Investigating Heterogeneous Effects in Survival Data

> **NIH NIH R03** · UNIVERSITY OF LOUISVILLE · 2021 · $78,000

## Abstract

Project Summary/Abstract
Functional biomarkers that are in the form of curves, images, and objects, are often collected in biomedical studies
nowadays, due to the rapid advances in data acquisition technology. In recent research, there has been growing
awareness that the underlying association between the functional biomarkers and outcomes may be prone to
considerable heterogeneity. Those heterogeneous associations often shed insight on scientific discoveries and
entail significant implications, but tend to be overlooked by many existing functional data analysis procedures with
a narrow focus on the response mean. Our proposal aims at offering researchers alternative tools to explore the
comprehensive information of the relationship between functional biomarkers and survival time.
 In contrast to statistical models that presume constant effects of covariates, quantile regression (QR) ac-
commodates varying effects and may reveal more detailed dependence structure of outcomes on covariates.
Regretfully, QR for functional data has barely been studied. The objective of this proposal is to make the QR
framework applicable for investigating the regression heterogeneity in functional survival data, to develop reliable
and efficient estimation approaches, and to obtain sharp inference on the effects of functional biomarkers. We
will propose a “local” functional censored QR (FCQR) method to evaluate the impacts of functional biomarkers
on the survival time at a single or multiple pre-specified quantile levels and develop a related significance test for
testing the impact of functional biomarkers (Aim 1). Then we will develop a “global” FCQR method to investigate
the varying effects of functional biomarkers on the survival time over a region of quantile levels, which will provide
researchers with a comprehensive picture about the covariates-response association. In addition, two inference
procedures, including a bootstrap resampling method for estimating the standard errors and the martingale-based
model diagnostics, will be developed (Aim 2). Moreover, we will extend the “local” FCQR method to longitudi-
nal measurements of functional biomarkers for dynamic prediction of residual life (Aim 3). Also, we will develop
statistical software that efficiently implements the proposed methods.
 The innovation of our proposal is at least three-fold. Firstly, it will produce reliable and efficient FCQR tools
that facilitate the identification and evaluation of new valuable functional biomarkers. Secondly, the successful
completion of my proposal can significantly advance the theory of QR and semi/non-parametric statistics, and
further, broaden their applications in lots of biomedical research. Thirdly, our proposed methods will also serve
as a flexible platform for examining the heterogeneity in functional data. They can be readily extended to other
public health applications.

## Key facts

- **NIH application ID:** 10164703
- **Project number:** 5R03AG067611-02
- **Recipient organization:** UNIVERSITY OF LOUISVILLE
- **Principal Investigator:** Qi Zheng
- **Activity code:** R03 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2021
- **Award amount:** $78,000
- **Award type:** 5
- **Project period:** 2020-05-15 → 2022-01-31

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/10164703

## Citation

> US National Institutes of Health, RePORTER application 10164703, Functional Censored Quantile Regression for Investigating Heterogeneous Effects in Survival Data (5R03AG067611-02). Retrieved via AI Analytics 2026-05-24 from https://api.ai-analytics.org/grant/nih/10164703. Licensed CC0.

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