A censored quantile transformation model for Alzheimer’s Disease data with multiple functional covariates

Author:

Ma Shaopei1,Tang Man-lai2,Yu Keming3,Härdle Wolfgang Karl4,Wang Zhihao5,Xiong Wei1,Zhang Xueliang6,Wang Kai6,Zhang Liping6,Tian Maozai76ORCID

Affiliation:

1. School of Statistics, University of International Business and Economics , Beijing , China

2. Centre of Data Innovation Research, Department of Physics, Astronomy and Mathematics, School of Physics, Engineering and Computer Science, University of Hertfordshire , Hatfield , UK

3. Department of Mathematics, Brunel University London , Uxbridge , UK

4. Blockchain Research Center, Humboldt-Universität zu Berlin , Berlin , Germany

5. Institute of Statistics and Data Science, Xinjiang University of Finance and Economics , Urumqi , China

6. Department of Medical Engineering and Technology, Xinjiang Medical University , Urumqi , China

7. Center for Applied Statistics, School of Statistics, Renmin University of China , Beijing , China

Abstract

Abstract Alzheimer’s disease (AD) is a progressive disease that starts from mild cognitive impairment and may eventually lead to irreversible memory loss. It is imperative to explore the risk factors associated with the conversion time to AD that is usually right-censored. Classical statistical models like mean regression and Cox models fail to quantify the impact of risk factors across different quantiles of a response distribution, and previous research has primarily focused on modelling a single functional covariate, possibly overlooking the interdependence among multiple functional covariates and other crucial features of the distribution. To address these issues, this paper proposes a multivariate functional censored quantile regression model based on dynamic power transformations, which relaxes the global linear assumption and provides more robustness and flexibility. Uniform consistency and weak convergence of the quantile process are established. Simulation studies suggest that the proposed method outperforms the existing approaches. Real data analysis shows the importance of both left and right hippocampal radial distance curves for predicting the conversion time to AD at different quantile levels.

Funder

Fundamental Research Funds for the Central Universities

Research Matching

FDS

Research Grants Council of the Hong Kong Special Administration Region

Hang Seng University of Hong Kong

Natural Science Foundation of Xinjiang Uygur Autonomous Region

Publisher

Oxford University Press (OUP)

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