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

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.