Regression analysis of additive hazards model with sparse longitudinal covariates

Sun, Zhuowei; Cao, Hongyuan; Chen, Li

doi:10.1007/s10985-022-09548-6

Cited by 2 publications

(1 citation statement)

References 24 publications

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“…(2015) and Chen and Cao (2017), the counting process is required to be independent of the response and the functional covariate in Assumption 1. The assumption of bounded

N_i(t, s)

is conventional in sparse longitudinal data (Diggle, 2002; Fan & Li, 2004; Lin et al., 2000; Sun et al., 2022). This differs from the dense setting where

L_i

and

M_i \rightarrow \infty

for all i .…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

Asynchronous Functional Linear Regression Models for Longitudinal Data in Reproducing Kernel Hilbert Space

Zhu

et al. 2022

Biometrics

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Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite‐sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).

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“…(2015) and Chen and Cao (2017), the counting process is required to be independent of the response and the functional covariate in Assumption 1. The assumption of bounded

N_i(t, s)

is conventional in sparse longitudinal data (Diggle, 2002; Fan & Li, 2004; Lin et al., 2000; Sun et al., 2022). This differs from the dense setting where