Cox regression models with functional covariates for survival data

Gellar, Jonathan; Colantuoni, Elizabeth; Crainiceanu, Ciprian M.

doi:10.1177/1471082x14565526

Cited by 28 publications

(54 citation statements)

References 60 publications

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“…To build the functional regression model, we adopt a penalized approach to incorporate functional components into functional predictor regression model 14,16 . We first express the time-invariant functional predictor

g_{i}^{(x)} (s)

in model (1) using the Karhunen-Loève decomposition.…”

Section: Methodsmentioning

confidence: 99%

“…Gertheiss et al 15 improved the longitudinal model to allow for different effects of subject-specific curves. More recently, Gellar et al 16 extended the Cox proportional hazards model to incorporate functional predictors and estimated the parameters via penalized partial likelihood approach. Lee et al 17 developed a Bayesian functional Cox regression model with both functional and scalar covariates, but used different regularization approaches.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic predictions in Bayesian functional joint models for longitudinal and time-to-event data: An application to Alzheimer’s disease

Luo

2017

Stat Methods Med Res

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In the study of Alzheimer’s disease (AD), researchers often collect repeated measurements of clinical variables, event history, and functional data. If the health measurements deteriorate rapidly, patients may reach a level of cognitive impairment and are diagnosed as having dementia. An accurate prediction of the time to dementia based on the information collected is helpful for physicians to monitor patients’ disease progression and to make early informed medical decisions. In this article, we first propose a functional joint model (FJM) to account for functional predictors in both longitudinal and survival submodels in the joint modeling framework. We then develop a Bayesian approach for parameter estimation and a dynamic prediction framework for predicting the subjects’ future outcome trajectories and risk of dementia, based on their scalar and functional measurements. The proposed Bayesian FJM provides a flexible framework to incorporate many features both in joint modeling of longitudinal and survival data and in functional data analysis. Our proposed model is evaluated by a simulation study and is applied to the motivating Alzheimer’s Disease Neuroimaging Initiative (ADNI) study.

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g_{i}^{(x)} (s)

in model (1) using the Karhunen-Loève decomposition.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic predictions in Bayesian functional joint models for longitudinal and time-to-event data: An application to Alzheimer’s disease

Luo

2017

Stat Methods Med Res

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show abstract

“…More recently, Gellar et al. extended the Cox proportional hazards model to incorporate functional predictors and estimated the parameters via penalized partial likelihood approach. Lee et al.…”

Section: Introductionmentioning

confidence: 99%

Functional joint model for longitudinal and time-to-event data: an application to Alzheimer's disease

Luo

2017

Statist. Med.

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Functional data are increasingly collected in public health and medical studies to better understand many complex diseases. Besides the functional data, other clinical measures are often collected repeatedly. Investigating the association between these longitudinal data and time to a survival event is of great interest to these studies. In this article, we develop a functional joint model (FJM) to account for functional predictors in both longitudinal and survival submodels in the joint modeling framework. The parameters of FJM are estimated in a maximum likelihood framework via EM algorithm. The proposed FJM provides a flexible framework to incorporate many features both in joint modeling of longitudinal and survival data and in functional data analysis. The FJM is evaluated by a simulation study and is applied to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study, a motivating clinical study testing whether serial brain imaging, clinical and neuropsychological assessments can be combined to measure the progression of Alzheimer’s disease.

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“…Gellar et al. () and Qu et al. () proposed to maximize penalized partial likelihood functions for model , whereas Lee et al.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, Gellar et al. () combined penalized signal regression with methods developed for mixed effects proportional hazards models under penalized B‐spline framework, and Qu et al. () estimated the model under the reproducing kernel Hilbert space framework.…”

Section: Introductionmentioning

confidence: 99%

FLCRM: Functional Linear Cox Regression Model

et al. 2017

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Summary We consider a functional linear Cox regression model for characterizing the association between time-to-event data and a set of functional and scalar predictors. The functional linear Cox regression model incorporates a functional principal component analysis for modeling the functional predictors and a high-dimensional Cox regression model to characterize the joint effects of both functional and scalar predictors on the time-to-event data. We develop an algorithm to calculate the maximum approximate partial likelihood estimates of unknown finite and infinite dimensional parameters. We also systematically investigate the rate of convergence of the maximum approximate partial likelihood estimates and a score test statistic for testing the nullity of the slope function associated with the functional predictors. We demonstrate our estimation and testing procedures by using simulations and the analysis of the Alzheimer’s Disease Neuroimaging Initiative (ADNI) data. Our real data analyses show that high-dimensional hippocampus surface data may be an important marker for predicting time to conversion to Alzheimer’s disease. Data used in the preparation of this article were obtained from the ADNI database (adni.loni.usc.edu).

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Cox regression models with functional covariates for survival data

Cited by 28 publications

References 60 publications

Dynamic predictions in Bayesian functional joint models for longitudinal and time-to-event data: An application to Alzheimer’s disease

Dynamic predictions in Bayesian functional joint models for longitudinal and time-to-event data: An application to Alzheimer’s disease

Functional joint model for longitudinal and time-to-event data: an application to Alzheimer's disease

FLCRM: Functional Linear Cox Regression Model

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