FLCRM: Functional Linear Cox Regression Model

Abstract

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).

Functional Linear Regression Model for Nonignorable Missing Scalar Responses

“…Assumptions (A.1)–(A.9) have been widely used in the literature. Specifically, we can find assumptions similar to (A.1) and (A.2) in Crambles and André (2013), those similar to (A.3) and (A.4) in Hall and Horowitz (2007), those similar to (A.5) in Hall and Hosseini-Nasab (2006), those similar to (A.7) in Kong et al (2015), and those similar to Condition (A.9) in Tang et al (2014). Assumptions (A.6) and (A.8) are very weak since they require some mild conditions on E (‖ W ‖ 2 ) and normalEfalse[W−true∑j=1∞normalEfalse(Wξjfalse)ξjfalse]⊗2=normalEWWT−true∑j=1∞normalEfalse(Wξjfalse)normalEfalse(WTξjfalse).…”

Sex-specific Associations Between Serum Hemoglobin Levels and the Risk of Cause-specific Death in Korea Using the National Health Insurance Service-National Health Screening Cohort (NHIS HEALS)

“…We assessed non-linear associations between serum Hgb levels and the respective risk of death by various causes using cubic spline regression models. To evaluate the linearity and non-linearity of these relationships, we calculated overall and non-linear p -values [15,16]. When we visualized a non-linear pattern in an association between Hgb and cause-specific mortality, we additionally stratified the findings by sex.…”

Partial least squares for functional joint models with applications to the Alzheimer's disease neuroimaging initiative study

“…For example, AD and MCI patients were shown to have 27% and 11% smaller hippocampal volumes, respectively, as compared with normal controls (Du et al, 2001). Lee et al (2015) and Kong et al (2018) both demonstrated the predictive value of the hippocampus surface data to the progression of AD.…”

“…Please see Cardot et al (1999Cardot et al ( , 2003, Müller and Stadtmüller (2005), and the references therein for an extensive review of GFLM. Then, Yao et al (2005) extended GFLM to longitudinal data, and Lee et al (2015) and Kong et al (2018) both extended GFLM to the proportional hazards model. Some of the earliest work on joint models of longitudinal and time to event data is in Tsiatis et al (1995) and Wulfsohn and Tsiatis (1997).…”