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

Abstract

Many biomedical studies have identified important imaging biomarkers that are associated with both repeated clinical measures and a survival outcome. The functional joint model (FJM) framework, proposed in Li and Luo (2017), investigates the association between repeated clinical measures and survival data, while adjusting for both high-dimensional images and low-dimensional covariates based upon the functional principal component analysis (FPCA).In this paper, we propose a novel algorithm for the estimation of FJM based on the functional partial least squares (FPLS). Our numerical studies demonstrate that, compared to FPCA, the proposed FPLS algorithm can yield more accurate and robust estimation and prediction performance in many important scenarios.We apply the proposed FPLS algorithm to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. Data used in the preparation of this article were obtained from the ADNI database.

Dynamic prediction with time‐dependent marker in survival analysis using supervised functional principal component analysis

“…and 0 otherwise, are fulfilled, k = 1, 2, 3. We then independently sample the scores according to 𝜆 i ∼ MVN(0, Σ), where Σ = diag (10,6,3). Given the set of true basis functions and scores, the longitudinal trajectory can be formulated according to the Karhunen-Loève expansion as,…”

“…Chen and Lei, 6 Lin et al, 7 and Nie and Cao 8 proposed to estimate FPCs which are only nonzero in a small interval in order to enhance the interpretability of FPCs. Other studies involving FPCA jointly with survival data can be found in Yan et al, 9 Wang et al, 10 and Jiang et al, 11 for example. However, FPCA does not consider the relationship between the functional predictor and the response variable.…”