Functional partial least squares with censored outcomes: Prediction of breast cancer risk with mammogram images

We consider the problem of predicting breast cancer risk using mammogram imaging data where the dimension of pixels greatly exceed the number of individuals in the cohort. The functional partial least squares (FPLS) is a popular dimensional reduction method in constructing latent explanatory components using linear combinations of the original predictor variables. While FPLS with scalar responses has been studied in the literature, the presence of right censoring under the survival framework poses challenges in modeling and estimation. Given several different representations for PLS with Cox regression in the literature, we unify and extend three formulations to deal with right censoring, that is, reweighing, mean imputation, and deviance residuals to the functional setting in this paper. We empirically investigate and compare the performance of the three proposed FPLS frameworks in the context of imaging predictor via intensive simulation studies. The proposed methods are applied to the Joanne Knight Breast Health Cohort where we show increased model discriminatory performance under the FPLS framework compared to competing models.