An important class of prediction problems in modern biomedical studies is to use medical images as well as genetic and clinical biomarkers at an earlier time point to predict important clinical outcomes, including continuous, discrete, survival and longitudinal outcomes, at a later time point. Functional regression is one of the statistical models to handle this problem by treating medical images as smooth functions. An appealing way is the functional partial least squares method (FPLS). Delaigle and Hall (2011) further developed an alternative FPLS algorithm (APLS) for simple functional linear models. The aim of this work is to extend APLS methods to a wider class of functional models. In the first part, we extend the APLS algorithm to functional partial linear model (FPLM) including both functional and scalar predictors, denoted as RAPLS algorithm. Then the RAPLS algorithm is extended for generalized functional linear models (GFLM) to handle discrete outcomes by integrating the FPLS method with the algorithm of iteratively reweighted least squares (IRLS). Simulation studies are used to examine the finite sample performance of the proposed RAPLS algorithms. We also illustrate our method in the analysis of the Alzheimer Disease Neuroimaging Initiative (ADNI) dataset to predict continuous Alzheimer’s Disease Assessment Scale (ADAS) cognitive score. We also systematically carried out theoretical analysis for the RAPLS algorithm. In the second part, we further extend the RAPLS method to functional linear cox regression model (FLCRM) for the prediction of censored survival outcomes, denoted as CoxRAPLS algorithm. Simulation studies are used to examine the finite sample performance of the CoxRAPLS algorithm, which is also demonstrated in ADNI to predict the time of conversion from mild cognition impairment (MCI) diagnosis to Alzheimer’s Disease (AD) diagnosis. Finally, we propose a functional joint model (FJM) framework to assess the association between longitudinal trajectory and survival outcome while adjusting for functional and scalar predictors. We propose a two-step JMRAPLS algorithm which integrates RAPLS method with EM algorithm for FJM. We conduct both simulation studies and real data analysis in ADNI to examine finite sample performance of the JMRAPLS algorithm.