The aim of this paper is to develop a Bayesian functional linear Cox regression model (BFLCRM) with both functional and scalar covariates. This new development is motivated by establishing the likelihood of conversion to Alzheimer’s disease (AD) in 346 patients with mild cognitive impairment (MCI) enrolled in the Alzheimer’s Disease Neuroimaging Initiative 1 (ADNI-1) and the early markers of conversion. These 346 MCI patients were followed over 48 months, with 161 MCI participants progressing to AD at 48 months. The functional linear Cox regression model was used to establish that functional covariates including hippocampus surface morphology and scalar covariates including brain MRI volumes, cognitive performance (ADAS-Cog) and APOE-$\varepsilon4$ status can accurately predict time to onset of AD. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of BFLCRM.
"BFLCRM: A Bayesian functional linear Cox regression model for predicting time to conversion to Alzheimer’s disease." Ann. Appl. Stat. 9 (4) 2153 - 2178, December 2015. https://doi.org/10.1214/15-AOAS879