Score Test for Functional Markov Process With Image Predictor

A functional multistate model is presented, which accommodates Markov processes governing disease transition in a finite set of states. Importantly, we consider a setting where the set of predictors contains a high-dimensional image with the goal of quantifying the association between the image and the transition of disease states. In the motivating application of breast cancer, women start from normal breast tissue, go through benign lesions, and then to the onset of DCIS/invasive cancer. As in the real data application, we consider the setting in which the individuals are observed intermittently and the transition times are interval censored. A score test is developed to test the nullity of the coefficient function for the image predictor at different transitions between states. The asymptotic distribution of the score statistic is provided. An application involving progression to the development of breast cancer with mammogram image data provides illustration. Our results demonstrate an important association between the mammogram image and the probability of transition in breast cancer.