Longitudinal First hitting-time Regression Models with Extension to Neural Network

Abstract

Disease progression in a patient can be described mathematically as a stochastic process. The patient experiences a failure event when his/her disease progression first reaches a critical threshold level. This happening defines the failure event itself and the first hitting time (FHT) is the event time. First hitting- time based threshold regression models incorporate regression functions for parameters of the underlying stochastic process. The FHT model is extended to the Levy family with stationary independent increments and a cumulant generating function. Extension to neural network applications will also be discussed.

Keywords: Levy processes, non-proportional hazards, Wiener processes.