Models for Degradation Processes and Event Times Based on Gaussian Processes

We present two stochastic models that describe the relationship between marker process values at random time points, event times, and a vector of covariates. In both models the marker processes are degradation processes that represent the decay of systems over time. In the first model the degradation process is a Wiener process whose drift is a function of the covariate vector; in the second model the degradation process is taken to be the difference between a stationary Gaussian process and a time drift whose drift parameter is a function of the covariates. For both models we present statistical methods for estimation of the regression coefficients. The first model is useful for predicting the residual time from study entry to the time a critical boundary is reached while the second model is useful for predicting the latency time from the event initiating degradation until the time the presence of degradation is detected. We present our methods principally in the context of conducting inference in a population of HIV infected individuals.