Joint linear and nonlinear mixed effects model with random change points for left-censored longitudinal data: application to HIV surveillance

A change-point model is useful for longitudinal data to infer the time to an event that induces a change of trajectory within the study period. We present a random change-point model that fits the linear and non-linear mixed effects for pre- and post-change-points, respectively. We address the left-censored observations in the model. The stochastic approximation expectation maximization (SAEM) with the Metropolis Hastings sampler is used to fit the random change-point non-linear mixed effects model. We apply our method to the viral load (VL) longitudinal data reported to the HIV surveillance registry in New York City. We evaluate the model with a data simulation.