Nonlinear mixed-effects HIV dynamic models with considering left-censored measurements

HIV dynamic model offers a different perspective of studying HIV pathogenesis and developing treatment strategies for AIDS patients. Many HIV dynamic models have recently been developed to characterize short-term AIDS treatment, whereas in long-term HIV dynamics, viral load often rebounds in the later stage of treatment primarily due to reduced drug efficacy. Although time-varying drug efficacy can be incorporated into the ordinary differential equations (ODE) model, such a system has no analytical solution, and the measurement of viral load is usually censored at the detection limit due to technological constraints. We consider nonlinear mixed-effects ODE model with stochastic approximation EM algorithm to overcome these difficulties. The performance of the proposed method is illustrated by means of a simulation study and a real-data application. Numerical evidence shows that the HIV infection is generally more severe when considering left-censored data. The T cell production rate from human body source varies, but the death rate of infected T cells, infection rate of virus, and other dynamic parameters do not have much difference among patients. We hope these findings inspire more research on clarifying biological mechanism of HIV infection and developing better treatment.