Statistical diagnosis for HIV dynamics based on mean shift outlier model

Ordinary differential equation (ODE) are widely used for quantifying HIV viral dynamics. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. In this study, the authors use the Mean Shift Outlier Model (MSOM) to detect outliers in HIV model based on the two-step estimation of ODE. Approximate formula for shift parameter is derived. Furthermore, a score test statistic is constructed and its approximating distribution is established. The simulation results show that: 1) The boundary points have more impact on the parameter estimation relative to interior points. 2) The proposed procedure can detect the outliers effectively. The authors illustrate the proposed approach using an application example from an HIV clinical trial and find similar pattern to the simulation studies.