My main research interests involve developing models and methodologies for complex biomedical data. I have developed approaches in information extraction from imperfect data due to measurement errors and incompleteness. My other methodology developments include model-based mixture modeling, non- and semiparametric modeling of longitudinal, dynamic and high dimensional data. I developed approaches that first gauge the effects of measurement errors on non-linear mixed effects models and provided statistical methods to analyze such data. Most methods I have developed are so called semi-parametric based. One strength of such approaches is that one does not need to make certain structure assumptions about part of the model. This modeling strategy enables data integration from measurements collected from sources that might not be completely homogeneous. My recently developed statistical methods focus on regularized approach and model building, selection and evaluation for high dimensional, dynamic or functional data.
Regularized time-varying ODE coefficients of SEI dynamic equation for the Canadian measles incidence data (Li, Zhu, Wang, 2015). Left panel: time-varying ODE coefficient curve that reflects both yearly and seasonal effects with the regularized yearly effect (red curve) embedded; right panel: regularized (red curve), non-regularized (blue) and two-year local constant (circles) estimates of yearly effects. The new regularized method shows that the yearly effect is relatively large in the early years and deceases gradually to a constant after 1958.