Grant: Discovery Grants Program - Individual

Longitudinal studies involve repeated observations of the same individual over time. Such studies are commonly conducted in health sciences, biochemistry, epidemiology, industry, economics and sociology where they are often called panel studies. For example, in HIV studies, the viral load of each patient is measured repeatedly over time; the banks record the transactions of clients over time. Mixed-effects models have been widely applied in longitudinal studies and can be conducted by the default functions in many statistical softwares, such as R/Splus and SAS. However, these models as well as the default functions are feasible only to ""complete"" data, i.e., no missing and censored data, no measurement errors, and no changepoints. Extensive research has demonstrated that ignoring any one or more of above problems in statistical analyses may lead to severely biased or misleading results. Moreover, in many longitudinal studies, there exists an individual-specific time-to-event process such as time to death. There is often association between the longitudinal and the time-to-event processes. Therefore, joint modeling for these two processes is preferable to separate modeling. With the incomplete data, many scientists and statisticians are often frustrated by the limitations of the existing statistical methods and the relevant computing tools.My research interests aim at the proposal of innovative statistical methods for time-to-event data and long-term longitudinal data with some incomplete features as well as the corresponding computational implement. If developed, these novel statistical methods and software packages can make significant contributions to longitudinal studies. The typical proposed approaches include ""exact"" likelihood inferences based on stochastic or Monte-Carlo EM algorithms and computationally more efficient approximate methods based on first- or higher-order Taylor/Laplace approximations to the observed-data likelihoods.