Grant: Discovery Grants Program - Individual

Parametric nonlinear mixed-effects (NLME) models have been widely used in longitudinal studies such as HIV viral dynamics, pharmacokinetic analyses, and studies of growth and decay. These parametric NLME models, however, may not be flexible enough in modeling complex longitudinal data, so semiparametric/nonparametric NLME models have been proposed. In many longitudinal studies, the inter-individual variation usually receives great attention and this variation may be partially explained by time-dependent covariates, but some covariates may be measured with substantial errors and may contain missing values as well. It is very common that some individuals may drop out of the study before the scheduled end for various reasons such as drug intolerance. In addition, the response may be subject to left censoring due to a detection limit. Moreover, there often exists an individual-specific time-to-event process such as time to dropout or time to death. Thus, existing standard complete-data methods are not applicable. I have considered approximate likelihood inference for semiparametric NLME models with dropouts and covariate measurement errors and missing data. Two approximate likelihood methods are proposed to obtain the maximum likelihood estimates of all model parameters. Asymptotic properties of the resulting estimates have been studied. In the future, I plan to develop the statistical methodology to address dropouts, censoring, time-to-event, measurement errors, and missing covariates simultaneously. Most of the proposed methods are extensions and modifications of my recently proposed methods. Specifically, I use Monte-Carlo methods to simulate missing and censoring data and then employ standard complete-data methods for likelihood inference, with missing values replaced by simulated values.