Joint Models for a Primary Endpoint and Longitudinal Covariate Processes
      Erning Li
      Texas A&M University
The relationship between a primary endpoint and longitudinal 
covariate processes is often of interest in medical and public 
health research.  Joint models that represent the association through 
shared dependence of the primary and longitudinal data on random effects 
are increasingly popular.  Naive implementation by imputing subject-specific 
effects from individual regression fits yields biased inference.  We have 
developed estimation procedures for regression parameters in the generalized 
linear models for the primary endpoint that require neither a distributional 
or covariance structural assumption on random-effects nor an independence 
assumption on within-subject measurement errors.  Meanwhile, we propose 
estimation methods to study the dependence of measurement error covariance 
matrix on observed covariates and conduct a variable selection.  The 
methodology is also extended to generalized functional linear models with 
error-in-variable longitudinal covariate curves.  The resulting estimators 
are shown to be consistent and asymptotically normally distributed.  The 
performances of the proposed methods are evaluated through simulations 
and real-life data sets.