The analysis of hierarchical biomedical data sometimes requires more modeling flexibility than that can be provided by standard parametric approaches. It is commonly believed that the effect of ignoring covariance structure is mainly on the loss of efficiency. There are situations that estimation biases could also be concerns. We argue that the modeling of variation in a longitudinal covariate process is in fact a very important task in the joint modeling approaches. I will use some recent applications as examples to illustrate the potential problems to be considered and provide some suggestions. I will also describe a simple semiparametric approach that allows us to model both the first and second moments in hierarchical data which can be
potentially useful in modeling the covariate process. In particular, the methods enable us to reduce estimation variation of the first moment through accounting for correlations in the data. It also enables us to obtain a simple covariance structure when simplification
can be achieved. I will use data from on-going biomedical studies to illustrate a few key points in the modeling strategy.