Abstract
Generalized estimating equations (GEE) are commonly utilized for the marginal analysis of longitudinal data. When certain types of time-dependent covariates are presented, these equations can be biased unless an independence working correlation structure is employed. However, in this case regression parameter estimation can be inefficient because not all valid moment conditions are incorporated within the corresponding estimating equations. Therefore, we propose a modified GEE approach and a selection method that will both ensure the validity of inference and improve regression parameter estimation. Additionally, these modified approaches assume the data analyst knows the type of time-dependent covariate, although this likely is not the case in practice. Whereas hypothesis testing has been used to determine covariate type, we propose a novel strategy to select a working covariate type in order to avoid potentially high type II error rates with these hypothesis testing procedures. Finally, we extend our approaches to modeling conditional quantiles of the response variable for skewed data with outliers and to exposure assessment and biomonitoring data with non-detects.