Generalized estimating equations are routinely utilized for the marginal analysis of longitudinal data. In order to obtain consistent regression parameter estimates, these estimating equations must be unbiased. However, when certain types of time-dependent covariates are presented, these equations can be biased unless the working independence structure is used. Unfortunately, regression parameter estimation can be very inefficient with this structure because not all valid moment conditions are incorporated within the corresponding equations. Therefore, approaches have been proposed to utilize all valid moment conditions. However, these approaches assume that 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. Parameter estimates resulting from our proposed method are consistent and have overall improved mean squared error relative to hypothesis testing approaches. Existing and proposed methods are compared in a simulation study and application example.
Generalized methods of moments in marginal models for longitudinal data with time-dependent covariates
