Improved methods for the marginal analysis of longitudinal data in the presence of time-dependent covariates

Generalized estimating equations (GEEs) are commonly used for the marginal analysis of longitudinal data. In order to obtain consistent regression parameter estimates, these estimating equations must be unbiased. However, in the presence of certain types of time-dependent covariates, these equations can be biased unless they incorporate the independence working correlation structure. Moreover, in this case, regression parameter estimation can be very inefficient because not all valid moment conditions are incorporated within the corresponding estimating equations. Therefore, approaches based on the generalized method of moments or quadratic inference functions have been proposed in order to utilize all valid moment conditions. However, we have found in previous studies, as well as the current study, that such methods will not always provide valid inference and can also be improved upon in terms of finite-sample regression parameter estimation. Therefore, we propose both a modified GEE approach and a method selection strategy in order to ensure valid inference with the goal of improving regression parameter estimation. In a simulation study and application example, we compare existing and proposed methods and demonstrate that our modified GEE approach performs well, and the correlation information criterion has good accuracy with respect to selecting the best approach in terms of regression parameter estimation.