Using modified approaches on marginal regression analysis of longitudinal data with time-dependent covariates

Quadratic inference functions (QIFs) and estimating equations using the conjugate gradient method (CGM) for fitting marginal models to longitudinal data show appealing features in improving the efficiency without making assumptions on the correlation structure. However, our simulation study shows that both methods produce biased and inefficient estimates of regression parameters when time-dependent covariates are present. In this paper, we extend both the QIF and CGM methods for fitting marginal models to longitudinal data with time-dependent covariates. The idea is to restrict the moment conditions to the ones that are only valid to certain types of time-dependent covariates. Our simulations show that efficiency on estimating regression parameters is achieved using modified approaches. Furthermore, we apply the modified approach to anthropometric screening data to evaluate the association between body mass index and morbidity in children in the Philippines.