Marginal Regression Analysis of Longitudinal Data With Time-Dependent Covariates: A Generalized Method of Moments Approach

We develop a new approach to using estimating equations to estimate marginal regression models for longitudinal data with time-dependent covariates. Our approach classifies time-dependent covariates into three types—types I, II and III. The type of covariate determines what estimating equations can be used involving the covariate. We use the generalized method of moments to make optimal use of the estimating equations that are made available by the covariates. Previous literature has suggested the use of generalized estimating equations with the independent working correlation when there are time-dependent covariates. We conduct a simulation study that shows that our approach can provide substantial gains in efficiency over generalized estimating equations with the independent working correlation when a time-dependent covariate is of types I or II, and our approach remains consistent and comparable in efficiency with generalized estimating equations with the independent working correlation when a time-dependent covariate is of type III. We apply our approach to analyse the relationship between the body mass index and future morbidity among children in the Philippines.