Marginal Regression Analysis of Longitudinal Data With Time-Dependent Covariates: A Generalised 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 generalised method of moments to make optimal use of the estimating equations made available by the covariates. Previous literature has suggested using generalised estimating equations (GEE) with the independent working correlation when there are time-dependent covariates. We conduct a simulation study that shows that our approach can provide substantial efficiency gains over GEE with the independent working correlation when a timedependent covariate is of Types I or II while our approach remains consistent and comparable in efficiency to GEE with the independent working correlation when a time-dependent covariate is of Type III. We apply our approach to analyze the relationship between body mass index and future morbidity among children in the Philippines.