Asymptotic theory for longitudinal data with missing responses adjusted by inverse probability weights

In this article, we propose a new method for analyzing longitudinal data which contain responses that are missing at random. This method consists in solving the generalized estimating equation (GEE) of Liang and Zeger (1986) in which the incomplete responses are replaced by values adjusted using the inverse probability weights proposed in Yi, Ma and Carroll (2012). We show that the root estimator is consistent and asymptotically normal, essentially under the some conditions on the marginal distribution and the surrogate correlation matrix as those presented in Xie and Yang (2003) in the case of complete data, and under minimal assumptions on the missingness probabilities. This method is applied to a real-life dataset taken from Sommer, Katz and Tarwotjo (1984), which examines the incidence of respiratory disease in a sample of 250 pre-school age Indonesian children which were examined every 3 months for 18 months, using as covariates the age, gender, and vitamin A deficiency.