Highly efficient aggregate unbiased estimating functions approach for correlated data with missing at random

We develop a consistent and highly efficient marginal model for missing at random data using an estimating function approach. Our approach differs from inverse weighted estimating equations (Robins, Rotnitzky, and Zhao 1995) and the imputation method (Paik 1997) in that our approach does not require estimating the probability of missing or imputing the missing response based on assumed models. The proposed method is based on an aggregate unbiased estimating function approach, which does not require the likelihood function; however, it is equivalent to the score equation if the likelihood is known. The aggregate-unbiased approach is based on the best linear approximation of efficient scores from the full dataset. We provide comparisons of the three approaches using simulated data and also a human immunodeficiency virus (HIV) data example.