Pseudoempirical-likelihood-based method using calibration for longitudinal data with dropout

In observational studies, interest mainly lies in estimation of the population level relationship between the explanatory variables and dependent variables, and the estimation is often undertaken by using a sample of longitudinal data. In some situations, the longitudinal data sample features biases and loss of estimation efficiency due to non-random dropout. However, inclusion of population level information can increase estimation efficiency. We propose an empirical-likelihood-based method to incorporate population level information in a longitudinal study with dropout. The population level information is incorporated via constraints on functions of the parameters, and non-random dropout bias is corrected by using a weighted generalized estimating equations method. We provide a three-step estimation procedure that makes computation easier. Some commonly used methods are compared in simulation studies, which demonstrate that our proposed method can correct the non-random dropout bias and increase the estimation efficiency, especially for small sample sizes or when the missing proportion is high. In some situations, the improvement in efficiency is substantial. Finally, we apply the method to an Alzheimer's disease study.